*65*

The most common way to compare the means between two independent groups is to use a two-sample t-test. However, this test assumes that the variances between the two groups is equal.

If you suspect that the variance between the two groups is *not *equal, then you can instead use Welch’s t-test, which is the non-parametric equivalent of the two-sample t-test.

This tutorial explains how to perform Welch’s t-test in Stata.

**Example: Welch’s t-test in Stata**

For this example we will use the *fuel3 *dataset, which contains the mpg of 12 cars that received a certain fuel treatment and 12 cars that did not.

Use the following steps to perform a Welch’t t-test to determine if there is a difference in the mean mpg between the two groups.

**Step 1: Load and view the data.**

First, load the dataset by typing the following command into the Command box:

use http://www.stata-press.com/data/r13/fuel3

View the raw data by using the following command:

list

**Step 2: Visualize the data.**

Before we perform Welch’s t-test, let’s first create two box plots to visualize the distribution of mpg for each group:

graph box mpg, over(treated)

We can see that the mpg for group 1 (the group that received the fuel treatment) tends to be higher than that of group 0. We can also see that the variance for group 1 looks quite a bit smaller than that of group 0 (the width of the box is smaller).

**Step 3: Perform Welch’s t-test**

Use the following syntax to perform Welch’s t-test:

**ttest variable_to_measure, by(grouping_variable) welch**

Here is the syntax for our particular example:

ttest mpg, by(treated) welch

Here is how to interpret the output:

- The mean mpg for Group 0 was
**21**. The 95% confidence interval for the true population mean was**(19.26525, 22.73745)**. - The mean mpg for Group 1 was
**22.75**. The 95% confidence interval for the true population mean was**(20.68449, 24.81551)**. - The mean difference in mpg for Group 0 – Group 1 was
**-1.75**. The 95% confidence interval for the true difference in population means was**(-4.28369, .7836902)**. - The test statistic,
*t*, for Welch’s t-test was**-1.4280**. - Because we are interested in the alternative hypothesis that the mean mpg was simply different between the two groups, we will look at the p-value associated with Ha: diff != 0, which turns out to be
**0.1666**. Since this value is not less than 0.05, we do not have sufficient evidence to say that the mean mpg between the two groups is different.

**Step 4: Report the results.**

Lastly, we want to report the results of our Welch’s t-test. Here is an example of how to do so:

A Welch’s t-test was performed to determine if there was a statistically significant difference in mpg between a group of cars that received a fuel treatment and a group that did not. The sample size for both groups was 12 cars.

A Welch’s t-test revealed that there was

nota statistically significant difference in means (t = -1.4280, p = 0.1666) between the two groups.

The 95% confidence interval for the true mean difference in group 0 (non-treatment group) and group 1(treatment group) was found to be (-4.28369, .7836902).