greater than (>) less than (<)
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30
H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
H 0 : The drug reduces cholesterol by 25%. p = 0.25
H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
H 0 : μ = 2.0
H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
H 0 : μ ≥ 5
H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
H 0 : p ≤ 0.066
H a : p > 0.066
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
H 0 and H a are contradictory.
The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.
H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.
Mathematical Symbols Used in H 0 and H a :
equal (=) | not equal (≠) greater than (>) less than (<) |
greater than or equal to (≥) | less than (<) |
less than or equal to (≤) | more than (>) |
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066
On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.
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Statistics By Jim
Making statistics intuitive
By Jim Frost 6 Comments
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.
In every study or experiment, researchers assess an effect or relationship. This effect can be the effectiveness of a new drug, building material, or other intervention that has benefits. There is a benefit or connection that the researchers hope to identify. Unfortunately, no effect may exist. In statistics, we call this lack of an effect the null hypothesis. Researchers assume that this notion of no effect is correct until they have enough evidence to suggest otherwise, similar to how a trial presumes innocence.
In this context, the analysts don’t necessarily believe the null hypothesis is correct. In fact, they typically want to reject it because that leads to more exciting finds about an effect or relationship. The new vaccine works!
You can think of it as the default theory that requires sufficiently strong evidence to reject. Like a prosecutor, researchers must collect sufficient evidence to overturn the presumption of no effect. Investigators must work hard to set up a study and a data collection system to obtain evidence that can reject the null hypothesis.
Related post : What is an Effect in Statistics?
Null hypotheses start as research questions that the investigator rephrases as a statement indicating there is no effect or relationship.
Does the vaccine prevent infections? | The vaccine does not affect the infection rate. |
Does the new additive increase product strength? | The additive does not affect mean product strength. |
Does the exercise intervention increase bone mineral density? | The intervention does not affect bone mineral density. |
As screen time increases, does test performance decrease? | There is no relationship between screen time and test performance. |
After reading these examples, you might think they’re a bit boring and pointless. However, the key is to remember that the null hypothesis defines the condition that the researchers need to discredit before suggesting an effect exists.
Let’s see how you reject the null hypothesis and get to those more exciting findings!
So, you want to reject the null hypothesis, but how and when can you do that? To start, you’ll need to perform a statistical test on your data. The following is an overview of performing a study that uses a hypothesis test.
The first step is to devise a research question and the appropriate null hypothesis. After that, the investigators need to formulate an experimental design and data collection procedures that will allow them to gather data that can answer the research question. Then they collect the data. For more information about designing a scientific study that uses statistics, read my post 5 Steps for Conducting Studies with Statistics .
After data collection is complete, statistics and hypothesis testing enter the picture. Hypothesis testing takes your sample data and evaluates how consistent they are with the null hypothesis. The p-value is a crucial part of the statistical results because it quantifies how strongly the sample data contradict the null hypothesis.
When the sample data provide sufficient evidence, you can reject the null hypothesis. In a hypothesis test, this process involves comparing the p-value to your significance level .
Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!
When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .
Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the p-value is high, the null must fly!
Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null .
That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!
Let’s move on to learning how to write the null hypothesis for different types of effects, relationships, and tests.
Related posts : How Hypothesis Tests Work and Interpreting P-values
The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. Consequently, when you write a null hypothesis, it must make a claim about the relevant population parameter . Further, that claim usually indicates that the effect does not exist in the population. Below are typical examples of writing a null hypothesis for various parameters and hypothesis tests.
Related posts : Descriptive vs. Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics
T-tests and ANOVA assess the differences between group means. For these tests, the null hypothesis states that there is no difference between group means in the population. In other words, the experimental conditions that define the groups do not affect the mean outcome. Mu (µ) is the population parameter for the mean, and you’ll need to include it in the statement for this type of study.
For example, an experiment compares the mean bone density changes for a new osteoporosis medication. The control group does not receive the medicine, while the treatment group does. The null states that the mean bone density changes for the control and treatment groups are equal.
Proportions tests assess the differences between group proportions. For these tests, the null hypothesis states that there is no difference between group proportions. Again, the experimental conditions did not affect the proportion of events in the groups. P is the population proportion parameter that you’ll need to include.
For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the control group does not. The null states that the infection rates for the control and treatment groups are equal.
Some studies assess the relationship between two continuous variables rather than differences between groups.
In these studies, analysts often use either correlation or regression analysis . For these tests, the null states that there is no relationship between the variables. Specifically, it says that the correlation or regression coefficient is zero. As one variable increases, there is no tendency for the other variable to increase or decrease. Rho (ρ) is the population correlation parameter and beta (β) is the regression coefficient parameter.
For example, a study assesses the relationship between screen time and test performance. The null states that there is no correlation between this pair of variables. As screen time increases, test performance does not tend to increase or decrease.
For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis.
The preceding examples are all for two-tailed hypothesis tests. To learn about one-tailed tests and how to write a null hypothesis for them, read my post One-Tailed vs. Two-Tailed Tests .
Related post : Understanding Correlation
Neyman, J; Pearson, E. S. (January 1, 1933). On the Problem of the most Efficient Tests of Statistical Hypotheses . Philosophical Transactions of the Royal Society A . 231 (694–706): 289–337.
January 11, 2024 at 2:57 pm
Thanks for the reply.
January 10, 2024 at 1:23 pm
Hi Jim, In your comment you state that equivalence test null and alternate hypotheses are reversed. For hypothesis tests of data fits to a probability distribution, the null hypothesis is that the probability distribution fits the data. Is this correct?
January 10, 2024 at 2:15 pm
Those two separate things, equivalence testing and normality tests. But, yes, you’re correct for both.
Hypotheses are switched for equivalence testing. You need to “work” (i.e., collect a large sample of good quality data) to be able to reject the null that the groups are different to be able to conclude they’re the same.
With typical hypothesis tests, if you have low quality data and a low sample size, you’ll fail to reject the null that they’re the same, concluding they’re equivalent. But that’s more a statement about the low quality and small sample size than anything to do with the groups being equal.
So, equivalence testing make you work to obtain a finding that the groups are the same (at least within some amount you define as a trivial difference).
For normality testing, and other distribution tests, the null states that the data follow the distribution (normal or whatever). If you reject the null, you have sufficient evidence to conclude that your sample data don’t follow the probability distribution. That’s a rare case where you hope to fail to reject the null. And it suffers from the problem I describe above where you might fail to reject the null simply because you have a small sample size. In that case, you’d conclude the data follow the probability distribution but it’s more that you don’t have enough data for the test to register the deviation. In this scenario, if you had a larger sample size, you’d reject the null and conclude it doesn’t follow that distribution.
I don’t know of any equivalence testing type approach for distribution fit tests where you’d need to work to show the data follow a distribution, although I haven’t looked for one either!
February 20, 2022 at 9:26 pm
Is a null hypothesis regularly (always) stated in the negative? “there is no” or “does not”
February 23, 2022 at 9:21 pm
Typically, the null hypothesis includes an equal sign. The null hypothesis states that the population parameter equals a particular value. That value is usually one that represents no effect. In the case of a one-sided hypothesis test, the null still contains an equal sign but it’s “greater than or equal to” or “less than or equal to.” If you wanted to translate the null hypothesis from its native mathematical expression, you could use the expression “there is no effect.” But the mathematical form more specifically states what it’s testing.
It’s the alternative hypothesis that typically contains does not equal.
There are some exceptions. For example, in an equivalence test where the researchers want to show that two things are equal, the null hypothesis states that they’re not equal.
In short, the null hypothesis states the condition that the researchers hope to reject. They need to work hard to set up an experiment and data collection that’ll gather enough evidence to be able to reject the null condition.
February 15, 2022 at 9:32 am
Dear sir I always read your notes on Research methods.. Kindly tell is there any available Book on all these..wonderfull Urgent
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Figuring out exactly what the null hypothesis and the alternative hypotheses are is not a walk in the park. Hypothesis testing is based on the knowledge that you can acquire by going over what we have previously covered about statistics in our blog.
So, if you don’t want to have a hard time keeping up, make sure you have read all the tutorials about confidence intervals , distributions , z-tables and t-tables .
We've also made a video on null hypothesis vs alternative hypothesis - you can watch it below or just scroll down if you prefer reading.
Confidence intervals provide us with an estimation of where the parameters are located. You can obtain them with our confidence interval calculator and learn more about them in the related article.
