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## Data Analysis in Research: Types & Methods

Content Index

## Why analyze data in research?

Types of data in research, finding patterns in the qualitative data, methods used for data analysis in qualitative research, preparing data for analysis, methods used for data analysis in quantitative research, considerations in research data analysis, what is data analysis in research.

Definition of research in data analysis: According to LeCompte and Schensul, research data analysis is a process used by researchers to reduce data to a story and interpret it to derive insights. The data analysis process helps reduce a large chunk of data into smaller fragments, which makes sense.

Three essential things occur during the data analysis process — the first is data organization . Summarization and categorization together contribute to becoming the second known method used for data reduction. It helps find patterns and themes in the data for easy identification and linking. The third and last way is data analysis – researchers do it in both top-down and bottom-up fashion.

LEARN ABOUT: Research Process Steps

On the other hand, Marshall and Rossman describe data analysis as a messy, ambiguous, and time-consuming but creative and fascinating process through which a mass of collected data is brought to order, structure and meaning.

We can say that “the data analysis and data interpretation is a process representing the application of deductive and inductive logic to the research and data analysis.”

Researchers rely heavily on data as they have a story to tell or research problems to solve. It starts with a question, and data is nothing but an answer to that question. But, what if there is no question to ask? Well! It is possible to explore data even without a problem – we call it ‘Data Mining’, which often reveals some interesting patterns within the data that are worth exploring.

Irrelevant to the type of data researchers explore, their mission and audiences’ vision guide them to find the patterns to shape the story they want to tell. One of the essential things expected from researchers while analyzing data is to stay open and remain unbiased toward unexpected patterns, expressions, and results. Remember, sometimes, data analysis tells the most unforeseen yet exciting stories that were not expected when initiating data analysis. Therefore, rely on the data you have at hand and enjoy the journey of exploratory research.

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Every kind of data has a rare quality of describing things after assigning a specific value to it. For analysis, you need to organize these values, processed and presented in a given context, to make it useful. Data can be in different forms; here are the primary data types.

- Qualitative data: When the data presented has words and descriptions, then we call it qualitative data . Although you can observe this data, it is subjective and harder to analyze data in research, especially for comparison. Example: Quality data represents everything describing taste, experience, texture, or an opinion that is considered quality data. This type of data is usually collected through focus groups, personal qualitative interviews , qualitative observation or using open-ended questions in surveys.
- Quantitative data: Any data expressed in numbers of numerical figures are called quantitative data . This type of data can be distinguished into categories, grouped, measured, calculated, or ranked. Example: questions such as age, rank, cost, length, weight, scores, etc. everything comes under this type of data. You can present such data in graphical format, charts, or apply statistical analysis methods to this data. The (Outcomes Measurement Systems) OMS questionnaires in surveys are a significant source of collecting numeric data.
- Categorical data: It is data presented in groups. However, an item included in the categorical data cannot belong to more than one group. Example: A person responding to a survey by telling his living style, marital status, smoking habit, or drinking habit comes under the categorical data. A chi-square test is a standard method used to analyze this data.

Learn More : Examples of Qualitative Data in Education

## Data analysis in qualitative research

Data analysis and qualitative data research work a little differently from the numerical data as the quality data is made up of words, descriptions, images, objects, and sometimes symbols. Getting insight from such complicated information is a complicated process. Hence it is typically used for exploratory research and data analysis .

Although there are several ways to find patterns in the textual information, a word-based method is the most relied and widely used global technique for research and data analysis. Notably, the data analysis process in qualitative research is manual. Here the researchers usually read the available data and find repetitive or commonly used words.

For example, while studying data collected from African countries to understand the most pressing issues people face, researchers might find “food” and “hunger” are the most commonly used words and will highlight them for further analysis.

LEARN ABOUT: Level of Analysis

The keyword context is another widely used word-based technique. In this method, the researcher tries to understand the concept by analyzing the context in which the participants use a particular keyword.

For example , researchers conducting research and data analysis for studying the concept of ‘diabetes’ amongst respondents might analyze the context of when and how the respondent has used or referred to the word ‘diabetes.’

The scrutiny-based technique is also one of the highly recommended text analysis methods used to identify a quality data pattern. Compare and contrast is the widely used method under this technique to differentiate how a specific text is similar or different from each other.

For example: To find out the “importance of resident doctor in a company,” the collected data is divided into people who think it is necessary to hire a resident doctor and those who think it is unnecessary. Compare and contrast is the best method that can be used to analyze the polls having single-answer questions types .

Metaphors can be used to reduce the data pile and find patterns in it so that it becomes easier to connect data with theory.

Variable Partitioning is another technique used to split variables so that researchers can find more coherent descriptions and explanations from the enormous data.

LEARN ABOUT: Qualitative Research Questions and Questionnaires

There are several techniques to analyze the data in qualitative research, but here are some commonly used methods,

- Content Analysis: It is widely accepted and the most frequently employed technique for data analysis in research methodology. It can be used to analyze the documented information from text, images, and sometimes from the physical items. It depends on the research questions to predict when and where to use this method.
- Narrative Analysis: This method is used to analyze content gathered from various sources such as personal interviews, field observation, and surveys . The majority of times, stories, or opinions shared by people are focused on finding answers to the research questions.
- Discourse Analysis: Similar to narrative analysis, discourse analysis is used to analyze the interactions with people. Nevertheless, this particular method considers the social context under which or within which the communication between the researcher and respondent takes place. In addition to that, discourse analysis also focuses on the lifestyle and day-to-day environment while deriving any conclusion.
- Grounded Theory: When you want to explain why a particular phenomenon happened, then using grounded theory for analyzing quality data is the best resort. Grounded theory is applied to study data about the host of similar cases occurring in different settings. When researchers are using this method, they might alter explanations or produce new ones until they arrive at some conclusion.

LEARN ABOUT: 12 Best Tools for Researchers

## Data analysis in quantitative research

The first stage in research and data analysis is to make it for the analysis so that the nominal data can be converted into something meaningful. Data preparation consists of the below phases.

## Phase I: Data Validation

Data validation is done to understand if the collected data sample is per the pre-set standards, or it is a biased data sample again divided into four different stages

- Fraud: To ensure an actual human being records each response to the survey or the questionnaire
- Screening: To make sure each participant or respondent is selected or chosen in compliance with the research criteria
- Procedure: To ensure ethical standards were maintained while collecting the data sample
- Completeness: To ensure that the respondent has answered all the questions in an online survey. Else, the interviewer had asked all the questions devised in the questionnaire.

## Phase II: Data Editing

More often, an extensive research data sample comes loaded with errors. Respondents sometimes fill in some fields incorrectly or sometimes skip them accidentally. Data editing is a process wherein the researchers have to confirm that the provided data is free of such errors. They need to conduct necessary checks and outlier checks to edit the raw edit and make it ready for analysis.

## Phase III: Data Coding

Out of all three, this is the most critical phase of data preparation associated with grouping and assigning values to the survey responses . If a survey is completed with a 1000 sample size, the researcher will create an age bracket to distinguish the respondents based on their age. Thus, it becomes easier to analyze small data buckets rather than deal with the massive data pile.

LEARN ABOUT: Steps in Qualitative Research

After the data is prepared for analysis, researchers are open to using different research and data analysis methods to derive meaningful insights. For sure, statistical analysis plans are the most favored to analyze numerical data. In statistical analysis, distinguishing between categorical data and numerical data is essential, as categorical data involves distinct categories or labels, while numerical data consists of measurable quantities. The method is again classified into two groups. First, ‘Descriptive Statistics’ used to describe data. Second, ‘Inferential statistics’ that helps in comparing the data .

## Descriptive statistics

This method is used to describe the basic features of versatile types of data in research. It presents the data in such a meaningful way that pattern in the data starts making sense. Nevertheless, the descriptive analysis does not go beyond making conclusions. The conclusions are again based on the hypothesis researchers have formulated so far. Here are a few major types of descriptive analysis methods.

## Measures of Frequency

- Count, Percent, Frequency
- It is used to denote home often a particular event occurs.
- Researchers use it when they want to showcase how often a response is given.

## Measures of Central Tendency

- Mean, Median, Mode
- The method is widely used to demonstrate distribution by various points.
- Researchers use this method when they want to showcase the most commonly or averagely indicated response.

## Measures of Dispersion or Variation

- Range, Variance, Standard deviation
- Here the field equals high/low points.
- Variance standard deviation = difference between the observed score and mean
- It is used to identify the spread of scores by stating intervals.
- Researchers use this method to showcase data spread out. It helps them identify the depth until which the data is spread out that it directly affects the mean.

## Measures of Position

- Percentile ranks, Quartile ranks
- It relies on standardized scores helping researchers to identify the relationship between different scores.
- It is often used when researchers want to compare scores with the average count.

For quantitative research use of descriptive analysis often give absolute numbers, but the in-depth analysis is never sufficient to demonstrate the rationale behind those numbers. Nevertheless, it is necessary to think of the best method for research and data analysis suiting your survey questionnaire and what story researchers want to tell. For example, the mean is the best way to demonstrate the students’ average scores in schools. It is better to rely on the descriptive statistics when the researchers intend to keep the research or outcome limited to the provided sample without generalizing it. For example, when you want to compare average voting done in two different cities, differential statistics are enough.

Descriptive analysis is also called a ‘univariate analysis’ since it is commonly used to analyze a single variable.

## Inferential statistics

Inferential statistics are used to make predictions about a larger population after research and data analysis of the representing population’s collected sample. For example, you can ask some odd 100 audiences at a movie theater if they like the movie they are watching. Researchers then use inferential statistics on the collected sample to reason that about 80-90% of people like the movie.

Here are two significant areas of inferential statistics.

- Estimating parameters: It takes statistics from the sample research data and demonstrates something about the population parameter.
- Hypothesis test: I t’s about sampling research data to answer the survey research questions. For example, researchers might be interested to understand if the new shade of lipstick recently launched is good or not, or if the multivitamin capsules help children to perform better at games.

These are sophisticated analysis methods used to showcase the relationship between different variables instead of describing a single variable. It is often used when researchers want something beyond absolute numbers to understand the relationship between variables.

Here are some of the commonly used methods for data analysis in research.

- Correlation: When researchers are not conducting experimental research or quasi-experimental research wherein the researchers are interested to understand the relationship between two or more variables, they opt for correlational research methods.
- Cross-tabulation: Also called contingency tables, cross-tabulation is used to analyze the relationship between multiple variables. Suppose provided data has age and gender categories presented in rows and columns. A two-dimensional cross-tabulation helps for seamless data analysis and research by showing the number of males and females in each age category.
- Regression analysis: For understanding the strong relationship between two variables, researchers do not look beyond the primary and commonly used regression analysis method, which is also a type of predictive analysis used. In this method, you have an essential factor called the dependent variable. You also have multiple independent variables in regression analysis. You undertake efforts to find out the impact of independent variables on the dependent variable. The values of both independent and dependent variables are assumed as being ascertained in an error-free random manner.
- Frequency tables: The statistical procedure is used for testing the degree to which two or more vary or differ in an experiment. A considerable degree of variation means research findings were significant. In many contexts, ANOVA testing and variance analysis are similar.
- Analysis of variance: The statistical procedure is used for testing the degree to which two or more vary or differ in an experiment. A considerable degree of variation means research findings were significant. In many contexts, ANOVA testing and variance analysis are similar.
- Researchers must have the necessary research skills to analyze and manipulation the data , Getting trained to demonstrate a high standard of research practice. Ideally, researchers must possess more than a basic understanding of the rationale of selecting one statistical method over the other to obtain better data insights.
- Usually, research and data analytics projects differ by scientific discipline; therefore, getting statistical advice at the beginning of analysis helps design a survey questionnaire, select data collection methods , and choose samples.

LEARN ABOUT: Best Data Collection Tools

- The primary aim of data research and analysis is to derive ultimate insights that are unbiased. Any mistake in or keeping a biased mind to collect data, selecting an analysis method, or choosing audience sample il to draw a biased inference.
- Irrelevant to the sophistication used in research data and analysis is enough to rectify the poorly defined objective outcome measurements. It does not matter if the design is at fault or intentions are not clear, but lack of clarity might mislead readers, so avoid the practice.
- The motive behind data analysis in research is to present accurate and reliable data. As far as possible, avoid statistical errors, and find a way to deal with everyday challenges like outliers, missing data, data altering, data mining , or developing graphical representation.

LEARN MORE: Descriptive Research vs Correlational Research The sheer amount of data generated daily is frightening. Especially when data analysis has taken center stage. in 2018. In last year, the total data supply amounted to 2.8 trillion gigabytes. Hence, it is clear that the enterprises willing to survive in the hypercompetitive world must possess an excellent capability to analyze complex research data, derive actionable insights, and adapt to the new market needs.

