A two sample t-test is used to determine whether or not two population means are equal.

This tutorial explains how to perform a two sample t-test in SAS.

**Example: Two Sample t-Test in SAS**

Suppose a botanist wants to know if the mean height of two different species of plants is equal. She collects a random sample of 12 plants from each species and and records their heights in inches.

The heights are as follows:

**Sample 1**: 13, 15, 15, 16, 16, 16, 17, 18, 18, 19, 20, 21

**Sample 2**: 15, 15, 16, 18, 19, 19, 19, 20, 21, 23, 23, 24

Use the following steps to conduct a two sample t-test to determine if the mean height is equal between the two species.

**Step 1: Create the data.**

First, we’ll use the following code to create the dataset in SAS:

/*create dataset*/ data my_data; input Species $ Height; datalines; 1 13 1 15 1 15 1 16 1 16 1 16 1 17 1 18 1 18 1 19 1 20 1 21 2 15 2 15 2 16 2 18 2 19 2 19 2 19 2 20 2 21 2 23 2 23 2 24 ; run;

**Step 2: Perform a two sample t-test.**

Next, we’ll use **proc ttest** to perform the two sample t-test:

/*perform two sample t-test*/ proc ttest data=my_data sides=2 alpha=0.05 h0=0; class Species; var Height; run;

The last table titled **Equality of Variances** performs an F-test to determine if the variances are equal between the two samples.

Since the p-value (.**3577**) of this test is not less than .05, we can assume the two sample variances are equal.

Thus, we can refer to the row titled **Equal** in the second to last table to determine the t value and corresponding p-value to use:

- t Value:
**-2.11** - p-value:
**.0460**

Recall that the two sample t-test uses the following null and alternative hypotheses:

**H**μ_{0}:_{1}= μ_{2}**H**μ_{A}:_{1}≠ μ_{2}

Since the p-value (**.0460**) is less than .05, we reject the null hypothesis.

This means we have sufficient evidence to say that the mean height between the two species of plants is not equal.

**Additional Resources**

The following tutorials explain how to perform other common statistical tests in SAS:

How to Perform a Wilcoxon Signed Rank Test in SAS

How to Perform a One-Way ANOVA in SAS