However, when we are making a decision, we need a yes or no answer. The correct approach, in this case, is to use a test .
Here we will start learning about one of the fundamental tasks in statistics - hypothesis testing !
First off, let’s talk about data-driven decision-making. It consists of the following steps:
Let’s start from the beginning.
Though there are many ways to define it, the most intuitive must be:
“A hypothesis is an idea that can be tested.”
This is not the formal definition, but it explains the point very well.
So, if we say that apples in New York are expensive, this is an idea or a statement. However, it is not testable, until we have something to compare it with.
For instance, if we define expensive as: any price higher than $1.75 dollars per pound, then it immediately becomes a hypothesis .
An example may be: would the USA do better or worse under a Clinton administration, compared to a Trump administration? Statistically speaking, this is an idea , but there is no data to test it. Therefore, it cannot be a hypothesis of a statistical test.
Actually, it is more likely to be a topic of another discipline.
Conversely, in statistics, we may compare different US presidencies that have already been completed. For example, the Obama administration and the Bush administration, as we have data on both.
Alright, let’s get out of politics and get into hypotheses . Here’s a simple topic that CAN be tested.
According to Glassdoor (the popular salary information website), the mean data scientist salary in the US is 113,000 dollars.
So, we want to test if their estimate is correct.
There are two hypotheses that are made: the null hypothesis , denoted H 0 , and the alternative hypothesis , denoted H 1 or H A .
The null hypothesis is the one to be tested and the alternative is everything else. In our example:
The null hypothesis would be: The mean data scientist salary is 113,000 dollars.
While the alternative : The mean data scientist salary is not 113,000 dollars.
Author's note: If you're interested in a data scientist career, check out our articles Data Scientist Career Path , 5 Business Basics for Data Scientists , Data Science Interview Questions , and 15 Data Science Consulting Companies Hiring Now .
You can also form one-sided or one-tailed tests.
Say your friend, Paul, told you that he thinks data scientists earn more than 125,000 dollars per year. You doubt him, so you design a test to see who’s right.
The null hypothesis of this test would be: The mean data scientist salary is more than 125,000 dollars.
The alternative will cover everything else, thus: The mean data scientist salary is less than or equal to 125,000 dollars.
Important: The outcomes of tests refer to the population parameter rather than the sample statistic! So, the result that we get is for the population.
Important: Another crucial consideration is that, generally, the researcher is trying to reject the null hypothesis . Think about the null hypothesis as the status quo and the alternative as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging.
Let’s go over it once more. In statistics, the null hypothesis is the statement we are trying to reject. Therefore, the null hypothesis is the present state of affairs, while the alternative is our personal opinion.
Right now, you may be feeling a little puzzled. This is normal because this whole concept is counter-intuitive at the beginning. However, there is an extremely easy way to continue your journey of exploring it. By diving into the linked tutorial, you will find out why hypothesis testing actually works.
Interested in learning more? You can take your skills from good to great with our statistics course!
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04.28.2023 • 5 min read
Subject Matter Expert
Learn about a null versus alternative hypothesis and what they show with examples for each. Also go over the main differences and similarities between them.
In This Article
What is an alternative hypothesis, outcomes of a hypothesis test.
Main Differences Between Null & Alternative Hypothesis
Similarities Between Null & Alternative Hypothesis
Hypothesis Testing & Errors
In statistics, you’ll draw insights or “inferences” about population parameters using data from a sample. This process is called inferential statistics.
To make statistical inferences, you need to determine if you have enough evidence to support a certain hypothesis about the population. This is where null and alternative hypotheses come into play!
In this article, we’ll explain the differences between these two types of hypotheses, and we’ll explain the role they play in hypothesis testing.
Imagine you want to know what percent of Americans are vegetarians. You find a Gallup poll claiming 5% of the population was vegetarian in 2018, but your intuition tells you vegetarianism is on the rise and that far more than 5% of Americans are vegetarian today.
To investigate further, you collect your own sample data by surveying 1,000 randomly selected Americans. You’ll use this random sample to determine whether it’s likely the true population proportion of vegetarians is, in fact, 5% (as the Gallup data suggests) or whether it could be the case that the percentage of vegetarians is now higher.
Notice that your investigation involves two rival hypotheses about the population. One hypothesis is that the proportion of vegetarians is 5%. The other hypothesis is that the proportion of vegetarians is greater than 5%. In statistics, we would call the first hypothesis the null hypothesis, and the second hypothesis the alternative hypothesis. The null hypothesis ( H 0 H_0 H 0 ) represents the status quo or what is assumed to be true about the population at the start of your investigation.
Null Hypothesis
In hypothesis testing, the null hypothesis ( H 0 H_0 H 0 ) is the default hypothesis.
It's what the status quo assumes to be true about the population.
The alternative hypothesis ( H a H_a H a or H 1 H_1 H 1 ) is the hypothesis that stands contrary to the null hypothesis. The alternative hypothesis represents the research hypothesis—what you as the statistician are trying to prove with your data .
In medical studies, where scientists are trying to demonstrate whether a treatment has a significant effect on patient outcomes, the alternative hypothesis represents the hypothesis that the treatment does have an effect, while the null hypothesis represents the assumption that the treatment has no effect.
Alternative Hypothesis
The alternative hypothesis ( H a H_a H a or H 1 H_1 H 1 ) is the hypothesis being proposed in opposition to the null hypothesis.
In a hypothesis test, the null and alternative hypotheses must be mutually exclusive statements, meaning both hypotheses cannot be true at the same time. For example, if the null hypothesis includes an equal sign, the alternative hypothesis must state that the values being mentioned are “not equal” in some way.
Your hypotheses will also depend on the formulation of your test—are you running a one-sample T-test, a two-sample T-test, F-test for ANOVA , or a Chi-squared test? It also matters whether you are conducting a directional one-tailed test or a nondirectional two-tailed test.
Null Hypothesis: The population mean is equal to some number, x. 𝝁 = x
Alternative Hypothesis: The population mean is not equal to x. 𝝁 ≠ x
Null Hypothesis: The population mean is less than or equal to some number, x. 𝝁 ≤ x Alternative Hypothesis: The population mean is greater than x. 𝝁 > x
Null Hypothesis: The population mean is greater than or equal to some number, x. 𝝁 ≥ x
Alternative Hypothesis: The population mean is less than x. 𝝁 < x
By the end of a hypothesis test, you will have reached one of two conclusions.
You will run into either 2 outcomes:
Fail to reject the null hypothesis on the grounds that there's insufficient evidence to move away from the null hypothesis
Reject the null hypothesis in favor of the alternative.
If you’re confused about the outcomes of a hypothesis test, a good analogy is a jury trial. In a jury trial, the defendant is innocent until proven guilty. To reach a verdict of guilt, the jury must find strong evidence (beyond a reasonable doubt) that the defendant committed the crime.
This is analogous to a statistician who must assume the null hypothesis is true unless they can uncover strong evidence ( a p-value less than or equal to the significance level) in support of the alternative hypothesis.
Notice also, that a jury never concludes a defendant is innocent—only that the defendant is guilty or not guilty. This is similar to how we never conclude that the null hypothesis is true. In a hypothesis test, we never conclude that the null hypothesis is true. We can only “reject” the null hypothesis or “fail to reject” it.
In this video, let’s look at the jury example again, the reasoning behind hypothesis testing, and how to form a test. It starts by stating your null and alternative hypotheses.
Here is a summary of the key differences between the null and the alternative hypothesis test.
The null hypothesis represents the status quo; the alternative hypothesis represents an alternative statement about the population.
The null and the alternative are mutually exclusive statements, meaning both statements cannot be true at the same time.
In a medical study, the null hypothesis represents the assumption that a treatment has no statistically significant effect on the outcome being studied. The alternative hypothesis represents the belief that the treatment does have an effect.
The null hypothesis is denoted by H_0 ; the alternative hypothesis is denoted by H_a H_1
You “fail to reject” the null hypothesis when the p-value is larger than the significance level. You “reject” the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to your test’s significance level.
The similarities between the null and alternative hypotheses are as follows.
Both the null and the alternative are statements about the same underlying data.
Both statements provide a possible answer to a statistician’s research question.
The same hypothesis test will provide evidence for or against the null and alternative hypotheses.
Always remember that statistical inference provides you with inferences based on probability rather than hard truths. Anytime you conduct a hypothesis test, there is a chance that you’ll reach the wrong conclusion about your data.