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## The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organizations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organize and summarize the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalize your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

## Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarize your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, other interesting articles.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

## Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

- Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
- Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
- Null hypothesis: Parental income and GPA have no relationship with each other in college students.
- Alternative hypothesis: Parental income and GPA are positively correlated in college students.

## Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

- In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
- In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
- In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

- In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
- In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
- In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
- Experimental
- Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

## Measuring variables

When planning a research design, you should operationalize your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

- Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
- Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

Variable | Type of data |
---|---|

Age | Quantitative (ratio) |

Gender | Categorical (nominal) |

Race or ethnicity | Categorical (nominal) |

Baseline test scores | Quantitative (interval) |

Final test scores | Quantitative (interval) |

Parental income | Quantitative (ratio) |
---|---|

GPA | Quantitative (interval) |

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In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

## Sampling for statistical analysis

There are two main approaches to selecting a sample.

- Probability sampling: every member of the population has a chance of being selected for the study through random selection.
- Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalizable findings, you should use a probability sampling method. Random selection reduces several types of research bias , like sampling bias , and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to at risk for biases like self-selection bias , they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

- your sample is representative of the population you’re generalizing your findings to.
- your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalize your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialized, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalized in your discussion section .

## Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

- Will you have resources to advertise your study widely, including outside of your university setting?
- Will you have the means to recruit a diverse sample that represents a broad population?
- Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

## Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

- Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
- Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
- Expected effect size : a standardized indication of how large the expected result of your study will be, usually based on other similar studies.
- Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarize them.

## Inspect your data

There are various ways to inspect your data, including the following:

- Organizing data from each variable in frequency distribution tables .
- Displaying data from a key variable in a bar chart to view the distribution of responses.
- Visualizing the relationship between two variables using a scatter plot .

By visualizing your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

## Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

- Mode : the most popular response or value in the data set.
- Median : the value in the exact middle of the data set when ordered from low to high.
- Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

## Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

- Range : the highest value minus the lowest value of the data set.
- Interquartile range : the range of the middle half of the data set.
- Standard deviation : the average distance between each value in your data set and the mean.
- Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

Pretest scores | Posttest scores | |
---|---|---|

Mean | 68.44 | 75.25 |

Standard deviation | 9.43 | 9.88 |

Variance | 88.96 | 97.96 |

Range | 36.25 | 45.12 |

30 |

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

Parental income (USD) | GPA | |
---|---|---|

Mean | 62,100 | 3.12 |

Standard deviation | 15,000 | 0.45 |

Variance | 225,000,000 | 0.16 |

Range | 8,000–378,000 | 2.64–4.00 |

653 |

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

- Estimation: calculating population parameters based on sample statistics.
- Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

- A point estimate : a value that represents your best guess of the exact parameter.
- An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

## Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

- A test statistic tells you how much your data differs from the null hypothesis of the test.
- A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

- Comparison tests assess group differences in outcomes.
- Regression tests assess cause-and-effect relationships between variables.
- Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

## Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

- A simple linear regression includes one predictor variable and one outcome variable.
- A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

- A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
- A z test is for exactly 1 or 2 groups when the sample is large.
- An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

- If you have only one sample that you want to compare to a population mean, use a one-sample test .
- If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
- If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
- If you expect a difference between groups in a specific direction, use a one-tailed test .
- If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

- a t value (test statistic) of 3.00
- a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

- a t value of 3.08
- a p value of 0.001

The final step of statistical analysis is interpreting your results.

## Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

## Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

## Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimize the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

## Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasizes null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

- Student’s t -distribution
- Normal distribution
- Null and Alternative Hypotheses
- Chi square tests
- Confidence interval

Methodology

- Cluster sampling
- Stratified sampling
- Data cleansing
- Reproducibility vs Replicability
- Peer review
- Likert scale

Research bias

- Implicit bias
- Framing effect
- Cognitive bias
- Placebo effect
- Hawthorne effect
- Hostile attribution bias
- Affect heuristic

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## Data Analysis Techniques in Research – Methods, Tools & Examples

Varun Saharawat is a seasoned professional in the fields of SEO and content writing. With a profound knowledge of the intricate aspects of these disciplines, Varun has established himself as a valuable asset in the world of digital marketing and online content creation.

Data analysis techniques in research are essential because they allow researchers to derive meaningful insights from data sets to support their hypotheses or research objectives.

Data Analysis Techniques in Research : While various groups, institutions, and professionals may have diverse approaches to data analysis, a universal definition captures its essence. Data analysis involves refining, transforming, and interpreting raw data to derive actionable insights that guide informed decision-making for businesses.

A straightforward illustration of data analysis emerges when we make everyday decisions, basing our choices on past experiences or predictions of potential outcomes.

If you want to learn more about this topic and acquire valuable skills that will set you apart in today’s data-driven world, we highly recommend enrolling in the Data Analytics Course by Physics Wallah . And as a special offer for our readers, use the coupon code “READER” to get a discount on this course.

Table of Contents

## What is Data Analysis?

Data analysis is the systematic process of inspecting, cleaning, transforming, and interpreting data with the objective of discovering valuable insights and drawing meaningful conclusions. This process involves several steps:

- Inspecting : Initial examination of data to understand its structure, quality, and completeness.
- Cleaning : Removing errors, inconsistencies, or irrelevant information to ensure accurate analysis.
- Transforming : Converting data into a format suitable for analysis, such as normalization or aggregation.
- Interpreting : Analyzing the transformed data to identify patterns, trends, and relationships.

## Types of Data Analysis Techniques in Research

Data analysis techniques in research are categorized into qualitative and quantitative methods, each with its specific approaches and tools. These techniques are instrumental in extracting meaningful insights, patterns, and relationships from data to support informed decision-making, validate hypotheses, and derive actionable recommendations. Below is an in-depth exploration of the various types of data analysis techniques commonly employed in research:

## 1) Qualitative Analysis:

Definition: Qualitative analysis focuses on understanding non-numerical data, such as opinions, concepts, or experiences, to derive insights into human behavior, attitudes, and perceptions.

- Content Analysis: Examines textual data, such as interview transcripts, articles, or open-ended survey responses, to identify themes, patterns, or trends.
- Narrative Analysis: Analyzes personal stories or narratives to understand individuals’ experiences, emotions, or perspectives.
- Ethnographic Studies: Involves observing and analyzing cultural practices, behaviors, and norms within specific communities or settings.

## 2) Quantitative Analysis:

Quantitative analysis emphasizes numerical data and employs statistical methods to explore relationships, patterns, and trends. It encompasses several approaches:

Descriptive Analysis:

- Frequency Distribution: Represents the number of occurrences of distinct values within a dataset.
- Central Tendency: Measures such as mean, median, and mode provide insights into the central values of a dataset.
- Dispersion: Techniques like variance and standard deviation indicate the spread or variability of data.

Diagnostic Analysis:

- Regression Analysis: Assesses the relationship between dependent and independent variables, enabling prediction or understanding causality.
- ANOVA (Analysis of Variance): Examines differences between groups to identify significant variations or effects.

Predictive Analysis:

- Time Series Forecasting: Uses historical data points to predict future trends or outcomes.
- Machine Learning Algorithms: Techniques like decision trees, random forests, and neural networks predict outcomes based on patterns in data.

Prescriptive Analysis:

- Optimization Models: Utilizes linear programming, integer programming, or other optimization techniques to identify the best solutions or strategies.
- Simulation: Mimics real-world scenarios to evaluate various strategies or decisions and determine optimal outcomes.

Specific Techniques:

- Monte Carlo Simulation: Models probabilistic outcomes to assess risk and uncertainty.
- Factor Analysis: Reduces the dimensionality of data by identifying underlying factors or components.
- Cohort Analysis: Studies specific groups or cohorts over time to understand trends, behaviors, or patterns within these groups.
- Cluster Analysis: Classifies objects or individuals into homogeneous groups or clusters based on similarities or attributes.
- Sentiment Analysis: Uses natural language processing and machine learning techniques to determine sentiment, emotions, or opinions from textual data.

Also Read: AI and Predictive Analytics: Examples, Tools, Uses, Ai Vs Predictive Analytics

## Data Analysis Techniques in Research Examples

To provide a clearer understanding of how data analysis techniques are applied in research, let’s consider a hypothetical research study focused on evaluating the impact of online learning platforms on students’ academic performance.

## Research Objective:

Determine if students using online learning platforms achieve higher academic performance compared to those relying solely on traditional classroom instruction.

## Data Collection:

- Quantitative Data: Academic scores (grades) of students using online platforms and those using traditional classroom methods.
- Qualitative Data: Feedback from students regarding their learning experiences, challenges faced, and preferences.

## Data Analysis Techniques Applied:

1) Descriptive Analysis:

- Calculate the mean, median, and mode of academic scores for both groups.
- Create frequency distributions to represent the distribution of grades in each group.

2) Diagnostic Analysis:

- Conduct an Analysis of Variance (ANOVA) to determine if there’s a statistically significant difference in academic scores between the two groups.
- Perform Regression Analysis to assess the relationship between the time spent on online platforms and academic performance.

3) Predictive Analysis:

- Utilize Time Series Forecasting to predict future academic performance trends based on historical data.
- Implement Machine Learning algorithms to develop a predictive model that identifies factors contributing to academic success on online platforms.

4) Prescriptive Analysis:

- Apply Optimization Models to identify the optimal combination of online learning resources (e.g., video lectures, interactive quizzes) that maximize academic performance.
- Use Simulation Techniques to evaluate different scenarios, such as varying student engagement levels with online resources, to determine the most effective strategies for improving learning outcomes.

5) Specific Techniques:

- Conduct Factor Analysis on qualitative feedback to identify common themes or factors influencing students’ perceptions and experiences with online learning.
- Perform Cluster Analysis to segment students based on their engagement levels, preferences, or academic outcomes, enabling targeted interventions or personalized learning strategies.
- Apply Sentiment Analysis on textual feedback to categorize students’ sentiments as positive, negative, or neutral regarding online learning experiences.

By applying a combination of qualitative and quantitative data analysis techniques, this research example aims to provide comprehensive insights into the effectiveness of online learning platforms.

Also Read: Learning Path to Become a Data Analyst in 2024

## Data Analysis Techniques in Quantitative Research

Quantitative research involves collecting numerical data to examine relationships, test hypotheses, and make predictions. Various data analysis techniques are employed to interpret and draw conclusions from quantitative data. Here are some key data analysis techniques commonly used in quantitative research:

## 1) Descriptive Statistics:

- Description: Descriptive statistics are used to summarize and describe the main aspects of a dataset, such as central tendency (mean, median, mode), variability (range, variance, standard deviation), and distribution (skewness, kurtosis).
- Applications: Summarizing data, identifying patterns, and providing initial insights into the dataset.

## 2) Inferential Statistics:

- Description: Inferential statistics involve making predictions or inferences about a population based on a sample of data. This technique includes hypothesis testing, confidence intervals, t-tests, chi-square tests, analysis of variance (ANOVA), regression analysis, and correlation analysis.
- Applications: Testing hypotheses, making predictions, and generalizing findings from a sample to a larger population.

## 3) Regression Analysis:

- Description: Regression analysis is a statistical technique used to model and examine the relationship between a dependent variable and one or more independent variables. Linear regression, multiple regression, logistic regression, and nonlinear regression are common types of regression analysis .
- Applications: Predicting outcomes, identifying relationships between variables, and understanding the impact of independent variables on the dependent variable.

## 4) Correlation Analysis:

- Description: Correlation analysis is used to measure and assess the strength and direction of the relationship between two or more variables. The Pearson correlation coefficient, Spearman rank correlation coefficient, and Kendall’s tau are commonly used measures of correlation.
- Applications: Identifying associations between variables and assessing the degree and nature of the relationship.

## 5) Factor Analysis:

- Description: Factor analysis is a multivariate statistical technique used to identify and analyze underlying relationships or factors among a set of observed variables. It helps in reducing the dimensionality of data and identifying latent variables or constructs.
- Applications: Identifying underlying factors or constructs, simplifying data structures, and understanding the underlying relationships among variables.

## 6) Time Series Analysis:

- Description: Time series analysis involves analyzing data collected or recorded over a specific period at regular intervals to identify patterns, trends, and seasonality. Techniques such as moving averages, exponential smoothing, autoregressive integrated moving average (ARIMA), and Fourier analysis are used.
- Applications: Forecasting future trends, analyzing seasonal patterns, and understanding time-dependent relationships in data.

