# What is a two sample unequal variance t-test?

## What is a two sample unequal variance t-test?

In statistics, Welch’s t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means.

How do you do t-test with unequal variances?

How the unequal variance t test is computed

1. Calculation of the standard error of the difference between means. The t ratio is computed by dividing the difference between the two sample means by the standard error of the difference between the two means.
2. Calculation of the df.

Can you do two sample t tests with unequal sample sizes?

You can perform the two-sample t-test if its assumptions are met. Even though you can perform a t-test when the sample size is unequal between two groups, it is more efficient to have an equal sample size in two groups to increase the power of the t-test.

### How do you find unequal variance?

There are two ways to do so:

1. Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test.
2. Perform an F-test.

What does it mean to have unequal variance?

The conservative choice is to use the “Unequal Variances” column, meaning that the data sets are not pooled. This doesn’t require you to make assumptions that you can’t really be sure of, and it almost never makes much of a change in your results.

How do you compare two samples with different sizes?

One way to compare the two different size data sets is to divide the large set into an N number of equal size sets. The comparison can be based on absolute sum of of difference. THis will measure how many sets from the Nset are in close match with the single 4 sample set.

#### Why are unequal sample sizes a problem?

Problems with Unequal Sample Sizes Unequal sample sizes can lead to: Unequal variances between samples, which affects the assumption of equal variances in tests like ANOVA. Having both unequal sample sizes and variances dramatically affects statistical power and Type I error rates (Rusticus & Lovato, 2014).

How do you know if variances are equal or unequal?

Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test.

What is the difference between t-test equal variance and unequal variance?

If the variances are equal then the equal and unequal variances versions of the t-test will yield similar results (even when the sample sizes are unequal), although the equal variances version will have slightly better statistical power.

## Should I use equal or unequal variance?

Shall you use the test for equal or unequal variances? If you have equal numbers of data points, or the numbers are nearly the same, then you should be able to safely use the two-sample test for equal variances.

What if variances are not equal?

Unequal variances (heteroscedasticity) can affect the Type I error rate and lead to false positives. If you are comparing two or more sample means, as in the 2-Sample t-test and ANOVA, a significantly different variance could overshadow the differences between means and lead to incorrect conclusions.

How to perform a two sample t test?

Perform the independent t-test in R using the following functions : t_test ()[rstatix package]: the result is a data frame for easy plotting using the ggpubr package.

• Interpret and report the two-sample t-test
• Add p-values and significance levels to a plot
• Calculate and report the independent samples t-test effect size using Cohen’s d.
• ### What is an example of a two sample t test?

Two-Sample t-Test Example The following two-sample t-test was generated for the AUTO83B.DATdata set. The data set contains miles per gallon for U.S. cars (sample 1) and for Japanese cars (sample 2); the summary statistics for each sample are shown below. SAMPLE 1: NUMBER OF OBSERVATIONS = 249 MEAN = 20.14458

What is a 2 sample t test?

The two-sample t -test (also known as the independent samples t -test) is a method used to test whether the unknown population means of two groups are equal or not. Is this the same as an A/B test? Yes, a two-sample t -test is used to analyze the results from A/B tests.

What is a two sample t test used for?

What is a Two-Sample T-Test? A two-sample t-test is used when you want to compare two independent groups to see if their means are different. “Independent” implies that the two samples must have come from two completely different populations. In other words, one population can’t have any bearing on the other.