In statistics, we categorize these wrong conclusions into two types of errors:
Type I Errors
Type II Errors
A Type I error occurs when you reject the null hypothesis when, in fact, the null hypothesis is true. This is sometimes called a false positive and is analogous to a jury that falsely convicts an innocent defendant. The probability of making this type of error is represented by alpha, ɑ.
A Type II error occurs when you fail to reject the null hypothesis when, in fact, the null hypothesis is false. This is sometimes called a false negative and is analogous to a jury that reaches a verdict of “not guilty,” when, in fact, the defendant has committed the crime. The probability of making this type of error is represented by beta, ꞵ.
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10.1 - setting the hypotheses: examples.
A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.
About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.
A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.
Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.
Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.
This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.
Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different.
How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference.
The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H 0 .
The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.
If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.
For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit . The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has a temperature of 98.6 degrees. We do not prove that this is true.
If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.
The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either H a or by H 1 .
The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis. Going back to the above example of mean human body temperature, the alternative hypothesis is “The average adult human body temperature is not 98.6 degrees Fahrenheit.”
If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.
The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook.
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There are 13 different types of hypothesis. These include simple, complex, null, alternative, composite, directional, non-directional, logical, empirical, statistical, associative, exact, and inexact.
A hypothesis can be categorized into one or more of these types. However, some are mutually exclusive and opposites. Simple and complex hypotheses are mutually exclusive, as are direction and non-direction, and null and alternative hypotheses.
Below I explain each hypothesis in simple terms for absolute beginners. These definitions may be too simple for some, but they’re designed to be clear introductions to the terms to help people wrap their heads around the concepts early on in their education about research methods .
Before you Proceed: Dependent vs Independent Variables
A research study and its hypotheses generally examine the relationships between independent and dependent variables – so you need to know these two concepts:
Read my full article on dependent vs independent variables for more examples.
Example: Eating carrots (independent variable) improves eyesight (dependent variable).
A simple hypothesis is a hypothesis that predicts a correlation between two test variables: an independent and a dependent variable.
This is the easiest and most straightforward type of hypothesis. You simply need to state an expected correlation between the dependant variable and the independent variable.
You do not need to predict causation (see: directional hypothesis). All you would need to do is prove that the two variables are linked.
Question | Simple Hypothesis |
---|---|
Do people over 50 like Coca-Cola more than people under 50? | On average, people over 50 like Coca-Cola more than people under 50. |
According to national registries of car accident data, are Canadians better drivers than Americans? | Canadians are better drivers than Americans. |
Are carpenters more liberal than plumbers? | Carpenters are more liberal than plumbers. |
Do guitarists live longer than pianists? | Guitarists do live longer than pianists. |
Do dogs eat more in summer than winter? | Dogs do eat more in summer than winter. |
A complex hypothesis is a hypothesis that contains multiple variables, making the hypothesis more specific but also harder to prove.
You can have multiple independent and dependant variables in this hypothesis.
Question | Complex Hypothesis |
---|---|
Do (1) age and (2) weight affect chances of getting (3) diabetes and (4) heart disease? | (1) Age and (2) weight increase your chances of getting (3) diabetes and (4) heart disease. |
In the above example, we have multiple independent and dependent variables:
Because there are multiple variables, this study is a lot more complex than a simple hypothesis. It quickly gets much more difficult to prove these hypotheses. This is why undergraduate and first-time researchers are usually encouraged to use simple hypotheses.
A null hypothesis will predict that there will be no significant relationship between the two test variables.
For example, you can say that “The study will show that there is no correlation between marriage and happiness.”
A good way to think about a null hypothesis is to think of it in the same way as “innocent until proven guilty”[1]. Unless you can come up with evidence otherwise, your null hypothesis will stand.
A null hypothesis may also highlight that a correlation will be inconclusive . This means that you can predict that the study will not be able to confirm your results one way or the other. For example, you can say “It is predicted that the study will be unable to confirm a correlation between the two variables due to foreseeable interference by a third variable .”
Beware that an inconclusive null hypothesis may be questioned by your teacher. Why would you conduct a test that you predict will not provide a clear result? Perhaps you should take a closer look at your methodology and re-examine it. Nevertheless, inconclusive null hypotheses can sometimes have merit.
Question | Null Hypothesis (H ) |
---|---|
Do people over 50 like Coca-Cola more than people under 50? | Age has no effect on preference for Coca-Cola. |
Are Canadians better drivers than Americans? | Nationality has no effect on driving ability. |
Are carpenters more liberal than plumbers? | There is no statistically significant difference in political views between carpenters and plumbers. |
Do guitarists live longer than pianists? | There is no statistically significant difference in life expectancy between guitarists and pianists. |
Do dogs eat more in summer than winter? | Time of year has no effect on dogs’ appetites. |
An alternative hypothesis is a hypothesis that is anything other than the null hypothesis. It will disprove the null hypothesis.
We use the symbol H A or H 1 to denote an alternative hypothesis.
The null and alternative hypotheses are usually used together. We will say the null hypothesis is the case where a relationship between two variables is non-existent. The alternative hypothesis is the case where there is a relationship between those two variables.
The following statement is always true: H 0 ≠ H A .
Let’s take the example of the hypothesis: “Does eating oatmeal before an exam impact test scores?”
We can have two hypotheses here:
For the alternative hypothesis to be true, all we have to do is disprove the null hypothesis for the alternative hypothesis to be true. We do not need an exact prediction of how much oatmeal will impact the test scores or even if the impact is positive or negative. So long as the null hypothesis is proven to be false, then the alternative hypothesis is proven to be true.
A composite hypothesis is a hypothesis that does not predict the exact parameters, distribution, or range of the dependent variable.
Often, we would predict an exact outcome. For example: “23 year old men are on average 189cm tall.” Here, we are giving an exact parameter. So, the hypothesis is not composite.
But, often, we cannot exactly hypothesize something. We assume that something will happen, but we’re not exactly sure what. In these cases, we might say: “23 year old men are not on average 189cm tall.”
We haven’t set a distribution range or exact parameters of the average height of 23 year old men. So, we’ve introduced a composite hypothesis as opposed to an exact hypothesis.
Generally, an alternative hypothesis (discussed above) is composite because it is defined as anything except the null hypothesis. This ‘anything except’ does not define parameters or distribution, and therefore it’s an example of a composite hypothesis.
A directional hypothesis makes a prediction about the positivity or negativity of the effect of an intervention prior to the test being conducted.
Instead of being agnostic about whether the effect will be positive or negative, it nominates the effect’s directionality.
We often call this a one-tailed hypothesis (in contrast to a two-tailed or non-directional hypothesis) because, looking at a distribution graph, we’re hypothesizing that the results will lean toward one particular tail on the graph – either the positive or negative.
Question | Directional Hypothesis |
---|---|
Does adding a 10c charge to plastic bags at grocery stores lead to changes in uptake of reusable bags? | Adding a 10c charge to plastic bags in grocery stores will lead to an in uptake of reusable bags. |
Does a Universal Basic Income influence retail worker wages? | Universal Basic Income retail worker wages. |
Does rainy weather impact the amount of moderate to high intensity exercise people do per week in the city of Vancouver? | Rainy weather the amount of moderate to high intensity exercise people do per week in the city of Vancouver. |
Does introducing fluoride to the water system in the city of Austin impact number of dental visits per capita per year? | Introducing fluoride to the water system in the city of Austin the number of dental visits per capita per year? |
Does giving children chocolate rewards during study time for positive answers impact standardized test scores? | Giving children chocolate rewards during study time for positive answers standardized test scores. |
A non-directional hypothesis does not specify the predicted direction (e.g. positivity or negativity) of the effect of the independent variable on the dependent variable.
These hypotheses predict an effect, but stop short of saying what that effect will be.
A non-directional hypothesis is similar to composite and alternative hypotheses. All three types of hypothesis tend to make predictions without defining a direction. In a composite hypothesis, a specific prediction is not made (although a general direction may be indicated, so the overlap is not complete). For an alternative hypothesis, you often predict that the even will be anything but the null hypothesis, which means it could be more or less than H 0 (or in other words, non-directional).
Let’s turn the above directional hypotheses into non-directional hypotheses.