## 7) ANOVA (Analysis of Variance):

- Description: Analysis of variance (ANOVA) is a statistical technique used to analyze and compare the means of two or more groups or treatments to determine if they are statistically different from each other. One-way ANOVA, two-way ANOVA, and MANOVA (Multivariate Analysis of Variance) are common types of ANOVA.
- Applications: Comparing group means, testing hypotheses, and determining the effects of categorical independent variables on a continuous dependent variable.

## 8) Chi-Square Tests:

- Description: Chi-square tests are non-parametric statistical tests used to assess the association between categorical variables in a contingency table. The Chi-square test of independence, goodness-of-fit test, and test of homogeneity are common chi-square tests.
- Applications: Testing relationships between categorical variables, assessing goodness-of-fit, and evaluating independence.

These quantitative data analysis techniques provide researchers with valuable tools and methods to analyze, interpret, and derive meaningful insights from numerical data. The selection of a specific technique often depends on the research objectives, the nature of the data, and the underlying assumptions of the statistical methods being used.

Also Read: Analysis vs. Analytics: How Are They Different?

## Data Analysis Methods

Data analysis methods refer to the techniques and procedures used to analyze, interpret, and draw conclusions from data. These methods are essential for transforming raw data into meaningful insights, facilitating decision-making processes, and driving strategies across various fields. Here are some common data analysis methods:

- Description: Descriptive statistics summarize and organize data to provide a clear and concise overview of the dataset. Measures such as mean, median, mode, range, variance, and standard deviation are commonly used.
- Description: Inferential statistics involve making predictions or inferences about a population based on a sample of data. Techniques such as hypothesis testing, confidence intervals, and regression analysis are used.

## 3) Exploratory Data Analysis (EDA):

- Description: EDA techniques involve visually exploring and analyzing data to discover patterns, relationships, anomalies, and insights. Methods such as scatter plots, histograms, box plots, and correlation matrices are utilized.
- Applications: Identifying trends, patterns, outliers, and relationships within the dataset.

## 4) Predictive Analytics:

- Description: Predictive analytics use statistical algorithms and machine learning techniques to analyze historical data and make predictions about future events or outcomes. Techniques such as regression analysis, time series forecasting, and machine learning algorithms (e.g., decision trees, random forests, neural networks) are employed.
- Applications: Forecasting future trends, predicting outcomes, and identifying potential risks or opportunities.

## 5) Prescriptive Analytics:

- Description: Prescriptive analytics involve analyzing data to recommend actions or strategies that optimize specific objectives or outcomes. Optimization techniques, simulation models, and decision-making algorithms are utilized.
- Applications: Recommending optimal strategies, decision-making support, and resource allocation.

## 6) Qualitative Data Analysis:

- Description: Qualitative data analysis involves analyzing non-numerical data, such as text, images, videos, or audio, to identify themes, patterns, and insights. Methods such as content analysis, thematic analysis, and narrative analysis are used.
- Applications: Understanding human behavior, attitudes, perceptions, and experiences.

## 7) Big Data Analytics:

- Description: Big data analytics methods are designed to analyze large volumes of structured and unstructured data to extract valuable insights. Technologies such as Hadoop, Spark, and NoSQL databases are used to process and analyze big data.
- Applications: Analyzing large datasets, identifying trends, patterns, and insights from big data sources.

## 8) Text Analytics:

- Description: Text analytics methods involve analyzing textual data, such as customer reviews, social media posts, emails, and documents, to extract meaningful information and insights. Techniques such as sentiment analysis, text mining, and natural language processing (NLP) are used.
- Applications: Analyzing customer feedback, monitoring brand reputation, and extracting insights from textual data sources.

These data analysis methods are instrumental in transforming data into actionable insights, informing decision-making processes, and driving organizational success across various sectors, including business, healthcare, finance, marketing, and research. The selection of a specific method often depends on the nature of the data, the research objectives, and the analytical requirements of the project or organization.

Also Read: Quantitative Data Analysis: Types, Analysis & Examples

## Data Analysis Tools

Data analysis tools are essential instruments that facilitate the process of examining, cleaning, transforming, and modeling data to uncover useful information, make informed decisions, and drive strategies. Here are some prominent data analysis tools widely used across various industries:

## 1) Microsoft Excel:

- Description: A spreadsheet software that offers basic to advanced data analysis features, including pivot tables, data visualization tools, and statistical functions.
- Applications: Data cleaning, basic statistical analysis, visualization, and reporting.

## 2) R Programming Language:

- Description: An open-source programming language specifically designed for statistical computing and data visualization.
- Applications: Advanced statistical analysis, data manipulation, visualization, and machine learning.

## 3) Python (with Libraries like Pandas, NumPy, Matplotlib, and Seaborn):

- Description: A versatile programming language with libraries that support data manipulation, analysis, and visualization.
- Applications: Data cleaning, statistical analysis, machine learning, and data visualization.

## 4) SPSS (Statistical Package for the Social Sciences):

- Description: A comprehensive statistical software suite used for data analysis, data mining, and predictive analytics.
- Applications: Descriptive statistics, hypothesis testing, regression analysis, and advanced analytics.

## 5) SAS (Statistical Analysis System):

- Description: A software suite used for advanced analytics, multivariate analysis, and predictive modeling.
- Applications: Data management, statistical analysis, predictive modeling, and business intelligence.

## 6) Tableau:

- Description: A data visualization tool that allows users to create interactive and shareable dashboards and reports.
- Applications: Data visualization , business intelligence , and interactive dashboard creation.

## 7) Power BI:

- Description: A business analytics tool developed by Microsoft that provides interactive visualizations and business intelligence capabilities.
- Applications: Data visualization, business intelligence, reporting, and dashboard creation.

## 8) SQL (Structured Query Language) Databases (e.g., MySQL, PostgreSQL, Microsoft SQL Server):

- Description: Database management systems that support data storage, retrieval, and manipulation using SQL queries.
- Applications: Data retrieval, data cleaning, data transformation, and database management.

## 9) Apache Spark:

- Description: A fast and general-purpose distributed computing system designed for big data processing and analytics.
- Applications: Big data processing, machine learning, data streaming, and real-time analytics.

## 10) IBM SPSS Modeler:

- Description: A data mining software application used for building predictive models and conducting advanced analytics.
- Applications: Predictive modeling, data mining, statistical analysis, and decision optimization.

These tools serve various purposes and cater to different data analysis needs, from basic statistical analysis and data visualization to advanced analytics, machine learning, and big data processing. The choice of a specific tool often depends on the nature of the data, the complexity of the analysis, and the specific requirements of the project or organization.

Also Read: How to Analyze Survey Data: Methods & Examples

## Importance of Data Analysis in Research

The importance of data analysis in research cannot be overstated; it serves as the backbone of any scientific investigation or study. Here are several key reasons why data analysis is crucial in the research process:

- Data analysis helps ensure that the results obtained are valid and reliable. By systematically examining the data, researchers can identify any inconsistencies or anomalies that may affect the credibility of the findings.
- Effective data analysis provides researchers with the necessary information to make informed decisions. By interpreting the collected data, researchers can draw conclusions, make predictions, or formulate recommendations based on evidence rather than intuition or guesswork.
- Data analysis allows researchers to identify patterns, trends, and relationships within the data. This can lead to a deeper understanding of the research topic, enabling researchers to uncover insights that may not be immediately apparent.
- In empirical research, data analysis plays a critical role in testing hypotheses. Researchers collect data to either support or refute their hypotheses, and data analysis provides the tools and techniques to evaluate these hypotheses rigorously.
- Transparent and well-executed data analysis enhances the credibility of research findings. By clearly documenting the data analysis methods and procedures, researchers allow others to replicate the study, thereby contributing to the reproducibility of research findings.
- In fields such as business or healthcare, data analysis helps organizations allocate resources more efficiently. By analyzing data on consumer behavior, market trends, or patient outcomes, organizations can make strategic decisions about resource allocation, budgeting, and planning.
- In public policy and social sciences, data analysis is instrumental in developing and evaluating policies and interventions. By analyzing data on social, economic, or environmental factors, policymakers can assess the effectiveness of existing policies and inform the development of new ones.
- Data analysis allows for continuous improvement in research methods and practices. By analyzing past research projects, identifying areas for improvement, and implementing changes based on data-driven insights, researchers can refine their approaches and enhance the quality of future research endeavors.

However, it is important to remember that mastering these techniques requires practice and continuous learning. That’s why we highly recommend the Data Analytics Course by Physics Wallah . Not only does it cover all the fundamentals of data analysis, but it also provides hands-on experience with various tools such as Excel, Python, and Tableau. Plus, if you use the “ READER ” coupon code at checkout, you can get a special discount on the course.

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## Data Analysis Techniques in Research FAQs

What are the 5 techniques for data analysis.

The five techniques for data analysis include: Descriptive Analysis Diagnostic Analysis Predictive Analysis Prescriptive Analysis Qualitative Analysis

## What are techniques of data analysis in research?

Techniques of data analysis in research encompass both qualitative and quantitative methods. These techniques involve processes like summarizing raw data, investigating causes of events, forecasting future outcomes, offering recommendations based on predictions, and examining non-numerical data to understand concepts or experiences.

## What are the 3 methods of data analysis?

The three primary methods of data analysis are: Qualitative Analysis Quantitative Analysis Mixed-Methods Analysis

## What are the four types of data analysis techniques?

The four types of data analysis techniques are: Descriptive Analysis Diagnostic Analysis Predictive Analysis Prescriptive Analysis

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## Research Methods Guide: Data Analysis

- Introduction
- Research Design & Method
- Survey Research
- Interview Research
- Resources & Consultation

## Tools for Analyzing Survey Data

- R (open source)
- Stata
- DataCracker (free up to 100 responses per survey)
- SurveyMonkey (free up to 100 responses per survey)

## Tools for Analyzing Interview Data

- AQUAD (open source)
- NVivo

## Data Analysis and Presentation Techniques that Apply to both Survey and Interview Research

- Create a documentation of the data and the process of data collection.
- Analyze the data rather than just describing it - use it to tell a story that focuses on answering the research question.
- Use charts or tables to help the reader understand the data and then highlight the most interesting findings.
- Don’t get bogged down in the detail - tell the reader about the main themes as they relate to the research question, rather than reporting everything that survey respondents or interviewees said.
- State that ‘most people said …’ or ‘few people felt …’ rather than giving the number of people who said a particular thing.
- Use brief quotes where these illustrate a particular point really well.
- Respect confidentiality - you could attribute a quote to 'a faculty member', ‘a student’, or 'a customer' rather than ‘Dr. Nicholls.'

## Survey Data Analysis

- If you used an online survey, the software will automatically collate the data – you will just need to download the data, for example as a spreadsheet.
- If you used a paper questionnaire, you will need to manually transfer the responses from the questionnaires into a spreadsheet. Put each question number as a column heading, and use one row for each person’s answers. Then assign each possible answer a number or ‘code’.
- When all the data is present and correct, calculate how many people selected each response.
- Once you have calculated how many people selected each response, you can set up tables and/or graph to display the data. This could take the form of a table or chart.
- In addition to descriptive statistics that characterize findings from your survey, you can use statistical and analytical reporting techniques if needed.

## Interview Data Analysis

- Data Reduction and Organization: Try not to feel overwhelmed by quantity of information that has been collected from interviews- a one-hour interview can generate 20 to 25 pages of single-spaced text. Once you start organizing your fieldwork notes around themes, you can easily identify which part of your data to be used for further analysis.
- What were the main issues or themes that struck you in this contact / interviewee?"
- Was there anything else that struck you as salient, interesting, illuminating or important in this contact / interviewee?
- What information did you get (or failed to get) on each of the target questions you had for this contact / interviewee?
- Connection of the data: You can connect data around themes and concepts - then you can show how one concept may influence another.
- Examination of Relationships: Examining relationships is the centerpiece of the analytic process, because it allows you to move from simple description of the people and settings to explanations of why things happened as they did with those people in that setting.
- << Previous: Interview Research
- Next: Resources & Consultation >>
- Last Updated: Aug 21, 2023 10:42 AM

## What Is Data Analysis in Research? Why It Matters & What Data Analysts Do

Data analysis in research is the process of uncovering insights from data sets. Data analysts can use their knowledge of statistical techniques, research theories and methods, and research practices to analyze data. They take data and uncover what it’s trying to tell us, whether that’s through charts, graphs, or other visual representations. To analyze data effectively you need a strong background in mathematics and statistics, excellent communication skills, and the ability to identify relevant information.

Read on for more information about data analysis roles in research and what it takes to become one.

