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ANOVA vs t-test: with a comparison chart Mosaic Plot

ANOVA vs t-Test: Definition & Working

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When it comes to achieving the mean of two or more population groups, ANOVA (Analysis of variance) and t-test are the two best practices preferred. Although there is a thin line of difference between both of them. 

The t-test is conducted when you have to find the population means between two groups. But when there are three or more groups you go for the ANOVA test. 

Both t-test and ANOVA are the statistical methods of testing a hypothesis. And they both share the assumptions:

  • Sample drawn from the population is normally distributed 
  • Homogeneous variance
  • Random data sampling 
  • Observations are independent
  • Dependent variable is measured in ratio or interval levels

This is why most people seem to misinterpret t-tests and Analysis of Variance for each other. 

In this article, we are going to see, despite their similarities, how t-tests and ANOVA tests are different from each other by using a comparison chart to make it simple and understandable.

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What are the differences between ANOVA & T-tests?

The comparison chart for ANOVA vs t-test only gives you an overview of the differences between the two data analysis methods. In this section, we are diving deeper into the differences by comparing the definition and working of the two analysis methods.

Comparison variableT-TESTANOVA
Definition t-test is statistical hypothesis test used to compare the means of two population groups.ANOVA is an observable technique used to compare the means of more than two population groups.
Feature t-test compares two sample sizes (n) both below 30.ANOVA equates three or more such groups.
Error t-test is less likely to commit an error.ANOVA has more error risks.
ExampleSample from class A and B students have given a mathematics course may have different mean and standard deviation.When one crop is being cultivated from various seed varieties. 
Testt-test can be performed in a double-sided or single-sided test.ANOVA is one-sided test due to no negative variance.
Population t-test is used when the population is less than 30.ANOVA is used for huge population counts.

The following diagram will give you a better understanding of when to use t-test and ANOVA:

ANOVA vs t-test: with a comparison chart Mosaic Plot

ANOVA VS t-test: Definition

The definition is the best way to understand how the two differ, so let’s start with that. 

What is a t-test?

This method of data analysis examines how greatly the population means of two samples differ from each other. 

The best use of the t-test is to test a hypothesis. The data analysis method helps determine if a process has any effect on the target population. The method should be used when you want to compare the means of two groups. 

Read how to use t-test. 

dependent variable and the cause of it. 

Let’s understand this by taking an example of ANOVA tests. You can use the test to determine how the age or gender of your different customer groups affect the traffic or clicks on your online magazine. 

Read an in-depth blog on Analysis of Variance. 

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ANOVA vs t-test: how to perform?

Now that we know what the two statistical analysis methods are and when to use them, let’s see how to perform them. 

How to perform the t-test?

The T-test is a statistical hypothesis testing method that examines whether the sample population means of two groups largely differ from one another. 

It uses the t distribution method when the standard deviation is the unknown and small sample size. The T-test is based on t statistics which assumes the normal distribution of variables and a known mean. Population variance is then calculated from the sample. 

  • Null hypothesis H0: µ(x) = µ(y) against 
  • Alternative hypothesis H1: µ(x) ≠ µ(y) 

Where µ(x) and µ(y) represent the population means. 

The degree of freedom of the t-test is n1 + n2 – 2. 

How to perform ANOVA?

Analysis of Variance is used when there is a comparison between more than two population means. 

It assumes that the sample is drawn from a normally distributed population and that its variances are equal. 

The total amount of variation is split into two: the amount assigned to chance, and the amount assigned to particular causes. So the ANOVA proceeds to test the variance in population means by evaluating the variance among the group items which is proportional to the amount of variance in the groups. This variance occurs due to an unexplained disturbance because of different treatments. 

It tests the hypothesis:

  • Null hypothesis H0: All population means are the same
  • Alternative hypothesis H1: At least one population mean is different

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Conclusion

After studying the above differences, we can safely say that t-test is a special type of Analysis of Variance which is used when we only have two population means to compare. Hence, to avoid an increase in error while using a t-test to compare more than two population groups, we use ANOVA.

To eliminate human error and pace up the analysis you can also use online survey software that allows you to conduct the two statistical analyses with ease.

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