Question | Non-Directional Hypothesis |
---|---|
Does adding a 10c charge to plastic bags at grocery stores lead to changes in uptake of reusable bags? | Adding a 10c charge to plastic bags in grocery stores will lead to a in uptake of reusable bags. |
Does a Universal Basic Income influence retail worker wages? | Universal Basic Income retail worker wages. |
Does rainy weather impact the amount of moderate to high intensity exercise people do per week in the city of Vancouver? | Rainy weather the amount of moderate to high intensity exercise people do per week in the city of Vancouver. |
Does introducing fluoride to the water system in the city of Austin impact number of dental visits per capita per year? | Introducing fluoride to the water system in the city of Austin the number of dental visits per capita per year? |
Does giving children chocolate rewards during study time for positive answers impact standardized test scores? | Giving children chocolate rewards during study time for positive answers standardized test scores. |
A logical hypothesis is a hypothesis that cannot be tested, but has some logical basis underpinning our assumptions.
These are most commonly used in philosophy because philosophical questions are often untestable and therefore we must rely on our logic to formulate logical theories.
Usually, we would want to turn a logical hypothesis into an empirical one through testing if we got the chance. Unfortunately, we don’t always have this opportunity because the test is too complex, expensive, or simply unrealistic.
Here are some examples:
An empirical hypothesis is the opposite of a logical hypothesis. It is a hypothesis that is currently being tested using scientific analysis. We can also call this a ‘working hypothesis’.
We can to separate research into two types: theoretical and empirical. Theoretical research relies on logic and thought experiments. Empirical research relies on tests that can be verified by observation and measurement.
So, an empirical hypothesis is a hypothesis that can and will be tested.
Each of the above hypotheses can be tested, making them empirical rather than just logical (aka theoretical).
A statistical hypothesis utilizes representative statistical models to draw conclusions about broader populations.
It requires the use of datasets or carefully selected representative samples so that statistical inference can be drawn across a larger dataset.
This type of research is necessary when it is impossible to assess every single possible case. Imagine, for example, if you wanted to determine if men are taller than women. You would be unable to measure the height of every man and woman on the planet. But, by conducting sufficient random samples, you would be able to predict with high probability that the results of your study would remain stable across the whole population.
You would be right in guessing that almost all quantitative research studies conducted in academic settings today involve statistical hypotheses.
An associative hypothesis predicts that two variables are linked but does not explore whether one variable directly impacts upon the other variable.
We commonly refer to this as “ correlation does not mean causation ”. Just because there are a lot of sick people in a hospital, it doesn’t mean that the hospital made the people sick. There is something going on there that’s causing the issue (sick people are flocking to the hospital).
So, in an associative hypothesis, you note correlation between an independent and dependent variable but do not make a prediction about how the two interact. You stop short of saying one thing causes another thing.
A causal hypothesis predicts that two variables are not only associated, but that changes in one variable will cause changes in another.
A causal hypothesis is harder to prove than an associative hypothesis because the cause needs to be definitively proven. This will often require repeating tests in controlled environments with the researchers making manipulations to the independent variable, or the use of control groups and placebo effects .
If we were to take the above example of lice in the hair of sick people, researchers would have to put lice in sick people’s hair and see if it made those people healthier. Researchers would likely observe that the lice would flee the hair, but the sickness would remain, leading to a finding of association but not causation.
Question | Causation Hypothesis | Correlation Hypothesis |
---|---|---|
Does marriage cause baldness among men? | Marriage causes stress which leads to hair loss. | Marriage occurs at an age when men naturally start balding. |
What is the relationship between recreational drugs and psychosis? | Recreational drugs cause psychosis. | People with psychosis take drugs to self-medicate. |
Do ice cream sales lead to increase drownings? | Ice cream sales cause increased drownings. | Ice cream sales peak during summer, when more people are swimming and therefore more drownings are occurring. |
For brevity’s sake, I have paired these two hypotheses into the one point. The reality is that we’ve already seen both of these types of hypotheses at play already.
An exact hypothesis (also known as a point hypothesis) specifies a specific prediction whereas an inexact hypothesis assumes a range of possible values without giving an exact outcome. As Helwig [2] argues:
“An “exact” hypothesis specifies the exact value(s) of the parameter(s) of interest, whereas an “inexact” hypothesis specifies a range of possible values for the parameter(s) of interest.”
Generally, a null hypothesis is an exact hypothesis whereas alternative, composite, directional, and non-directional hypotheses are all inexact.
See Next: 15 Hypothesis Examples
This is introductory information that is basic and indeed quite simplified for absolute beginners. It’s worth doing further independent research to get deeper knowledge of research methods and how to conduct an effective research study. And if you’re in education studies, don’t miss out on my list of the best education studies dissertation ideas .
[1] https://jnnp.bmj.com/content/91/6/571.abstract
[2] http://users.stat.umn.edu/~helwig/notes/SignificanceTesting.pdf
Wow! This introductionary materials are very helpful. I teach the begginers in research for the first time in my career. The given tips and materials are very helpful. Chris, thank you so much! Excellent materials!
You’re more than welcome! If you want a pdf version of this article to provide for your students to use as a weekly reading on in-class discussion prompt for seminars, just drop me an email in the Contact form and I’ll get one sent out to you.
When I’ve taught this seminar, I’ve put my students into groups, cut these definitions into strips, and handed them out to the groups. Then I get them to try to come up with hypotheses that fit into each ‘type’. You can either just rotate hypothesis types so they get a chance at creating a hypothesis of each type, or get them to “teach” their hypothesis type and examples to the class at the end of the seminar.
Cheers, Chris
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Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.
In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.
Null Hypothesis: H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis : H a : Male factory workers have a higher salary than female factory workers.
Null Hypothesis : H 0 : There is no relationship between height and shoe size. Alternative Hypothesis : H a : There is a positive relationship between height and shoe size.
Null Hypothesis : H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis : H a : The quality of a brick mason’s work is influenced by on-the-job experience.
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The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups.
The following are some examples of null hypothesis:
H 0 : µ 1 = µ 2
H 0 = null hypothesis µ 1 = mean score of men µ 2 = mean score of women
An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study.
The following are some examples of alternative hypothesis:
1. If a researcher is assuming that the bearing capacity of a bridge is more than 10 tons, then the hypothesis under this study will be:
Null hypothesis H 0 : µ= 10 tons Alternative hypothesis H a : µ>10 tons
2. Under another study that is trying to test whether there is a significant difference between the effectiveness of medicine against heart arrest, the alternative hypothesis will be that there is a relationship between the medicine and chances of heart arrest.
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. | An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. | |
It is denoted by H . | It is denoted by H or H . | |
It is followed by ‘equals to’ sign. | It is followed by not equals to, ‘less than’ or ‘greater than’ sign. | |
The null hypothesis believes that the results are observed as a result of chance. | The alternative hypothesis believes that the results are observed as a result of some real causes. | |
It is the hypothesis that the researcher tries to disprove. | It is a hypothesis that the researcher tries to prove. | |
The result of the null hypothesis indicates no changes in opinions or actions. | The result of an alternative hypothesis causes changes in opinions and actions. | |
If the null hypothesis is accepted, the results of the study become insignificant. | If an alternative hypothesis is accepted, the results of the study become significant. | |
If the p-value is greater than the level of significance, the null hypothesis is accepted. | If the p-value is smaller than the level of significance, an alternative hypothesis is accepted. | |
The null hypothesis allows the acceptance of correct existing theories and the consistency of multiple experiments. | Alternative hypothesis are important as it establishes a relationship between two variables, resulting in new improved theories. |
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A hypothesis is a proposed explanation for a phenomenon, based on observation, reasoning, or scientific theory, awaiting verification or falsification through experimentation and data analysis. It serves as a starting point for investigation, guiding the research process by suggesting what outcomes to expect. In the realm of statistics and scientific research, hypotheses are crucial for designing experiments, analyzing results, and advancing knowledge.
The null hypothesis and alternative hypothesis are required to be fragmented properly before the data collection and interpretation phase in the research. Well fragmented hypotheses indicate that the researcher has adequate knowledge in that particular area and is thus able to take the investigation further because they can use a much more systematic system. It gives direction to the researcher on his/her collection and interpretation of data.
The null hypothesis and alternative hypothesis are useful only if they state the expected relationship between the variables or if they are consistent with the existing body of knowledge. They should be expressed as simply and concisely as possible. They are useful if they have explanatory power.
The purpose and importance of the null hypothesis and alternative hypothesis are that they provide an approximate description of the phenomena. The purpose is to provide the researcher or an investigator with a relational statement that is directly tested in a research study. The purpose is to provide the framework for reporting the inferences of the study. The purpose is to behave as a working instrument of the theory. The purpose is to prove whether or not the test is supported, which is separated from the investigator’s own values and decisions. They also provide direction to the research.