## In this article – What is data analysis in research?

## What is data analysis in research?

Why data analysis matters, what is data science, data analysis for quantitative research, data analysis for qualitative research, what are data analysis techniques in research, what do data analysts do, in related articles.

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Data analysis is looking at existing data and attempting to draw conclusions from it. It is the process of asking “what does this data show us?” There are many different types of data analysis and a range of methods and tools for analyzing data. You may hear some of these terms as you explore data analysis roles in research – data exploration, data visualization, and data modelling. Data exploration involves exploring and reviewing the data, asking questions like “Does the data exist?” and “Is it valid?”.

Data visualization is the process of creating charts, graphs, and other visual representations of data. The goal of visualization is to help us see and understand data more quickly and easily. Visualizations are powerful and can help us uncover insights from the data that we may have missed without the visual aid. Data modelling involves taking the data and creating a model out of it. Data modelling organises and visualises data to help us understand it better and make sense of it. This will often include creating an equation for the data or creating a statistical model.

Data analysis is important for all research areas, from quantitative surveys to qualitative projects. While researchers often conduct a data analysis at the end of the project, they should be analyzing data alongside their data collection. This allows researchers to monitor their progress and adjust their approach when needed.

The analysis is also important for verifying the quality of the data. What you discover through your analysis can also help you decide whether or not to continue with your project. If you find that your data isn’t consistent with your research questions, you might decide to end your research before collecting enough data to generalize your results.

Data science is the intersection between computer science and statistics. It’s been defined as the “conceptual basis for systematic operations on data”. This means that data scientists use their knowledge of statistics and research methods to find insights in data. They use data to find solutions to complex problems, from medical research to business intelligence. Data science involves collecting and exploring data, creating models and algorithms from that data, and using those models to make predictions and find other insights.

Data scientists might focus on the visual representation of data, exploring the data, or creating models and algorithms from the data. Many people in data science roles also work with artificial intelligence and machine learning. They feed the algorithms with data and the algorithms find patterns and make predictions. Data scientists often work with data engineers. These engineers build the systems that the data scientists use to collect and analyze data.

Data analysis techniques can be divided into two categories:

- Quantitative approach
- Qualitative approach

Note that, when discussing this subject, the term “data analysis” often refers to statistical techniques.

Qualitative research uses unquantifiable data like unstructured interviews, observations, and case studies. Quantitative research usually relies on generalizable data and statistical modelling, while qualitative research is more focused on finding the “why” behind the data. This means that qualitative data analysis is useful in exploring and making sense of the unstructured data that researchers collect.

Data analysts will take their data and explore it, asking questions like “what’s going on here?” and “what patterns can we see?” They will use data visualization to help readers understand the data and identify patterns. They might create maps, timelines, or other representations of the data. They will use their understanding of the data to create conclusions that help readers understand the data better.

Quantitative research relies on data that can be measured, like survey responses or test results. Quantitative data analysis is useful in drawing conclusions from this data. To do this, data analysts will explore the data, looking at the validity of the data and making sure that it’s reliable. They will then visualize the data, making charts and graphs to make the data more accessible to readers. Finally, they will create an equation or use statistical modelling to understand the data.

A common type of research where you’ll see these three steps is market research. Market researchers will collect data from surveys, focus groups, and other methods. They will then analyze that data and make conclusions from it, like how much consumers are willing to spend on a product or what factors make one product more desirable than another.

## Quantitative methods

These are useful in quantitatively analyzing data. These methods use a quantitative approach to analyzing data and their application includes in science and engineering, as well as in traditional business. This method is also useful for qualitative research.

Statistical methods are used to analyze data in a statistical manner. Data analysis is not limited only to statistics or probability. Still, it can also be applied in other areas, such as engineering, business, economics, marketing, and all parts of any field that seeks knowledge about something or someone.

If you are an entrepreneur or an investor who wants to develop your business or your company’s value proposition into a reality, you will need data analysis techniques. But if you want to understand how your company works, what you have done right so far, and what might happen next in terms of growth or profitability—you don’t need those kinds of experiences. Data analysis is most applicable when it comes to understanding information from external sources like research papers that aren’t necessarily objective.

## A brief intro to statistics

Statistics is a field of study that analyzes data to determine the number of people, firms, and companies in a population and their relative positions on a particular economic level. The application of statistics can be to any group or entity that has any kind of data or information (even if it’s only numbers), so you can use statistics to make an educated guess about your company, your customers, your competitors, your competitors’ customers, your peers, and so on. You can also use statistics to help you develop a business strategy.

Data analysis methods can help you understand how different groups are performing in a given area—and how they might perform differently from one another in the future—but they can also be used as an indicator for areas where there is better or worse performance than expected.

In addition to being able to see what trends are occurring within an industry or population within that industry or population—and why some companies may be doing better than others—you will also be able to see what changes have been made over time within that industry or population by comparing it with others and analyzing those differences over time.

## Data mining

Data mining is the use of mathematical techniques to analyze data with the goal of finding patterns and trends. A great example of this would be analyzing the sales patterns for a certain product line. In this case, a data mining technique would involve using statistical techniques to find patterns in the data and then analyzing them using mathematical techniques to identify relationships between variables and factors.

Note that these are different from each other and much more advanced than traditional statistics or probability.

As a data analyst, you’ll be responsible for analyzing data from different sources. You’ll work with multiple stakeholders and your job will vary depending on what projects you’re working on. You’ll likely work closely with data scientists and researchers on a daily basis, as you’re all analyzing the same data.

Communication is key, so being able to work with others is important. You’ll also likely work with researchers or principal investigators (PIs) to collect and organize data. Your data will be from various sources, from structured to unstructured data like interviews and observations. You’ll take that data and make sense of it, organizing it and visualizing it so readers can understand it better. You’ll use this data to create models and algorithms that make predictions and find other insights. This can include creating equations or mathematical models from the data or taking data and creating a statistical model.

Data analysis is an important part of all types of research. Quantitative researchers analyze the data they collect through surveys and experiments, while qualitative researchers collect unstructured data like interviews and observations. Data analysts take all of this data and turn it into something that other researchers and readers can understand and make use of.

With proper data analysis, researchers can make better decisions, understand their data better, and get a better picture of what’s going on in the world around them. Data analysis is a valuable skill, and many companies hire data analysts and data scientists to help them understand their customers and make better decisions.

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## Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

## S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

## INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

Classification of variables

## Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

## STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

## Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

## Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

## Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

Normal distribution curve

## Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

Curves showing negatively skewed and positively skewed distribution

## Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

## PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

- The assumption of normality which specifies that the means of the sample group are normally distributed
- The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

## Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

where X = sample mean, u = population mean and SE = standard error of mean

where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

- To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

## Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

## Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

## SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

- StatPages.net – provides links to a number of online power calculators
- G-Power – provides a downloadable power analysis program that runs under DOS
- Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
- SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

## Financial support and sponsorship

Conflicts of interest.

There are no conflicts of interest.

## How to Write the Analysis Section of My Research Paper

## How to Write a Technical Essay

Data collection is only the beginning of the research paper writing process. Writing up the analysis is the bulk of the project. As Purdue University’s Online Writing Lab notes, analysis is a useful tool for investigating content you find in various print and other sources, like journals and video media.

Locate and collect documents. Make multiple photocopies of all relevant print materials. Label and store these in a way that provides easy access. Conduct your analysis.

Create a heading for the analysis section of your paper. Specify the criteria you looked for in the data. For instance, a research paper analyzing the possibility of life on other planets may look for the weight of evidence supporting a particular theory, or the scientific validity of particular publications.

Write about the patterns you found, and note the number of instances a particular idea emerged during analysis. For example, an analysis of Native American cultures may look for similarities between spiritual beliefs, gender roles or agricultural techniques. Researchers frequently repeat the process to find patterns that were missed during the first analysis. You can also write about your comparative analysis, if you did one. It is common to ask a colleague to perform the process and compare their findings with yours.

Summarize your analysis in a paragraph or two. Write the transition for the conclusions section of your paper.

- Use compare and contrast language. Indicate where there are similarities and differences in the data through the use of phrases like ''in contrast'' and ''similarly.''

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- Purdue University Online Writing Lab - Analysis

Adam Simpson is an author and blogger who started writing professionally in 2006 and has written for OneStopEnglish and other Web sites. He has chapters in the volumes "Teaching and learning vocabulary in another language" and "Educational technology in the Arabian gulf," among others. Simpson attended the University of Central Lancashire where he earned a B.A. in international management.

## Different Types of Data Analysis; Data Analysis Methods and Techniques in Research Projects

International Journal of Academic Research in Management, 9(1):1-9, 2022 http://elvedit.com/journals/IJARM/wp-content/uploads/Different-Types-of-Data-Analysis-Data-Analysis-Methods-and-Tec

9 Pages Posted: 18 Aug 2022

## Hamed Taherdoost

Hamta Group

Date Written: August 1, 2022

This article is concentrated to define data analysis and the concept of data preparation. Then, the data analysis methods will be discussed. For doing so, the first six main categories are described briefly. Then, the statistical tools of the most commonly used methods including descriptive, explanatory, and inferential analyses are investigated in detail. Finally, we focus more on qualitative data analysis to get familiar with the data preparation and strategies in this concept.

Keywords: Data Analysis, Data Preparation, Data Analysis Methods, Data Analysis Types, Descriptive Analysis, Explanatory Analysis, Inferential Analysis, Predictive Analysis, Explanatory Analysis, Causal Analysis and Mechanistic Analysis, Statistical Analysis.

Suggested Citation: Suggested Citation

## Hamed Taherdoost (Contact Author)

Hamta group ( email ).

Vancouver Canada

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## Qualitative case study data analysis: an example from practice

Affiliation.

- 1 School of Nursing and Midwifery, National University of Ireland, Galway, Republic of Ireland.
- PMID: 25976531
- DOI: 10.7748/nr.22.5.8.e1307

Aim: To illustrate an approach to data analysis in qualitative case study methodology.

Background: There is often little detail in case study research about how data were analysed. However, it is important that comprehensive analysis procedures are used because there are often large sets of data from multiple sources of evidence. Furthermore, the ability to describe in detail how the analysis was conducted ensures rigour in reporting qualitative research.

Data sources: The research example used is a multiple case study that explored the role of the clinical skills laboratory in preparing students for the real world of practice. Data analysis was conducted using a framework guided by the four stages of analysis outlined by Morse ( 1994 ): comprehending, synthesising, theorising and recontextualising. The specific strategies for analysis in these stages centred on the work of Miles and Huberman ( 1994 ), which has been successfully used in case study research. The data were managed using NVivo software.

Review methods: Literature examining qualitative data analysis was reviewed and strategies illustrated by the case study example provided. Discussion Each stage of the analysis framework is described with illustration from the research example for the purpose of highlighting the benefits of a systematic approach to handling large data sets from multiple sources.

Conclusion: By providing an example of how each stage of the analysis was conducted, it is hoped that researchers will be able to consider the benefits of such an approach to their own case study analysis.

Implications for research/practice: This paper illustrates specific strategies that can be employed when conducting data analysis in case study research and other qualitative research designs.

Keywords: Case study data analysis; case study research methodology; clinical skills research; qualitative case study methodology; qualitative data analysis; qualitative research.

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## Helpful Tips on Composing a Research Paper Data Analysis Section

If you are given a research paper assignment, you should create a list of tasks to be done and try to stick to your working schedule. It is recommended that you complete your research and then start writing your work. One of the important steps is to prepare your data analysis section. However, that step is vital as it aims to explain how the data will be described in the results section. Use the following helpful tips to complete that section without a hitch.

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## How to Compose a Data Analysis Section for Your Research Paper

Usually, a data analysis section is provided right after the methods and approaches used. There, you should explain how you organized your data, what statistical tests were applied, and how you evaluated the obtained results. Follow these simple tips to compose a strong piece of writing:

- Avoid analyzing your results in the data analysis section.
- Indicate whether your research is quantitative or qualitative.
- Provide your main research questions and the analysis methods that were applied to answer them.
- Report what software you used to gather and analyze your data.
- List the data sources, including electronic archives and online reports of different institutions.
- Explain how the data were summarized and what measures of variability you have used.
- Remember to mention the data transformations if any, including data normalizing.
- Make sure that you included the full name of statistical tests used.
- Describe graphical techniques used to analyze the raw data and the results.

## Where to Find the Necessary Assistance If You Get Stuck

Research paper writing is hard, so if you get stuck, do not wait for enlightenment and start searching for some assistance. It is a good idea to consult a statistics expert if you have a large amount of data and have no idea on how to summarize it. Your academic advisor may suggest you where to find a statistician to ask your questions.