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The null hypothesis is generally denoted as H0. It states the exact opposite of what an investigator or an experimenter predicts or expects. It basically defines the statement which states that there is no exact or actual relationship between the variables.
The alternative hypothesis is generally denoted as H1. It makes a statement that suggests or advises a potential result or an outcome that an investigator or the researcher may expect. It has been categorized into two categories: directional alternative hypothesis and non directional alternative hypothesis.
The directional hypothesis is a kind that explains the direction of the expected findings. Sometimes this type of alternative hypothesis is developed to examine the relationship among the variables rather than a comparison between the groups.
The non directional hypothesis is a kind that has no definite direction of the expected findings being specified.
Related Pages:
Hypothesis Testing
Research Hypotheses
Ready to test your hypothesis? Check out Intellectus Statistics , the easy to use statistics software for the non-statistician.
All research starts with a problem that needs to be solved. From this problem, hypotheses are developed to provide the researcher with a clear statement of the problem.
To understand alternative hypotheses also known as alternate hypotheses, you must first understand what the hypothesis is .
When you hear the word hypothesis it means the accurate explanations in relation to a set of facts that can be analyzed when studied, using some specific method of research.
There are primarily two types of hypothesis which are null hypothesis and alternative hypothesis.
When you think about the word “null” what should come to mind is something that can not change, what you expect is what you get, unlike alternate hypotheses which can change.
Now, the research problems or questions which could be in the form of null hypothesis or alternative hypothesis are expressed as the relationship that exists between two or more variables. The process for this states that the questions should be what expresses the relationship between two variables that can be measured.
Both null hypotheses and alternative hypotheses are used by statisticians and researchers to conduct research in various industries or fields such as mathematics, psychology, science, medicine, and technology.
We are going to discuss alternative hypotheses and null hypotheses in this post and how they work in research.
Alternative hypothesis simply put is another viable option to the null hypothesis. It means looking for a substantial change or option that can allow you to reject the null hypothesis.
It is an opposing theory to a null hypothesis.
If you develop a null hypothesis, you make an informed guess on whether a thing is true or whether there is a relationship between that thing and another variable. An alternate hypothesis will always take an opposite stand against a null hypothesis. So if according to a null hypothesis something is correct to an alternate hypothesis that same thing will be incorrect.
For example, let’s assume that you develop a null hypothesis that states “I”m going to be $500 richer” the alternate hypothesis will be “I’m going to get $500 or be richer”
When you are trying to disprove a null hypothesis, that is when you test an alternate hypothesis. If there is enough data to back up the alternative hypothesis then you can dispose of the null hypothesis.
Get Answers: What is Empirical Research Study? [Examples & Method]
The null hypothesis is best explained as the statement showing that no relationship exists between two variables that are being considered or that two groups are not related. As we have earlier established, a hypothesis is an assumed statement that has not been proven with sufficient data that could serve as a piece of evidence.
The null hypothesis is now the statement that a researcher or an investigator wants to disprove. The null hypothesis is capable of being tested, being verifiable, and also capable of being rejected.
For example, if you want to conduct a study that will compare the relationship between project A and project B if the study is based on the assumption that both projects are of equal standard, the assumption is referred to as the null hypothesis.
This is because the null hypothesis should be specific at all times.
Learn: Hypothesis Testing in Research: Definition, Procedure, Uses, Limitations + Examples
For the curious: Sampling Bias: Definition, Types + [Examples]
Here are the purposes of the null hypothesis in an experiment or study:
Now, these are the principles of the null hypothesis:
1. The primary principle of the null hypothesis is to prove that the assumed statement is true. This is done by collecting data and analyzing in the study , what chance the collected data has in the random sample.
2. If the collected data does not meet the expectation of the null hypothesis, it is determined that the data lacks sufficient evidence to back up the null hypothesis therefore the null hypothesis statement is rejected.
Just as in the case of the alternative hypothesis the collected data in a null hypothesis is analyzed using some statistical tools that are made to measure the extent to which data left the null hypothesis.
The process will determine whether the data that left the null hypothesis is larger than a set value. If the data collected from the random sample is enough to serve as evidence to prove the null hypothesis then the null hypothesis will be accepted as true. And also defined that it has no relationship with other variables .
Learn About: Research Reports: Definition, Types + [Writing Guide]
There are four types of alternative hypotheses, and we will briefly discuss them below.
Read: Type I vs Type II Errors: Definition, Examples & Prevention
We are going to look at the differences between the alternate hypothesis and the null hypothesis based on these six factors which are:
Null hypothesis is followed by an ‘equals to’ (=) sign. While the Alternative hypothesis is followed by these three signs;
In the null hypothesis, it is believed that the results that are observed are as a result of chance. While In the alternative hypothesis, it is believed that the observed results are the outcome of some real causes.
The result of the null hypothesis always shows that there have been no changes in statements or opinions. While the result of the alternative hypothesis shows that there have been significant changes in statements and opinions.
If the p-value in a null hypothesis is greater than the significance level, then the null hypothesis is accepted.
If the p-value in an alternate hypothesis is smaller than the significance level, then the alternative hypothesis is accepted.
The null hypothesis accepts true existing theories and also if there has been consistency in multiple experiments of similar hypotheses.
The alternative hypothesis establishes whether a relationship exists between two variables, and the result will then lead to new improved theories.
Read: T-testing: Definition, Formula & Interpretations
Here are some examples of the alternative hypothesis:.
A researcher assumes that a bridge’s bearing capacity is over 10 tons, the researcher will then develop an hypothesis to support this study. The hypothesis will be:
For the null hypothesis H0: µ= 10 tons
For the alternate hypothesis Ha: µ>10 tons
In another study being conducted, the researcher wants to find out whether there is a noticeable difference or change in a patient’s heart arrest medicine and the patient’s heart condition.
For the alternate hypothesis: The hypothesis is that there might indeed be a relationship between the new medicine and the frequency or chances of heart arrest in a patient.
The hypothesis from example 2 in the alternate hypothesis implies that the use of one specific medicine can reduce the frequency and chances of heart arrest.
For the null hypothesis: The hypothesis will be that the use of that particular medicine cannot reduce the chance and frequency of heart arrest in a patient.
An alternate hypothesis states that the random exam scores are collected from both men and women. But are the scores of the two groups (men and women) the same or are they different?
For the null hypothesis: The hypothesis will state that the calculated mean of the men’s exam score is equal to the exam score of the women.
This is represented as
H0= The null hypothesis
µ1= The calculated mean score of men
µ2= The calculated mean score of women
Read: What is Empirical Research Study? [Examples & Method]
It is quite inappropriate to say or report that an alternate hypothesis was rejected. It is much better to use the phrase “the alternate hypothesis was rather not supported”.
The reason behind this use of words is that only the null hypothesis is designed to be rejected in a study. The alternative hypothesis is designed to prove the null hypothesis incorrect, to introduce new facts that can disprove the null hypothesis but it is not designed to be rejected.
It can either be accepted or not supported.
A researcher can use this formula to identify the alternate hypothesis in a study or experiment.
H0 and Ha are in contrast.
Therefore, if Ho has:
Equal to (=)
Greater than or equal to (≥)
Less than or equal to (≤)
And then Ha has:
Not equal (≠)
Greater than (>) or less than (
Less than ( )
If in a study, α ≤ p-value, then the researcher should not reject H0.
If in a study, α > p-value, then the researcher should reject H0.
α is preconceived. The value of α is determined even before the hypothesis test is conducted. While the p-value is derived from the calculation in the data.
The study a researcher wants to conduct will determine what hypothesis should be developed. However, the researcher should keep in mind what the purpose of the null and alternative two hypotheses are while developing the study hypothesis. So while the null hypothesis will accept existing theories that it found to be true or correct, and measure the consistency of multiple experiments, alternative hypotheses will find the relationship that exists (if any) between two phenomena and may lead to the development of a new and improved theory.
In this article, it has been clearly defined the relationship that exists between the null hypothesis and the alternative hypothesis. While the null hypothesis is always an assumption that needs to be proven with evidence for it to be accepted, the alternative hypothesis puts in all the effort to make sure the null hypothesis is disproved.
Researchers should note that for every null hypothesis, one or more alternate hypotheses can be developed.
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This article will discuss the two different types of errors in hypothesis testing and how you can prevent them from occurring in your research
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Know the Differences & Comparisons
Null hypothesis implies a statement that expects no difference or effect. On the contrary, an alternative hypothesis is one that expects some difference or effect. Null hypothesis This article excerpt shed light on the fundamental differences between null and alternative hypothesis.
Comparison chart.
Basis for Comparison | Null Hypothesis | Alternative Hypothesis |
---|---|---|
Meaning | A null hypothesis is a statement, in which there is no relationship between two variables. | An alternative hypothesis is statement in which there is some statistical significance between two measured phenomenon. |
Represents | No observed effect | Some observed effect |
What is it? | It is what the researcher tries to disprove. | It is what the researcher tries to prove. |
Acceptance | No changes in opinions or actions | Changes in opinions or actions |
Testing | Indirect and implicit | Direct and explicit |
Observations | Result of chance | Result of real effect |
Denoted by | H-zero | H-one |
Mathematical formulation | Equal sign | Unequal sign |
A null hypothesis is a statistical hypothesis in which there is no significant difference exist between the set of variables. It is the original or default statement, with no effect, often represented by H 0 (H-zero). It is always the hypothesis that is tested. It denotes the certain value of population parameter such as µ, s, p. A null hypothesis can be rejected, but it cannot be accepted just on the basis of a single test.
A statistical hypothesis used in hypothesis testing, which states that there is a significant difference between the set of variables. It is often referred to as the hypothesis other than the null hypothesis, often denoted by H 1 (H-one). It is what the researcher seeks to prove in an indirect way, by using the test. It refers to a certain value of sample statistic, e.g., x¯, s, p
The acceptance of alternative hypothesis depends on the rejection of the null hypothesis i.e. until and unless null hypothesis is rejected, an alternative hypothesis cannot be accepted.
The important points of differences between null and alternative hypothesis are explained as under:
There are two outcomes of a statistical test, i.e. first, a null hypothesis is rejected and alternative hypothesis is accepted, second, null hypothesis is accepted, on the basis of the evidence. In simple terms, a null hypothesis is just opposite of alternative hypothesis.
Zipporah Thuo says
February 22, 2018 at 6:06 pm
The comparisons between the two hypothesis i.e Null hypothesis and the Alternative hypothesis are the best.Thank you.
Getu Gamo says
March 4, 2019 at 3:42 am
Thank you so much for the detail explanation on two hypotheses. Now I understood both very well, including their differences.
Jyoti Bhardwaj says
May 28, 2019 at 6:26 am
Thanks, Surbhi! Appreciate the clarity and precision of this content.
January 9, 2020 at 6:16 am
John Jenstad says
July 20, 2020 at 2:52 am
Thanks very much, Surbhi, for your clear explanation!!
Navita says
July 2, 2021 at 11:48 am
Thanks for the Comparison chart! it clears much of my doubt.
GURU UPPALA says
July 21, 2022 at 8:36 pm
Thanks for the Comparison chart!
Enock kipkoech says
September 22, 2022 at 1:57 pm
What are the examples of null hypothesis and substantive hypothesis
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In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .
In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.
Table of contents:
The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .
In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .
The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.
Here, the hypothesis test formulas are given below for reference.
The formula for the null hypothesis is:
H 0 : p = p 0
The formula for the alternative hypothesis is:
H a = p >p 0 , < p 0 ≠ p 0
The formula for the test static is:
Remember that, p 0 is the null hypothesis and p – hat is the sample proportion.
Also, read:
There are different types of hypothesis. They are:
Simple Hypothesis
It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.
Composite Hypothesis
The composite hypothesis is one that does not completely specify the population distribution.
Exact Hypothesis
Exact hypothesis defines the exact value of the parameter. For example μ= 50
Inexact Hypothesis
This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60
Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.
The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).
The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.
Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.
|
| |
1 | The null hypothesis is a statement. There exists no relation between two variables | Alternative hypothesis a statement, there exists some relationship between two measured phenomenon |
2 | Denoted by H | Denoted by H |
3 | The observations of this hypothesis are the result of chance | The observations of this hypothesis are the result of real effect |
4 | The mathematical formulation of the null hypothesis is an equal sign | The mathematical formulation alternative hypothesis is an inequality sign such as greater than, less than, etc. |
Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.
If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.
Few more examples are:
1). Are there is 100% chance of getting affected by dengue?
Ans: There could be chances of getting affected by dengue but not 100%.
2). Do teenagers are using mobile phones more than grown-ups to access the internet?
Ans: Age has no limit on using mobile phones to access the internet.
3). Does having apple daily will not cause fever?
Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.
4). Do the children more good in doing mathematical calculations than grown-ups?
Ans: Age has no effect on Mathematical skills.
In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives.
The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data.
What is meant by the null hypothesis.
In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.
The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.
The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.
If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.
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I'm practicing with the hypothesis test and I find myself in trouble with the decision about how to set a null and an alternative hypothesis. My main issue is to determine, in every situation, a "general rule" on how I can decide correctly which is the null and which is the alternative hypothesis.. can someone help me?
Here is an example: As an established scholar, you are requested to evaluate if Customer Relationship Management affects the financial performance of firms. The main issue will be solved by means of a test of hypothesis. Two hypothesis will be tested one against the other: CRM is related to performance, CRM is not related.
The rule for the proper formulation of a hypothesis test is that the alternative or research hypothesis is the statement that, if true, is strongly supported by the evidence furnished by the data.
The null hypothesis is generally the complement of the alternative hypothesis. Frequently, it is (or contains) the assumption that you are making about how the data are distributed in order to calculate the test statistic.
Here are a few examples to help you understand how these are properly chosen.
Suppose I am an epidemiologist in public health, and I'm investigating whether the incidence of smoking among a certain ethnic group is greater than the population as a whole, and therefore there is a need to target anti-smoking campaigns for this sub-population through greater community outreach and education. From previous studies that have been published in the literature, I find that the incidence among the general population is $p_0$. I can then go about collecting sample data (that's actually the hard part!) to test $$H_0 : p = p_0 \quad \mathrm{vs.} \quad H_a : p > p_0.$$ This is a one-sided binomial proportion test. $H_a$ is the statement that, if it were true, would need to be strongly supported by the data we collected. It is the statement that carries the burden of proof . This is because any conclusion we draw from the test is conditional upon assuming that the null is true: either $H_a$ is accepted, or the test is inconclusive and there is insufficient evidence from the data to suggest $H_a$ is true. The choice of $H_0$ reflects the underlying assumption that there is no difference in the smoking rates of the sub-population compared to the whole.
Now suppose I am a researcher investigating a new drug that I believe to be equally effective to an existing standard of treatment, but with fewer side effects and therefore a more desirable safety profile. I would like to demonstrate the equal efficacy by conducting a bioequivalence test. If $\mu_0$ is the mean existing standard treatment effect, then my hypothesis might look like this: $$H_0 : |\mu - \mu_0| \ge \Delta \quad \mathrm{vs.} \quad H_a : |\mu - \mu_0| < \Delta,$$ for some choice of margin $\Delta$ that I consider to be clinically significant. For example, a clinician might say that two treatments are sufficiently bioequivalent if there is less than a $\Delta = 10\%$ difference in treatment effect. Note again that $H_a$ is the statement that carries the burden of proof: the data we collect must strongly support it, in order for us to accept it; otherwise, it could still be true but we don't have the evidence to support the claim .
Now suppose I am doing an analysis for a small business owner who sells three products $A$, $B$, $C$. They suspect that there is a statistically significant preference for these three products. Then my hypothesis is $$H_0 : \mu_A = \mu_B = \mu_C \quad \mathrm{vs.} \quad H_a : \exists i \ne j \text{ such that } \mu_i \ne \mu_j.$$ Really, all that $H_a$ is saying is that there are two means that are not equal to each other, which would then suggest that some difference in preference exists.
The null hypothesis is nearly always "something didn't happen" or "there is no effect" or "there is no relationship" or something similar. But it need not be this.
In your case, the null would be "there is no relationship between CRM and performance"
The usual method is to test the null at some significance level (most often, 0.05). Whether this is a good method is another matter, but it is what is commonly done.
In science proofs, you can never prove anything, you can only demonstrate that your model describes the data better than another model. You want your alternate hypothesis to come from the new model under test, and the null hypothesis to be from a different model.