Another great help option is getting a sample of a data analysis section. At the school’s library, you can find sample research papers written by your fellow students, get a few works, and study how the students analyzed data. Pay special attention to the word choices and the structure of the writing.

If you decide to follow a section template, you should be careful and keep your professor’s instructions in mind. For example, you may be asked to place all the page-long data tables in the appendices or build graphs instead of providing tables.

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## Thematic Analysis – A Guide with Examples

Published by Alvin Nicolas at August 16th, 2021 , Revised On August 29, 2023

Thematic analysis is one of the most important types of analysis used for qualitative data . When researchers have to analyse audio or video transcripts, they give preference to thematic analysis. A researcher needs to look keenly at the content to identify the context and the message conveyed by the speaker.

Moreover, with the help of this analysis, data can be simplified.

## Importance of Thematic Analysis

Thematic analysis has so many unique and dynamic features, some of which are given below:

Thematic analysis is used because:

- It is flexible.
- It is best for complex data sets.
- It is applied to qualitative data sets.
- It takes less complexity compared to other theories of analysis.

Intellectuals and researchers give preference to thematic analysis due to its effectiveness in the research.

## How to Conduct a Thematic Analysis?

While doing any research , if your data and procedure are clear, it will be easier for your reader to understand how you concluded the results . This will add much clarity to your research.

## Understand the Data

This is the first step of your thematic analysis. At this stage, you have to understand the data set. You need to read the entire data instead of reading the small portion. If you do not have the data in the textual form, you have to transcribe it.

Example: If you are visiting an adult dating website, you have to make a data corpus. You should read and re-read the data and consider several profiles. It will give you an idea of how adults represent themselves on dating sites. You may get the following results:

I am a tall, single(widowed), easy-going, honest, good listener with a good sense of humor. Being a handyperson, I keep busy working around the house, and I also like to follow my favourite hockey team on TV or spoil my two granddaughters when I get the chance!! Enjoy most music except Rap! I keep fit by jogging, walking, and bicycling (at least three times a week). I have travelled to many places and RVD the South-West U.S., but I would now like to find that special travel partner to do more travel to warm and interesting countries. I now feel it’s time to meet a nice, kind, honest woman who has some of the same interests as I do; to share the happy times, quiet times, and adventures together

I enjoy photography, lapidary & seeking collectibles in the form of classic movies & 33 1/3, 45 & 78 RPM recordings from the 1920s, ’30s & ’40s. I am retired & looking forward to travelling to Canada, the USA, the UK & Europe, China. I am unique since I do not judge a book by its cover. I accept people for who they are. I will not demand or request perfection from anyone until I am perfect, so I guess that means everyone is safe. My musical tastes range from Classical, big band era, early jazz, classic ’50s & 60’s rock & roll & country since its inception.

## Development of Initial Coding:

At this stage, you have to do coding. It’s the essential step of your research . Here you have two options for coding. Either you can do the coding manually or take the help of any tool. A software named the NOVIC is considered the best tool for doing automatic coding.

For manual coding, you can follow the steps given below:

- Please write down the data in a proper format so that it can be easier to proceed.
- Use a highlighter to highlight all the essential points from data.
- Make as many points as possible.
- Take notes very carefully at this stage.
- Apply themes as much possible.
- Now check out the themes of the same pattern or concept.
- Turn all the same themes into the single one.

Example: For better understanding, the previously explained example of Step 1 is continued here. You can observe the coded profiles below:

Profile No. | Data Item | Initial Codes |
---|---|---|

1 | I am a tall, single(widowed), easy-going, honest, good listener with a good sense of humour. Being a handyperson, I keep busy working around the house; I also like to follow my favourite hockey team on TV or spoiling my two granddaughters when I get the chance!! I enjoy most music except for Rap! I keep fit by jogging, walking, and bicycling(at least three times a week). I have travelled to many places and RVD the South-West U.S., but I would now like to find that special travel partner to do more travel to warm and interesting countries. I now feel it’s time to meet a nice, kind, honest woman who has some of the same interests as I do; to share the happy times, quiet times and adventures together. | Physical description Widowed Positive qualities Humour Keep busy Hobbies Family Music Active Travel Plans Partner qualities Plans |

Profile No. | Data Item | Initial Codes |
---|---|---|

2 | I enjoy photography, lapidary & seeking collectables in the form of classic movies & 33 1/3, 45 & 78 RPM recordings from the 1920s, ’30s & ’40s. I am retired & looking forward to travelling to Canada, the USA, the UK & Europe, China. I am unique since I do not judge a book by its cover. I accept people for who they are. I will not demand or request perfection from anyone until I am perfect, so I guess that means everyone is safe. My musical tastes range from Classical, big band era, early jazz, classic ’50s & 60’s rock & roll & country since its inception. | HobbiesFuture plans Travel Unique Values Humour Music |

## Make Themes

At this stage, you have to make the themes. These themes should be categorised based on the codes. All the codes which have previously been generated should be turned into themes. Moreover, with the help of the codes, some themes and sub-themes can also be created. This process is usually done with the help of visuals so that a reader can take an in-depth look at first glance itself.

## Extracted Data Review

Now you have to take an in-depth look at all the awarded themes again. You have to check whether all the given themes are organised properly or not. It would help if you were careful and focused because you have to note down the symmetry here. If you find that all the themes are not coherent, you can revise them. You can also reshape the data so that there will be symmetry between the themes and dataset here.

For better understanding, a mind-mapping example is given here:

## Reviewing all the Themes Again

You need to review the themes after coding them. At this stage, you are allowed to play with your themes in a more detailed manner. You have to convert the bigger themes into smaller themes here. If you want to combine some similar themes into a single theme, then you can do it. This step involves two steps for better fragmentation.

You need to observe the coded data separately so that you can have a precise view. If you find that the themes which are given are following the dataset, it’s okay. Otherwise, you may have to rearrange the data again to coherence in the coded data.

## Corpus Data

Here you have to take into consideration all the corpus data again. It would help if you found how themes are arranged here. It would help if you used the visuals to check out the relationship between them. Suppose all the things are not done accordingly, so you should check out the previous steps for a refined process. Otherwise, you can move to the next step. However, make sure that all the themes are satisfactory and you are not confused.

When all the two steps are completed, you need to make a more précised mind map. An example following the previous cases has been given below:

## Define all the Themes here

Now you have to define all the themes which you have given to your data set. You can recheck them carefully if you feel that some of them can fit into one concept, you can keep them, and eliminate the other irrelevant themes. Because it should be precise and clear, there should not be any ambiguity. Now you have to think about the main idea and check out that all the given themes are parallel to your main idea or not. This can change the concept for you.

The given names should be so that it can give any reader a clear idea about your findings. However, it should not oppose your thematic analysis; rather, everything should be organised accurately.

## Does your Research Methodology Have the Following?

- Great Research/Sources
- Perfect Language
- Accurate Sources

If not, we can help. Our panel of experts makes sure to keep the 3 pillars of Research Methodology strong.

Also, read about discourse analysis , content analysis and survey conducting . we have provided comprehensive guides.

## Make a Report

You need to make the final report of all the findings you have done at this stage. You should include the dataset, findings, and every aspect of your analysis in it.

While making the final report , do not forget to consider your audience. For instance, you are writing for the Newsletter, Journal, Public awareness, etc., your report should be according to your audience. It should be concise and have some logic; it should not be repetitive. You can use the references of other relevant sources as evidence to support your discussion.

## Frequently Asked Questions

What is meant by thematic analysis.

Thematic Analysis is a qualitative research method that involves identifying, analyzing, and interpreting recurring themes or patterns in data. It aims to uncover underlying meanings, ideas, and concepts within the dataset, providing insights into participants’ perspectives and experiences.

## You May Also Like

Quantitative research is associated with measurable numerical data. Qualitative research is where a researcher collects evidence to seek answers to a question.

A survey includes questions relevant to the research topic. The participants are selected, and the questionnaire is distributed to collect the data.

Textual analysis is the method of analysing and understanding the text. We need to look carefully at the text to identify the writer’s context and message.

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## The Future of Academia: How AI Tools are Changing the Way We Do Research

Table of Contents

The integration of Artificial Intelligence (AI) in research is not merely a trend but a transformation of the academic landscape. The impact of AI on research is profound and multifaceted. AI tools not only streamline the collection, analysis, and reporting of data but also transform how we conceptualize and execute research projects. They enable researchers to handle larger datasets than ever before, uncover patterns and insights that would be impossible to detect manually, and significantly speed up the research cycle. Moreover, AI tools are supporting researchers in reading and writing research papers far more efficiently. AI’s ability to automate routine tasks frees up researcher time so they can focus on more complex and creative aspects of their work, thereby enhancing the innovation and depth of academic inquiries.

## How AI Transformed My Research Journey

My journey into AI-powered research began during my post-doctoral studies at The University of Adelaide, where I focused on big data and cyber security. The experience opened my eyes to the immense potential of AI in speeding up research processes and enhancing its accuracy. As academicians, we used AI in research keeping in mind the ethical and institutional boundaries. One striking example was during a project, where we utilized AI to analyze complex datasets. This not only expedited our research but also enhanced the depth of our analysis, leading to several key insights that would have been difficult to obtain manually.

Similarly, in another recent project, we encountered a significant challenge in accessing and reviewing relevant literature due to the vast amount of emerging research. By using R Discovery , an AI-powered literature search and reading platform, we managed to streamline our literature review process significantly. This tool not only saved us time but also ensured that we didn’t overlook critical research being published, allowing us to develop a more comprehensive foundation for our research project.

## Enhancing Literature Review and Research Writing with AI

AI tools like R Discovery have revolutionized the way literature reviews are conducted. Traditionally, a literature review could take weeks, involving painstaking manual searches and reviews. Now, AI can automate these tasks, allowing researchers to focus on analysis and interpretation. For instance, during a project on software vulnerabilities, R Discovery helped us identify key literature in less than half the usual time. As a result, we were able to move forward quickly with our experimental setup.

The impact of AI in research extends beyond data gathering to assisting in research writing and analysis. Paperpal , for example, is a comprehensive AI writing assistant that significantly improves the quality of research papers by ensuring clarity and adherence to academic standards. It helps you with finding factual answers to your research queries, assists with the writing, citing, and editing process, and even has plagiarism and submission readiness checks, making it an ideal assistant for academics. Reflecting on my past publication efforts now, I realize how AI tools like Paperpal could have refined the writing process, making it smoother and more efficient.

In the realm of data analysis, AI tools like Chat2Stats have been instrumental. These tools allow researchers to perform sophisticated statistical analyses more accurately and faster than traditional methods. For example, you can use Chat2Stats to analyze data patterns that are crucial for your research outcomes.

## Revolutionizing Research Presentation and Productivity

While it is important to conduct high-quality research, it is also equally important to present and communicate that research effectively. While academics traditionally turned to professional writing and editing services, these are no longer enough. The growing use of AI in research is ensuring real-time assistance, enhancing quality, and boosting productivity—all without burning a hole in your pocket. Organizations like Editage, known for its exceptional author publication support services, have delved into the AI space, introducing a host of AI tools for researchers designed to improve their academic writing, presentation, and productivity. The Editage All Access subscription combines top AI tools and expert-led services to enhance and support researchers at every step of their publication journey.

I’ve explored several of the AI tools included in this comprehensive plan, including Paperpal, R Discovery, and Mind the Graph.

- R Discovery revolutionizes how researchers stay updated by providing personalized reading recommendations, with functionalities like audio papers, translations, and daily alerts when relevant papers become available. I often use the R Discovery mobile app to listen to the latest papers published while I am in the train on my way to work in the morning. I find it especially useful and refreshing to listen to the amazing research being published in my niche area.
- Paperpal , the all-in-one academic writing tool is one of my favorites. It has a wide range of features that can help right authors move faster from ideation to submission readiness. The latest features that allow users to get fact-based insights and instantly cite sources in the recommended style expands its offering, making it especially useful for busy users.
- Mind the Graph , a scientific illustration tool, emerges as a vital resource for researchers to visualize and present their work effectively, bridging the gap between scientific data and the broader audience. This infographic maker is specially designed for the scientific community, enabling researchers to transform dense and complex information into engaging, understandable visual formats. Studies, such as those published in prominent journals, have shown that incorporating infographics can lead to a substantial increase in citations, highlighting the importance of visual elements in scientific communication.¹, ²

By integrating these AI tools for researchers, Editage All Access not only saves valuable time but also optimizes the overall research workflow, making it an indispensable resource for the academic community.