The null hypothesis should come from a model which others would choose to use when challenging your scientific claims! The most common pattern for a scientific claim is "I think that X is a factor in process Y. If everyone already believes X is a factor in the process, then there is nothing to prove, and everyone can just go out and talk about it over drinks. Scientific arguments with null hypothesis are interesting because, if someone takes the opposing view, "X is not a factor in process Y, then there is a disagreement. This is where science does its thing.
If you believe "X is a factor in process Y" enough to run an experiment, you should generally know what you're looking to see in the results. So now your phrase becomes "X is a factor in process Y, producing visible outcome Z."
This is where you pick your null hypothesis. If someone believes X is not a factor, and your experiment does indeed show Z, then they need an explanation for Z. With your choice of null hypothesis, you are effectively challenging their explanation . The dead simplest explanation is always "Z was caused by random chance because science is based on statistics." Accordingly, most null hypothesis are in the form of "The outcome should be predicted using the previously accepted model plus some random chance to account for statistics.
Both hypothesis should be phrased in terms of the visible outcome, NOT the model you intend to prove. [note] You never start with an alternate hypothesis of "I believe X is a factor." You phrase it "I expect to see this result when I observe Z." The null hypothesis will be phrased similarly, "The status quo predicts that we will see this different result when I observe Z." There is always a statistical phrasing in there such as "I expect to observe a normal distribution on Z when I do this experiment over and over." Once you observe results that defend your alternate hypothesis and reject the null hypothsis, you are THEN in a position to make claims about the validity of your model.
[note] This bolded statement is my opinion, but I feel confident enough in its wording choice to post it. The hypotheses draw a strong line between the intuitive portion of the science, and the data and analysis of the science. If your phrasing is too close to the model, it becomes hard to separate the model from the data, and makes it harder for the next scientist to use your data
In the case of our simple model with process Y and visible outcome Z, the existing belief is that Z will fit a distribution that everyone is already comfortable with, such as "the randomness expected by your particular laboratory equipment setup" or "the purity of the reagents used in the experiment." When you "reject the null hypothesis" what you are saying is most literally, "I have run this experiment, and it is so tremendously unlikely that random chance generated the observed behavior, that everybody should start considering that maybe there's more to this than meets the eye."
The alternative hypothesis is what you offer to the world to replace the null hypothesis . It is one thing to go do experiments to poke at holes in other's models, but that doesn't promote science nearly as well as poking holes in other's models and then replacing them with new models that do a better job.
With the null and alternate hypothesis, you are trying to challenge the current conventional thinking of the day. Choose the hypotheses so that they effectively declare "Here is a result everybody would expect (null hypothesis). However, I actually went out and did the experiment and gathered data, and it is VERY unlikely that the null hypothesis is true. Here is the result I expected (the alternate hypothesis). Nobody expected this hypothesis to be true but me, but when I gathered the data and did the statistics, it is very likely that my model does a better job of describing reality than the existing model . Accordingly, I reject the null hypothesis, accept my hypothesis, and challenge my fellow scientists to work from this new data."
And the fellow scientists are free to:
The last outcome causes strife and bickering, but is ABSOLUTELY part of the scientific process. By using the scientific method to publish your results, you accept that others are free to use the scientific method to contradict your results. They will do so, and publish their results.
At this point, the scientific community will make a political decision: who has to go out and spend the money to test their model, and whose model do we accept. TYPICALLY, because you published the model and the data first, and they are refuting your data, the onus is on them to run the experiments which proves why their model is better than yours. But this is now WELL beyond the hypothesis that caused the strife in the first place, so I leave you to experience them in your lifetime!
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A long-standing but poorly tested hypothesis in plant ecology and evolution is that biotic interactions play a more important role in producing and maintaining species diversity in the tropics than in the temperate zone. A core prediction of this hypothesis is that tropical plants deploy a higher diversity of phytochemicals within and across communities because they experience more herbivore pressure than temperate plants. However, simultaneous comparisons of phytochemical diversity and herbivore pressure in plant communities from the tropical to the temperate zone are lacking. Here we provide clear support for this prediction by examining phytochemical diversity and herbivory in 60 tree communities ranging from species-rich tropical rainforests to species-poor subalpine forests. Using a community metabolomics approach, we show that phytochemical diversity is higher within and among tropical tree communities than within and among subtropical and subalpine communities, and that herbivore pressure and specialization are highest in the tropics. Furthermore, we show that the phytochemical similarity of trees has little phylogenetic signal, indicating rapid divergence between closely related species. In sum, we provide several lines of evidence from entire tree communities showing that biotic interactions probably play an increasingly important role in generating and maintaining tree diversity in the lower latitudes.
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Data availability.
The MS data (.mzML) have been deposited in the MassIVE public repository and are available under accession number MSV000092950 . The datasets analysed in the current study, including the molecular network, sample–sample chemical structural and compositional similarity, plot-species-abundance community data, phytochemical richness and the phylogenetic tree of 206 tree species, are available via Figshare at https://doi.org/10.6084/m9.figshare.22758269 (ref. 69 ).
The R code used in the current study is available via Figshare at https://doi.org/10.6084/m9.figshare.22758269 (ref. 69 ).
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This research was supported by the NSFC China–US Dimensions of Biodiversity Grant (DEB: no. 32061123003 to M.C.); the National Natural Science Foundation of China (grant nos. 32201318 to L.S. and 31870410 to J.Y.); the Chinese Academy of Sciences Youth Innovation Promotion Association (grant no. Y202080 to J.Y.); the Distinguished Youth Scholar of Yunnan (grant no. 202101AV070005 to J.Y.); the Ten Thousand Talent Plans for Young Top-Notch Talents of Yunnan Province (grant no. YNWR-QNBJ-2018-309 to J.Y.); a Postdoctoral Fellowship of Xishuangbanna Tropical Botanical Garden, CAS, to L.S.; the Postdoctoral Science Foundation of Yunnan Province to L.S.; the 14th Five-Year Plan of the Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences (grant nos. XTBG-1450101 and E3ZKFF2B01 to J.Y.); and an NSF US–China Dimensions of Biodiversity Grant (DEB: no. 2124466) to N.G.S. We acknowledge support from Xishuangbanna Station for Tropical Rain Forest Ecosystem Studies, Ailaoshan Station for Subtropical Forest Ecosystem Studies and Lijiang Forest Ecosystem Research Station. We thank the Molecular Biology Experiment Center in Germplasm Bank of Wild Species, Chinese Academy of Sciences, for facilitating the extraction of plant metabolites, and the State Key Laboratory of Phytochemistry and Plant Resources in West China, Chinese Academy of Sciences, for performing the UHPLC–MS/MS analysis. We thank J. Wang, C. Xu, P. Song, T. Liang and many local residents for their assistance in collecting leaf samples. We also thank J. Yang, H. Liu and Y. Tan for their kind assistance during extracting plant metabolites and metabolite analysis.
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CAS Key Laboratory of Tropical Forest Ecology, Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences, Mengla, China
Lu Sun, Yunyun He, Min Cao, Xuezhao Wang & Jie Yang
University of Chinese Academy Sciences, Beijing, China
Yunyun He & Xuezhao Wang
School of Ethnic Medicine, Key Lab of Chemistry in Ethnic Medicinal Resources, State Ethnic Affairs Commission & Ministry of Education of China, Yunnan Minzu University, Kunming, China
Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
Nathan G. Swenson
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J.Y., L.S. and N.G.S. designed the study. M.C. set up the forest inventory plots. L.S., X.Z., Y.H. and X.W. collected and processed the metabolomics data. L.S., Y.H. and X.W. collected and processed the leaf samples. L.S. and J.Y. analysed the data with input from all authors. J.Y., N.G.S. and L.S. wrote the paper. All authors provided feedback on the final version of the paper.
Correspondence to Jie Yang .
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The authors declare no competing interests.
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Extended data fig. 1 observed phytochemical alpha diversity for seven biosynthetic pathway categories within each climatic zone (tropical, sub-tropical and sub-alpine) with diverse q exponents (qorder = 0, 1, 2)..
( a ) terpenoids (n = 20 in tropical zone, n = 20 in sub-tropical zone, n = 20 in sub-alpine zone, for one of q exponents), ( b ) shikimates and phenylpropanoids (n = 20 in tropical zone, n = 20 in sub-tropical zone, n = 20 in sub-alpine zone, for one of q exponents), ( c ) polyketides (n = 20 in tropical zone, n = 20 in sub-tropical zone, n = 20 in sub-alpine zone, for one of q exponents), ( d ) alkaloids (n = 20 in tropical zone, n = 20 in sub-tropical zone, n = 20 in sub-alpine zone, for one of q exponents), ( e ) fatty acids (n = 20 in tropical zone, n = 20 in sub-tropical zone, n = 17 in sub-alpine zone, for one of q exponents), ( f ) amino acids/peptides (n = 18 in tropical zone, n = 19 in sub-tropical zone, n = 12 in sub-alpine zone, for one of q exponents), ( g ) carbohydrates (n = 17 in tropical zone, n = 20 in sub-tropical zone, n = 17 in sub-alpine zone, for one of q exponents). In all panels, the significance of difference of phytochemical alpha diversity across forest type pairs were tested using a one-way ANOVA with a post-hoc Tukey test. In boxplots: the centre line represents the median; the lower and upper hinges correspond to the 25th and 75th percentiles; the lower and upper whiskers extend to the lowest and highest points to a limit of 1.5× the interquartile range from the closest hinge.
( a ) terpenoids (n = 190 in tropical zone, n = 190 in sub-tropical zone, n = 190 in sub-alpine zone, for one of q exponents), ( b ) shikimates and phenylpropanoids (n = 190 in tropical zone, n = 190 in sub-tropical zone, n = 190 in sub-alpine zone, for one of q exponents), ( c ) polyketides (n = 190 in tropical zone, n = 190 in sub-tropical zone, n = 190 in sub-alpine zone, for one of q exponents), ( d ) alkaloids (n = 190 in tropical zone, n = 190 in sub-tropical zone, n = 190 in sub-alpine zone, for one of q exponents), ( e ) fatty acids (n = 190 in tropical zone, n = 190 in sub-tropical zone, n = 136 in sub-alpine zone, for one of q exponents), ( f ) amino acids/peptides (n = 153 in tropical zone, n = 171 in sub-tropical zone, n = 66 in sub-alpine zone, for one of q exponents), ( g ) carbohydrates (n = 136 in tropical zone, n = 190 in sub-tropical zone, n = 136 in sub-alpine zone, for one of q exponents). In all panels, the significance of difference of phytochemical beta diversity across forest type pairs were tested using a one-way ANOVA with a post-hoc Tukey test. In boxplots: the centre line represents the median; the lower and upper hinges correspond to the 25th and 75th percentiles; the lower and upper whiskers extend to the lowest and highest points to a limit of 1.5× the interquartile range from the closest hinge.
The rate of decay (slope) and corresponding significance level were estimated by regressing the chemical similarity against elevational distance via generalized linear model with link log and a quasi-binomial family. The trend lines represent linear fits from regressions, and coloured shaded areas indicate 95% confidence interval (CI) of the prediction. Colours denote whole study region (grey), tropical zone (red), sub-tropical zone (blue) and sub-alpine zone (yellow). Panels, a, d, g and j show the slope of the relationship when q exponents is 0. Panels, b, e, h and k . show the slope of the relationship when q exponents is 1. Panels, c, f, i and l show the slope of the relationship when q exponents is 2.
Extended data fig. 5 distance-decay curves for the plant specialized metabolites on shikimates and phenylpropanoids with diverse q exponents of 0, 1, 2., extended data fig. 6 distance-decay curves for the plant specialized metabolites on polyketides with diverse q exponents of 0, 1, 2..
The rate of decay (slope) and corresponding significance level were estimated by regressing the chemical similarity against elevational distance via generalized linear model with link log and a quasi-binomial family. The trend lines represent linear fits from regressions, and coloured shaded areas indicate 95% confidence interval (CI) of the prediction. Colours denote whole study region (grey), tropical zone (red), sub-tropical zone (blue), sub-alpine zone (yellow). Panels, a, d, g and j show the slope of the relationship when q exponents is 0. Panels, b, e, h and k . show the slope of the relationship when q exponents is 1. Panels, c, f, i and l show the slope of the relationship when q exponents is 2.
Extended data fig. 8 distance-decay curves for the plant specialized metabolites on fatty acids with diverse q exponents of 0, 1, 2., extended data fig. 9 distance-decay curves for the plant specialized metabolites on amino acids/ peptides with diverse q exponents of 0, 1, 2., extended data fig. 10 distance-decay curves for the plant specialized metabolites on carbohydrates with diverse q exponents of 0, 1, 2., supplementary information, supplementary information.
Supplementary Figs. 1–6, Tables 1–7, materials and methods.
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Sun, L., He, Y., Cao, M. et al. Tree phytochemical diversity and herbivory are higher in the tropics. Nat Ecol Evol (2024). https://doi.org/10.1038/s41559-024-02444-2
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The null hypothesis (H 0) answers "No, there's no effect in the population." The alternative hypothesis (H a) answers "Yes, there is an effect in the population." The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
Concept Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with H 0.The null is not rejected unless the hypothesis test shows otherwise.
Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\).The null is not rejected unless the hypothesis test shows otherwise.
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "cannot accept \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis.
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
Section 9.1 Null and Alternative Hypothesis. Learning Objective: In this section, you will: • Understand the general concept and use the terminology of hypothesis testing. I claim that my coin is a fair coin. This means that the probability of heads and the probability of tails are both 50% or 0.50. Out of 200 flips of the coin, tails is ...
The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. ... Alternative Hypothesis H A: Group proportions are not equal in the population: p 1 ≠ p 2. Correlation and Regression Coefficients.
The Null and Alternative Hypotheses. There are two hypotheses that are made: the null hypothesis, denoted H 0, and the alternative hypothesis, denoted H 1 or H A. The null hypothesis is the one to be tested and the alternative is everything else. In our example: The null hypothesis would be: The mean data scientist salary is 113,000 dollars.
The alternative hypothesis ( Ha H a) is a claim about the population that is contradictory to H0 H 0 and what we conclude when we reject H0 H 0. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample ...
Here is a summary of the key differences between the null and the alternative hypothesis test. The null hypothesis represents the status quo; the alternative hypothesis represents an alternative statement about the population. The null and the alternative are mutually exclusive statements, meaning both statements cannot be true at the same time.
10.1 - Setting the Hypotheses: Examples. A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or ...
Alternative hypothesis " x is not equal to y .". Null hypothesis: " x is at least y .". Alternative hypothesis " x is less than y .". Null hypothesis: " x is at most y .". Alternative hypothesis " x is greater than y .". Here are the differences between the null and alternative hypotheses and how to distinguish between them.
There are 13 different types of hypothesis. These include simple, complex, null, alternative, composite, directional, non-directional, logical, empirical, statistical, associative, exact, and inexact. A hypothesis can be categorized into one or more of these types. However, some are mutually exclusive and opposites.
In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong. Null Hypothesis (H0) - This can be thought of as the implied hypothesis. "Null" meaning "nothing.". This hypothesis states that there is no difference between groups or no relationship between ...
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. Symbol. It is denoted by H 0.
Basic definition. The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making judgments on the basis of data. In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements.
Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\).The null is not rejected unless the hypothesis test shows otherwise.
The null hypothesis and alternative hypothesis are useful only if they state the expected relationship between the variables or if they are consistent with the existing body of knowledge. They should be expressed as simply and concisely as possible. They are useful if they have explanatory power. The purpose and importance of the null ...
Here are some examples of the alternative hypothesis: Example 1. A researcher assumes that a bridge's bearing capacity is over 10 tons, the researcher will then develop an hypothesis to support this study. The hypothesis will be: For the null hypothesis H0: µ= 10 tons. For the alternate hypothesis Ha: µ>10 tons.
A null hypothesis is what, the researcher tries to disprove whereas an alternative hypothesis is what the researcher wants to prove. A null hypothesis represents, no observed effect whereas an alternative hypothesis reflects, some observed effect. If the null hypothesis is accepted, no changes will be made in the opinions or actions.
Here, the hypothesis test formulas are given below for reference. The formula for the null hypothesis is: H 0 : p = p 0. The formula for the alternative hypothesis is: H a = p >p 0, < p 0 ≠ p 0. The formula for the test static is: Remember that, p 0 is the null hypothesis and p - hat is the sample proportion.
14. The rule for the proper formulation of a hypothesis test is that the alternative or research hypothesis is the statement that, if true, is strongly supported by the evidence furnished by the data. The null hypothesis is generally the complement of the alternative hypothesis. Frequently, it is (or contains) the assumption that you are making ...
A long-standing but poorly tested hypothesis in plant ecology and evolution is that biotic interactions play a more important role in producing and maintaining species diversity in the tropics ...