## The Use of AI and Research Ethics

AI tools are widely being incorporated in research. However, the increasing reliance on AI tools brings up significant ethical considerations. In my teaching and research, I emphasize the importance of using AI responsibly . We must ensure data privacy and mitigate any biases in AI algorithms. Maintaining transparency in how AI tools are used in research processes is critical to uphold the integrity of our findings and the trust of the academic community. The use of AI should in no way lead to lowering the quality of research output. At the same time, these practices should not be adopted in a way that it hits the learning curve of our new and young researchers. These AI tools should be considered as helping hands but never be pushed or will be able to completely replace humans. The critical thinking ability a human has is far more than the ability of any AI tool (at least as of now).

## Reflections on AI’s Ongoing Impact in Academia

Looking at recent advancements in research methodologies, it’s clear that AI tools have profoundly influenced how we do research. These tools have not only enhanced our efficiency and productivity but also allowed us to maintain high standards of academic rigor. Looking to the future, the potential of AI in research and academia is boundless. We are just beginning to tap into the capabilities of AI tools. As we continue to explore and integrate AI in our academic practices, the potential for enhancing research capabilities is immense. Embracing AI can lead to groundbreaking discoveries and innovations, shaping the future of academia. I believe that this exciting journey with AI will bring about a new era of academic research, marked by increased innovation, efficiency, and global collaboration.

## About the Author

Dr Faheem Ullah: Assistant Professor and Cyber Security Program Director, University of Adelaide, Australia

Dr. Faheem is an Assistant Professor and Cyber Security Program Director at the University of Adelaide, Australia, with wide-ranging expertise in AI tools for research. With a PhD and Postdoc in computer science focusing on AI from the University of Adelaide, he is a highly accomplished academic and a Big Data Lead at CREST (Center for Research on Engineering Software Technologies). Dedicated to advancing knowledge and fostering innovation in computer science and cybersecurity, Dr. Faheem regularly conducts webinars and gives talks on AI in research. He also shares his knowledge on platforms like LinkedIn and X (Twitter), engaging over 135K+ followers.

Throughout his career, Dr. Faheem has received numerous accolades, including two Gold Medals, one Silver Medal, and six academic distinctions. His research interests include AI, cybersecurity, big data analytics, and software engineering and he is currently working on projects related to Big Data Analytics for Climate Change Analysis, Data Exfiltration, and Cybersecurity Skills. He has published his research in top-notch journals and conferences. He has supervised more than 40 undergrad + Masters + PhD students.

References:

- Elaldi, Senel, and Taner Çifçi. “The Effectiveness of Using Infographics on Academic Achievement: A Meta-Analysis and a Meta-Thematic Analysis.” Journal of Pedagogical Research 5, no. 4 (2021): 92-118.
- Murray, Iain R., A. D. Murray, Sarah J. Wordie, Chris W. Oliver, A. W. Murray, and A. H. R. W. Simpson. “Maximising the impact of your work using infographics.” Bone & joint research 6, no. 11 (2017): 619-620.

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Get accurate academic translations, rewriting support, grammar checks, vocabulary suggestions, and generative AI assistance that delivers human precision at machine speed. Try for free or upgrade to Paperpal Prime starting at US$19 a month to access premium features, including consistency, plagiarism, and 30+ submission readiness checks to help you succeed.

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## Is College Worth It? A Comprehensive Return on Investment Analysis

- Preston Cooper

Photo by Rochelle Nicole on Unsplash

## Title Goes Here

Key findings.

- This report estimates return on investment (ROI) — the increase in lifetime earnings minus the costs of college — for nearly 30,000 bachelor’s degrees.
- For students who graduate on time, the median bachelor’s degree has a net ROI of $306,000 . But some degrees are worth millions of dollars, while others have no net financial value at all.
- After accounting for the risk of dropping out, ROI for the median bachelor’s degree drops to $129,000. Over a quarter of programs have negative ROI .
- Four in five engineering programs have ROI above $500,000, but the same is true for just 1% of psychology programs.
- Elite schools such as Caltech and Penn dominate the list of highest ROI programs. But attending an elite school is not a golden ticket; some Ivy League degrees have negative ROI .

## Executive Summary

Most students attend college in order to get a better job with a higher salary. But the financial returns to college vary widely depending on the institution a student attends and the subject he or she studies. While prospective students often ask themselves whether college is worth it, the more important question is how they can make college worth it.

This report presents estimates of return on investment (ROI) for nearly 30,000 bachelor’s degree programs, drawing on a new Department of Education dataset and Census Bureau surveys.

In financial markets, ROI measures the profitability of an investment relative to its cost. In our study, we define the ROI of a college degree as the increase in lifetime earnings a student can expect from that degree, minus the direct and indirect costs of college.

The median bachelor’s degree is worth $306,000 for students who graduate on time. But the median conceals enormous variation. Some fields of study, including engineering, computer science, nursing, and economics, can produce returns of $1 million or more. Others, including art, music, religion, and psychology, often have a zero or even negative net financial value.

When accounting for the risk that a student will take longer than four years to finish college, or drop out entirely, median ROI drops to $129,000. Twenty-eight percent of bachelor’s degree programs have negative ROI when adjusting for the risk of non-completion. If ROI is adjusted to reflect the underlying cost of education, not just tuition charges, the share of non-performing programs rises to 37%.

The ROI estimates presented in this report can help students make better decisions regarding higher education. They may also be of interest to other stakeholders, including policymakers, trustees, and institutions themselves. The full dataset, including measures of ROI for all 30,000 programs, is available here .

## Introduction

Students constantly hear the refrain that they must attend college to be successful. As a result, two-thirds of high school graduates enroll in college the following autumn. Almost all students cite getting a better job as a primary reason for attending college.

But as this report shows, the decision to attend college is less important than the choices that come next: which school to attend, and which subject to study.

This report assesses the economic value of nearly 30,000 bachelor’s degree programs at 1,775 colleges and universities across the United States. A key measure of economic value is return on investment (ROI), which we define as the amount a student can expect to gain financially from each individual degree. ROI compares the main financial benefit of college—the increase in lifetime income attributable to the degree—to the costs, including tuition and foregone earnings.

The analysis reveals that a student’s choice of program is perhaps the most important financial decision he or she will ever make. Most bachelor’s degree programs in engineering, computer science, economics, and nursing increase lifetime earnings by $500,000 or more, even after subtracting the costs of college. But most programs in fields such as art, music, philosophy, religion, and psychology leave students financially worse off than if they had never gone to college at all.

Differences in ROI between programs can amount to millions of dollars. Financially, the best program anywhere in the nation is the computer science major at the California Institute of Technology. Students in this program can expect an ROI of over $4.4 million. But 28% of programs have negative returns on investment, meaning that students will be financially worse off for having participated in those programs.

Our preferred measure of ROI incorporates the significant chance that the student will not complete college, and thus fail to realize the economic benefits of a college degree. We also report a “clean” measure of ROI, which assumes the chance of on-time graduation is 100%. Many programs which have high ROI in theory see their economic value fall dramatically when taking low completion rates into account.

We calculate ROI with respect to the net tuition that students pay, taking financial aid into account. But net tuition is usually less than the underlying cost of college. Governments and private interests subsidize college through financial aid, direct appropriations, donations, and endowment spending. Other stakeholders, including policymakers and trustees, may wish to assess ROI after accounting for the full underlying cost of college, not just tuition. Therefore, we also provide a measure of ROI with respect to the full cost of education, not just tuition charges.

Individual financial returns to college are the paramount consideration for most students. Almost all students say access to a well-paying job is a primary reason for attending college.

The results improve on existing estimates of college ROI in multiple ways. First, the analysis leverages a new dataset, the program-level College Scorecard , to report results for individual majors at each college rather than the college overall. Second, it augments the Scorecard with data from the U.S. Census Bureau to estimate earnings throughout students’ careers, rather than just the first two years after graduation. Third, it provides more accurate estimates of the increase in earnings attributable to each degree by adjusting for demographics, ability, family background, and local labor markets.

The measures of ROI reported here do not incorporate everything a prospective student might care about. There are non-financial benefits to certain degrees; theology majors, for instance, usually don’t study religion for its lucrative returns. These measures of ROI also don’t incorporate externalities to college education. College degrees have both social benefits and social costs .

But the individual financial returns to college are the paramount consideration for most students. Almost all students say access to a well-paying job is a primary reason for attending college. Moreover, those who deliberately choose a low-paying major for its non-financial benefits should know just how much money they’re giving up to pursue a “dream” career. These measures of ROI supply the knowledge necessary to navigate those tradeoffs.

If students make better choices regarding where to go and what to study, their bank accounts won’t be the only thing that benefits. Wages and salaries are the mechanism through which the economy signals its labor needs. High earnings for engineers are a sign that we need more engineers. Knowledge of ROI is the path not only to individual prosperity, but higher economic growth overall.

## What do college graduates earn?

According to the Bureau of Labor Statistics, people with a bachelor’s degree earn 67% more than people who only have a high school degree. The wage premium associated with college is well-established and a major reason why so many students view the bachelor’s degree as a “golden ticket” to economic prosperity.

But the average conceals variation. Some bachelor’s degree programs vault their graduates into jobs that pay two or three times as much as a high school graduate earns. But other programs leave their students with incomes barely above high school level. Once again, the most pertinent question isn’t “does college pay?” but “when does college pay?”

Fortunately, students now have access to a new dataset, the program-level College Scorecard , which includes the median earnings for graduates of over 30,000 bachelor’s degree programs. But the Scorecard has a major limitation: right now, it only reports earnings for the first two years after graduation. This is a problem as earnings tend to rise considerably throughout college graduates’ early careers. To estimate lifetime earnings for all 30,000 programs, I extrapolate Scorecard earnings using data from the Census Bureau’s American Community Survey (ACS). More details may be found in the methodology article accompanying this paper .

The analysis reveals a clear difference in earnings by major. Ninety-five percent of engineering programs, weighted by the number of graduates, will produce median earnings above $80,000 per year by the time their graduates reach mid-career. (Unless otherwise noted, all figures in this paper are weighted by the number of graduates.) Other majors with strong earnings outcomes include computer science, health and nursing, and economics.

But just 1% of psychology programs will yield earnings above $80,000 per year when their graduates are aged 35. Similarly, it is unlikely that graduates of arts, music, philosophy, religion, or education programs will reach annual earnings of $80,000 or more by mid-career.

Individual programs at the same institution can produce vastly different earnings outcomes for their graduates. One of the most lucrative programs anywhere is the finance major at the University of Pennsylvania. Graduates of this program will have median earnings of over $288,000 by age 35, according to my estimates. But students at the exact same school who choose a major in film and photographic arts can expect earnings of just over $45,000 by age 35.

For college graduates, earnings tend to start at a relatively low level but rise steeply throughout the early career. Median earnings for bachelor’s degree programs in the Scorecard are roughly $39,000 at age 25. Earnings then rise rapidly year after year until the mid-thirties. At age 35, the median program produces earnings of $65,000. Incomes plateau in the late thirties; by age 45, the median program’s earnings have risen to just over $71,000. After age 50, earnings begin to decline.

It is important for students to know that their earnings immediately after graduation significantly understate their earnings capacity later on in life. However, earnings immediately after graduation are a reasonable guide to what a student will earn relative to peers in other programs . In other words, the ranking of programs changes little throughout life. Engineering and computer science will almost always be lucrative majors, while art and religion will usually disappoint those in search of large paychecks. The correlation between earnings at age 25 and earnings at age 45 for the 30,000 programs in the Scorecard dataset is 0.94.

There are exceptions, of course. Nursing majors tend to start their careers at a high level of earnings, but their earnings capacity grows more slowly than other majors. Though nursing majors significantly out-earn physics and economics majors during the early career, by age 45 the physicists and economists have caught up with the nurses. Conversely, while education and communications majors start out with roughly the same salary, by age 45 the communications majors earn $10,000 more annually than their education-major peers.

Use the searchable table below to find estimated earnings for your college and major at ages 25, 35, and 45.

While earnings by themselves are a useful measure of the value of college, they are only one half of the ROI equation. To ascertain a full picture of the economic value of college, we also need to consider costs.

## What is the full cost of college?

The full cost of college is more than just the price of tuition. A student who attends a four-year college necessarily gives up other alternatives. The student must spend a minimum of four years out of the labor force, and the wages he or she gives up during that time may exceed the cost of tuition. If the student takes longer than four years to graduate, the opportunity cost of his or her degree goes up.

ROI must also consider counterfactual earnings, or what each student would have earned in a parallel universe where he or she did not attend college. Assessments of ROI often compare the earnings of college graduates to the earnings of the median high school graduate. However, this simple analysis is insufficient for an accurate estimate of ROI. People who choose to attend college are different from those who do not. The two groups have different earnings potential. The counterfactual earnings for a college graduate are likely to exceed the earnings of the median high school graduate.

The same principle applies to different majors. Does an engineering graduate have high earnings because of his degree, or because engineering tends to attract people with scientific minds who would earn high wages no matter what? If so, an engineering major might have different counterfactual earnings than an English major. What about students who attend public colleges versus private colleges? Private college students often come from wealthier families. Are high earnings for private-college graduates due to the school, or due to family background?

Obviously, it is impossible to look into parallel universes and observe what each student would have earned had he or she not gone to college. We can, however, estimate counterfactual earnings for each program based on the observable characteristics of its graduates, such as demographics, geographic location, family background, and cognitive ability. The full details of this adjustment are available in the methodology article . By comparing observed earnings to counterfactual earnings, we can estimate the true financial value of each individual college degree.

Similar to the earnings of college graduates, typical counterfactual earnings start at a relatively low level but rise throughout the career. Despite lacking a college degree, high school graduates gain experience and skills as they work in the labor market. Unlike college graduates, they can start building this workforce experience at age 18 rather than age 23. By age 48, typical counterfactual earnings exceed $45,000 per year.

For the most part, students’ earnings with a degree exceed their earnings without a degree. At age 45, the typical college graduate out-earns her counterfactual self by over $25,000 per year. But there are exceptions. About 7% of programs, mostly in art, music, and religion, have higher counterfactual earnings at age 45. In other words, these programs would not pay off even if there were no other costs to college.

But there are other costs to college. Most students cannot work full-time while they are enrolled. Earning a bachelor’s degree means spending time out of the labor force. Every year a student spends in college costs her around $24,000 in lost earnings, according to my estimates.

Students must also pay tuition while enrolled. To calculate ROI, I use net tuition after grants and scholarships. Financial aid programs such as the Pell Grant, along with institutional scholarships, significantly reduce tuition charges for most students. The typical student does not pay the “sticker price” tuition rate advertised on colleges’ websites. The average public college in the Scorecard dataset charges net tuition of $4,000 per year to state resident students, while the average private nonprofit college charges nearly $15,000.

I do not count living expenses as a “cost” of college, since students would have to pay for food and rent regardless of whether they attend college. Living expenses may still represent a significant barrier for some students, who may struggle to come up with the cash liquidity to meet their needs if they are not working full-time. But they do not represent an extra cost associated with college and thus should not figure into the ROI calculation. I do, however, include students’ estimated spending on books and equipment as a cost of college.

## ROI for 30,000 bachelor’s degrees

I define ROI as the present discounted value of lifetime earnings with a college degree, minus the present discounted value of counterfactual earnings (including earnings while enrolled in college), minus the cost of tuition, required fees, books, and equipment. For the initial ROI calculation, I assume the student spends exactly four years in college, graduates, starts working at age 23, and retires at age 65. (We’ll relax some of these assumptions in a bit.)

Consider the physics program at the University of Maryland-College Park. I estimate that over the course of her career, a Maryland physics graduate will earn approximately $1.79 million in present value terms. The counterfactual earnings for this student, including the foregone earnings while he or she is enrolled in school, amount to $1.23 million in present value terms. Net tuition is $18,000 over four years. The ROI for this program is equivalent to lifetime earnings minus counterfactual earnings minus tuition costs, or approximately $545,000. In other words, Maryland’s physics degree has a net economic value of $545,000 over its graduates’ lifetimes.

Present value of lifetime earnings with the degree: $1,786,867

Subtract present value of counterfactual lifetime earnings (including earnings while enrolled): $1,223,332

Subtract present value of tuition, fees, books, and equipment: $18,056

Return on investment (ROI): $545,478

Weighted by student counts, the median ROI across all 30,000 bachelor’s degree programs in the College Scorecard is $306,000. In other words, the median bachelor’s degree has a net financial value of just over $300,000, after accounting for tuition and opportunity cost.

But the median conceals substantial variation. Sixteen percent of programs have negative ROI. These programs have no financial value for their graduates after accounting for tuition and opportunity cost. At the other end of the spectrum, 12% of programs have ROI of $1 million or more. Students who graduate with one of these degrees can expect a seven-figure lifetime payoff.

Put simply, choosing a bachelor’s degree program is the most important financial decision many people will ever make.

ROI varies substantially by major. Sixty-nine percent of engineering programs deliver a lifetime payoff of $1 million or more, and 97% have ROI of at least $500,000. Another strong major is computer science, where 85% of programs have ROI exceeding half a million dollars. Programs in transportation, construction, and architecture also deliver handsome rewards to their students: 77% have a payoff above $500,000.

But plenty of programs have ROI that students might consider disappointing. 68 percent of programs in visual arts and music have negative ROI, meaning graduates are worse off financially for having received their degree. A majority of programs in philosophy and religious studies leave their students in the red, along with 28% of programs in psychology, English, liberal arts, and humanities.

A surprisingly high 31% of programs in life sciences and biology have negative ROI. The most likely explanation is that many students pursue these majors in preparation for a lucrative graduate degree in medicine. The ROI analysis in this report considers returns on the bachelor’s degree alone. If biology students don’t use their degree as a springboard for medical school, they will typically see disappointing returns. Preparation for a graduate degree is certainly important for students to consider when choosing a major, but it is beyond the scope of the ROI estimates presented here. (A forthcoming report will calculate ROI for graduate degrees.)

It’s possible to calculate not just how much each college degree is worth, financially, but how long it will take for a student to recoup the costs of college. In other words, how many years must a student work before he or she “breaks even” on her degree? I calculate that a majority of new college graduates will recoup the costs of their degree within eleven years of finishing college, assuming once again that they graduate on-time.

But the results once again look different depending on field of study. Within ten years of graduating college, students in 99% of engineering programs have fully recovered the costs of college. But the same is true for just 33% of communications and journalism programs and a paltry 2% of psychology programs. The median psychology student has to wait for 23 years before ROI turns positive. After 40 years, only 71% of psychology programs have reached positive ROI.

Even psychology looks good, however, compared to majors at the back of the pack. By the time they reach retirement age, students in just 40% of programs in philosophy and religious studies have recovered their college costs. The same is true for just 32% of programs in art and music.

One word of caution: the estimates reported here are for the median graduate of each program. If a program has negative ROI, that means its median graduate receives no financial return from her degree. However, it is possible that some graduates of that program will see positive returns, though they will be in the minority. Similarly, a program with positive overall ROI may still produce some graduates for whom the degree was not financially worthwhile. While outcomes for the median graduate are the best way to analyze the overall worth of a college degree, prospective students should remember that exceptions to the norm can and do occur.

## What if some students don’t finish college?

The above figures assume that pursuing a college degree is riskless for the student. In practice, college is an extremely risky investment. Many students take longer than the standard four years to finish college, and between a quarter and a third of four-year college students never get their degrees at all. Dropping out leaves students responsible for many of the costs of college, but they usually receive none of the benefits of the degree.

Students in doubt about their ability to finish college on time (or finish college at all) should consider not just the financial value of various degrees, but their chance of on-time graduation. Some schools, such as Pomona College and Georgetown University, have on-time graduation rates above 90%. But nearly a quarter of schools in the Scorecard dataset have an on-time graduation rate below 20%.

While choice of major is arguably more important than choice of college for the “clean” measure of ROI, in which all students are assumed to graduate on time, institution quality is a key determinant of graduation rates, which in turn have a major effect on the true ROI of each program. A program with high post-graduation earnings but a middling completion rate may have the same true ROI as a program with moderate earnings but a strong completion rate.

Assuming all students finish their degrees in four years, just 16% of programs have negative ROI. But if students take five years to finish, then 21% of programs have negative ROI. Assuming completion in six years, the value of the degree is negative for 27% of programs. Naturally, among students who drop out, 100% of programs have negative ROI. I estimate that a student who drops out of college will typically lose over $100,000 in tuition payments and foregone earnings.

Using institutions’ reported completion outcomes and making appropriate allowances for transfer students, I adjust ROI for each program in the College Scorecard to account for the risk of noncompletion or extra years of study. Median ROI drops from $306,000 before the completion adjustment to just $129,000 after the adjustment. These results suggest that college is still a good bet on average , but that’s not true for every program.

With the completion adjustment, 28% of programs show negative ROI. Over 3,000 programs flip from positive ROI to negative ROI after applying the adjustment. Many of these are in fields with marginally positive earnings outcomes, such as psychology, education, and public administration.

The case of for-profit colleges is illustrative. For-profit schools often provide education in career-oriented fields such as business and nursing. As a result, the “clean” ROI for for-profit colleges is higher than it is for public and private nonprofit schools, which are weighed down by low-value programs such as English literature. But for-profit colleges also have extremely poor completion outcomes. The on-time graduation rate at for-profits is just 19%, compared to 41% at public institutions and 57% at private nonprofits.

After making the completion adjustment, 55% of programs at for-profit colleges have negative ROI, compared to 24% of programs at public institutions and 30% of programs at private nonprofits. While private nonprofits have more negative-ROI programs than public colleges, they also represent a disproportionate share of high-ROI programs: 25% of programs at private nonprofits have ROI above $500,000, compared to 17% of programs at public institutions and 14% at for-profits.

The completion adjustment turns some programs from sure bets into question marks. Without adjusting for completion rates, fewer than 2% of programs in business, finance, and management have negative ROI. But after the adjustment, nearly 10% of these programs don’t pay off.

Psychology already has questionable value as a major before the completion adjustment (28% of programs don’t pay off). But when accounting for completion rates, a majority of psychology programs (58%) are negative-ROI. Even for very lucrative majors, the completion adjustment reduces the estimated payoff. Sixty-eight percent of engineering programs have ROI above $1 million before the adjustment, compared to just 22% of engineering programs after the adjustment.

Prospective students often wonder whether paying for a more expensive college is worth the cost. If earnings outcomes are equal, then higher tuition means lower ROI. But in practice, more expensive colleges often have higher graduation rates and access to professional networks that can raise earnings and ROI. The question is whether these beneficial effects make up for the higher tuition.

Programs at the most expensive schools (those with net tuition above $12,700) have a median completion-adjusted ROI of $198,000, compared to $129,000 for all programs. On average, the higher payoff from more expensive schools is enough to make the heftier tuition bill worth it.

But there are exceptions. Twenty-eight percent of programs at the most expensive schools still have negative ROI. High tuition is therefore no guarantee of quality, as consumers sometimes assume . Major is the most important factor. At the most expensive schools, 81% of arts and music programs and 62% of psychology programs have negative ROI. While attending a more expensive school might boost ROI at the margins — particularly if that school has stronger graduation rates — it generally won’t salvage the financial value of a degree in the wrong field.

Moreover, 15% of programs at the cheapest schools (those with net tuition below $2,000) have a payoff above $500,000. At these inexpensive colleges, 82% of engineering programs, 51% of computer science programs, and 37% of health and nursing programs net their graduates more than half a million dollars.

Attending a very elite school and choosing the right field often has a significant payoff. The best program anywhere in the United States is the computer science major at the California Institute of Technology. Graduates of this well-regarded program can expect an ROI of $4.41 million over the course of their careers. Not far behind is the finance major at the University of Pennsylvania’s famous Wharton School, where lifetime ROI is $4.35 million.

The top 25 programs all have an ROI above $2.7 million. Twelve are in computer science, five are in engineering, three are in business or finance, two are in mathematics, one is in economics, and the remaining two are specialized programs. Twenty-four programs are at private nonprofit universities (the exception is the University of California-Berkeley’s electrical engineering major). Almost all the universities appearing in the top 25 are considered elite colleges, which suggests that access to these schools’ professional networks is an important determinant of earnings at the very top.

But some schools without a powerful name brand can still offer excellent financial returns if students know where to look. Touro College in New York places 284th on the U.S. News and World Report College Rankings, but graduates of its health sciences program can expect a lifetime ROI of $2.27 million.

Though elite colleges dominate the list of top programs in the country, attending an elite school is no golden ticket. Over 100 programs at colleges with an acceptance rate below 20% have negative ROI. Several U.S. News juggernauts such as Harvard, Penn, and Chicago all offer at least one program that leaves its students financially worse off.

At Harvard University, students who major in ethnic and gender studies can expect an ROI of negative $47,000. The film and photographic arts program at the University of Pennsylvania has an ROI of negative $140,000. Seventeen different programs at New York University have negative ROI, with the worst among them (music) leaving students over $500,000 in the hole.

While major is the most important determinant of ROI, there are exceptions to the trend. A handful of psychology programs have respectable ROI, particularly those oriented towards research and experimental psychology. The programs at Harvard University, Amherst College, and the University of Chicago all deliver payoffs of $800,000 or more.

Even in the arts, there are diamonds in the rough. Michigan Technological University operates a program in drama and stagecraft that delivers ROI of $795,000. Music students at the University of Texas-Austin can expect an ROI of $586,000. Two philosophy programs (the University of Pennsylvania and Dartmouth College) each have an ROI above $1 million.

Find the ROI for your college and major in the table below.

## What is ROI relative to the full cost of education?

Most colleges do not charge students the full cost of their education. Net tuition at most colleges is significantly lower than underlying spending per student, meaning most students get a subsidy of one form or another. Federal and state governments provide students with Pell Grants and other financial aid to subsidize students’ education. Public institutions get direct appropriations from state governments, which reduce tuition charges. Some schools have endowments or generous private donors to draw upon for revenue. Foreign students and graduate students pay higher tuition rates and cross-subsidize domestic undergraduates, who are the focus of this analysis.

As a result, the average public college in the Scorecard dataset spends over $21,000 per full-time equivalent student on education-related expenditures. (Education-related expenditures include spending on instruction and administration, but not research, dormitories, dining halls, or hospitals.) Despite the heavy cost of education, net tuition for in-state undergraduates is just over $4,000. Even private nonprofit universities, which do not receive direct appropriations, still subsidize their undergraduates: per-student spending exceeds $29,000 but net tuition is just under $15,000.

This report’s estimates of ROI incorporate net tuition as the direct cost of college, as students should want to know ROI based on the costs that they and their families face. But other stakeholders, such as policymakers, trustees, donors, and college administrators, may wish to incorporate the full underlying cost of college into the ROI calculation.

Because spending exceeds tuition at most schools, a program that has positive ROI with respect to net tuition may have negative ROI with respect to spending. In other words, the positive ROI of some degrees may be an illusion facilitated by subsidies, rather than a reflection of the degrees’ inherent value. A program that delivers a positive earnings payoff only with a significant outside subsidy may not be worth subsidizing.

The median program in the Scorecard has an ROI of $129,000 when ROI is calculated with respect to net tuition (including the completion rate adjustment). But when ROI is calculated with respect to underlying spending, the median program’s payoff drops to just $77,000. While a majority of degrees still justify their underlying costs, the return shrinks substantially.

Twenty-eight percent of programs have negative ROI when calculated with respect to net tuition. With respect to spending, the share of programs with no economic value rises to 37%. A majority of programs in several major categories — including liberal arts and humanities, public administration, and the social sciences — have negative ROI with respect to spending.

Of course, several fields largely survive the spending adjustment: a majority of programs in engineering still boast an ROI above $500,000. Most programs in computer science, economics, mathematics, health, and architecture maintain an ROI exceeding $250,000. Even if students were responsible for the full cost of their education, it would still be financially worthwhile to pursue one of these programs.

All else being equal, higher spending translates to lower ROI. But many institutions with high expenditures nevertheless maintain respectable ROI. Programs at institutions in the top quintile for spending ($27,400 per student or more) have a median ROI of $187,000, compared to $77,000 overall. The top spending category includes many elite private institutions, state flagship universities, and renowned research schools. These schools also tend to have strong graduation rates and access to high-wage professional networks, which may boost ROI.

But high spending is no guarantee of strong ROI. Nearly a third of programs at schools in the top spending quintile have negative ROI with respect to spending. It is possible that additional spending, if wisely invested, can improve ROI — particularly if that spending is targeted towards boosting graduation rates. But for too many programs, high institutional spending has not resulted in positive ROI.

Most young Americans say they want to get a college degree. But from a financial perspective, the choice of program is much more important than the decision to attend college at all. Some programs leave students worse off financially than if they’d never attended college at all, while others can increase net lifetime earnings by millions of dollars.

The estimates of ROI provided in this report can help students make better decisions about postsecondary education. The ROI estimates for all 30,000 programs are available in the tables above and for download here . The results also offer some broad takeaways for students, other stakeholders, and those interested in higher education policy.

Major is the most important factor. College rankings like the U.S. News and World Report emphasize choice of institution. But from a financial perspective, choice of major is the more important consideration. Major alone explains nearly half the variation in ROI. Students will have a much greater chance of financial success if they study engineering, computer science, nursing, or economics, rather than art, music, religion, psychology, or education.

This isn’t to say that lower-earning majors are worthless. Society needs artists and musicians. But low incomes for these majors signal a supply-demand mismatch. Universities are producing too many art majors and too few engineering majors relative to the number of jobs available in each of these fields. As a result, employers bid up the wages of engineers while surplus artists flood the labor market. The answer is not to eliminate low-earning majors nationwide, but to reduce their scale.

Elite institutions can pay off — but not always. Should you pay more to attend a fancy private school? Sometimes. The very best programs in the country are usually located at “elite” schools. These schools may offer more supports to boost completion rates, and graduates of elite colleges also have access to professional networks that supply lucrative job opportunities. Pricier tuition can be worth the money if expensive colleges can deliver higher earnings.

But elite schools are not a golden ticket. Even at Ivy League schools, there are several programs with negative ROI. The choice of major matters more. Engineering and computer science programs at schools without powerful brand names almost always have higher ROI than film or gender studies programs in the Ivy League.

Many bachelor’s degree programs don’t make sense, financially. Having a bachelor’s degree is usually better than not having a bachelor’s degree, even if the degree comes with $30,000 of student debt. But after accounting for mediocre completion rates and high underlying spending, many bachelor’s degree programs don’t look as good. Thirty-seven percent of programs do not deliver a financial return when adjusting for spending and completion. Another 32% have a lifetime ROI below $250,000.

Mediocre or nonexistent ROI suggests a misallocation of resources. It is likely that many of the students in programs with poor ROI might be better served if those resources were shifted to other forms of postsecondary training, such as apprenticeships, vocational schools, or career-oriented associate’s degrees. As students do not directly fund most of their own education, there is a role for policymakers in such a reallocation of funding.

Granted, many bachelor’s degrees have nonfinancial benefits, and students should certainly take those into account when choosing a program. There are also social benefits to some degrees. The engineers who developed the iPhone probably captured only a small fraction of the social value they created. But it’s likely that degrees which generate large social benefits also come with large private rewards. The idea that most negative-ROI programs are generating enough “social benefits” to justify themselves is doubtful. The degrees with large social benefits probably also have large private ROI.

Moreover, bachelor’s degrees can generate social costs. As the share of the population with a college degree rises, employers request higher educational credentials from job candidates, even though the underlying skills required to do those jobs have not changed. It follows that some college graduates simply take jobs away from non-college graduates. This displacement effect likely explains much of the college wage premium. While college graduates benefit, the economy does not grow overall.

For prospective college students, though, those considerations are largely beyond the immediate decisions lying ahead. I hope the estimates of ROI in this paper will empower students and their families to make more informed decisions. The most important financial question they can answer is not whether college is worth it, but how they can make college worth it.

## Trump and Biden trade policies would hurt poorest Americans

- Michael Tanner

## 22 Million Children Now Have Access to New Education Options

Kamala harris on poverty and welfare, the sweeping effects of closing a nuclear plant, do low-income students benefit from college what the data say, jonathan blanks on the curious task.

- Jonathan Blanks

## Evaluation of the Zenith Tropospheric Delay (ZTD) Derived from VMF3_FC and VMF3_OP Products Based on the CMONOC Data

- Zhang, Haoran
- Chen, Liang
- Zhang, Junya

Prior tropospheric information, especially zenith tropospheric delay (ZTD), is particularly important in GNSS data processing. The two types of ZTD models, those that require and do not require meteorological parameters, are the most commonly used models, whether the non-difference or double-difference mode is applied. To improve the accuracy of prior tropospheric information, the Vienna Mapping Functions (VMFs) data server provides a gridded set of global tropospheric products based on the ray-tracing technique using Numerical Weather Models (NWMs). Note that two types of gridded tropospheric products are provided: the VMF3_OP for the post-processing applications and the VMF3_FC for real-time applications. To explore the accuracy and adaptability of these two grid products, a comprehensive analysis and discussion were conducted in this study using the ZTD data from 255 stations of the Crustal Movement Observation Network of China (CMONOC) as references. The numerical results indicate that both VMF3_FC and VMF3_OP exhibit high accuracy, with RMSE/Bias values of 17.53/2.25 mm and 14.62/2.67 mm, respectively. Both products displayed a temporal trend, with larger RMSE values occurring in summer and smaller values in winter, along with a spatial trend of higher values in the southeast of China and lower values in the northwest of China. Additionally, VMF3_OP demonstrated superior performance to VMF3_FC, with smaller RMSE values for each month and each hour. For the RMSE difference between these two products, 108 stations had a difference of more than 3 mm, and the number of stations with a difference exceeding 1 mm reached 217. Moreover, the difference was more significant in the southeast than in the northwest. This study contributes to the understanding of the differences between the two precision products, aiding in the selection of suitable ZTD products based on specific requirements.

- tropospheric products;
- zenith tropospheric delay (ZTD);

## IMAGES

## VIDEO

## COMMENTS

Definition of research in data analysis: According to LeCompte and Schensul, research data analysis is a process used by researchers to reduce data to a story and interpret it to derive insights. The data analysis process helps reduce a large chunk of data into smaller fragments, which makes sense. Three essential things occur during the data ...

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It is important to know w hat kind of data you are planning to collect or analyse as this w ill. affect your analysis method. A 12 step approach to quantitative data analysis. Step 1: Start with ...

Survey Data Analysis. If you used an online survey, the software will automatically collate the data - you will just need to download the data, for example as a spreadsheet. If you used a paper questionnaire, you will need to manually transfer the responses from the questionnaires into a spreadsheet. Put each question number as a column ...

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Abstract. Qualitative data is often subjective, rich, and consists of in-depth information normally presented in the form of words. Analysing qualitative data entails reading a large amount of transcripts looking for similarities or differences, and subsequently finding themes and developing categories. Traditionally, researchers 'cut and ...

Data analysis in research is the process of uncovering insights from data sets. Data analysts can use their knowledge of statistical techniques, research theories and methods, and research practices to analyze data. They take data and uncover what it's trying to tell us, whether that's through charts, graphs, or other visual representations.

Analyzing Group Interactions by Matthias Huber (Editor); Dominik E. Froehlich (Editor) Analyzing Group Interactions gives a comprehensive overview of the use of different methods for the analysis of group interactions. International experts from a range of different disciplines within the social sciences illustrate their step-by-step procedures of how they analyze interactions within groups ...

Abstract. Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise ...

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This article is concentrated to define data analysis and the concept of data preparation. Then, the data analysis methods will be discussed. For doing so, the f

Furthermore, the ability to describe in detail how the analysis was conducted ensures rigour in reporting qualitative research. Data sources: The research example used is a multiple case study that explored the role of the clinical skills laboratory in preparing students for the real world of practice. Data analysis was conducted using a ...

Follow these simple tips to compose a strong piece of writing: Avoid analyzing your results in the data analysis section. Indicate whether your research is quantitative or qualitative. Provide your main research questions and the analysis methods that were applied to answer them. Report what software you used to gather and analyze your data.

from this study. The analysis and interpretation of data is carried out in two phases. The. first part, which is based on the results of the questionnaire, deals with a quantitative. analysis of data. The second, which is based on the results of the interview and focus group. discussions, is a qualitative interpretation.

Understand the Data. This is the first step of your thematic analysis. At this stage, you have to understand the data set. You need to read the entire data instead of reading the small portion. If you do not have the data in the textual form, you have to transcribe it. Example: If you are visiting an adult dating website, you have to make a ...

The impact of AI in research extends beyond data gathering to assisting in research writing and analysis. Paperpal, for example, is a comprehensive AI writing assistant that significantly improves the quality of research papers by ensuring clarity and adherence to academic standards. It helps you with finding factual answers to your research ...

First, the analysis leverages a new dataset, the program-level College Scorecard, to report results for individual majors at each college rather than the college overall. Second, it augments the Scorecard with data from the U.S. Census Bureau to estimate earnings throughout students' careers, rather than just the first two years after graduation.

The protocol also has been published along with a structured abstract. 8 Provision of pooled data in prespecified subgroups facilitated rapid analysis and dissemination because a need for multiple data-sharing agreements was avoided. As is standard in meta-analyses, patients were compared only with other patients randomized in the same trial.

Prior tropospheric information, especially zenith tropospheric delay (ZTD), is particularly important in GNSS data processing. The two types of ZTD models, those that require and do not require meteorological parameters, are the most commonly used models, whether the non-difference or double-difference mode is applied. To improve the accuracy of prior tropospheric information, the Vienna ...