A two sample t-test is used to test whether or not the means of two populations are equal.

This tutorial provides a complete guide on how to interpret the results of a two sample t-test in R.

**Step 1: Create the Data**

Suppose we want to know if two different species of plants have the same mean height. To test this, we collect a simple random sample of 12 plants from each species.

#create vector of plant heights from group 1 group1 <- c(8, 8, 9, 9, 9, 11, 12, 13, 13, 14, 15, 19) #create vector of plant heights from group 2 group2 <- c(11, 12, 13, 13, 14, 14, 14, 15, 16, 18, 18, 19)

**Step 2: Perform & Interpret the Two Sample t-test**

Next, we will use the **t.test()** command to perform a two sample t-test:

#perform two sample t-test t.test(group1, group2) Welch Two Sample t-test data: group1 and group2 t = -2.5505, df = 20.488, p-value = 0.01884 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -5.6012568 -0.5654098 sample estimates: mean of x mean of y 11.66667 14.75000

Here’s how to interpret the results of the test:

**data:** This tells us the data that was used in the two sample t-test. In this case, we used the vectors called group1 and group2.

**t:** This is the t test-statistic. In this case, it is **-2.5505**.

**df**: This is the degrees of freedom associated with the t test-statistic. In this case, it’s **20.488**. Refer to the Satterthwaire approximation for an explanation of how this degrees of freedom value is calculated.

**p-value:** This is the p-value that corresponds to a t test-statistic of -2.5505 and df = 20.488. The p-value turns out to be **.01884**. We can confirm this value by using the T Score to P Value calculator.

**alternative hypothesis:** This tells us the alternative hypothesis used for this particular t-test. In this case, the alternative hypothesis is that the true difference in means between the two groups is not equal to zero.

**95 percent confidence interval:** This tells us the 95% confidence interval for the true difference in means between the two groups. It turns out to be **[-5.601, -.5654]**.

**sample estimates:** This tells us the sample mean of each group. In this case, the sample mean of group 1 was **11.667** and the sample mean of group 2 was **14.75**.

The two hypotheses for this particular two sample t-test are as follows:

**H _{0}: **µ

_{1}= µ

_{2}(the two population means are equal)

**H _{A}: **µ

_{1}≠µ

_{2}(the two population means are

*not*equal)

Because the p-value of our test** (.01884) **is less than alpha = 0.05, we reject the null hypothesis of the test. This means we have sufficient evidence to say that the mean height of plants between the two populations is different.

**Notes**

The **t.test()** function in R uses the following syntax:

t.test(x, y, alternative = “two.sided”, mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.95)

where:

**x, y:**The names of the two vectors that contain the data.**alternative:**The alternative hypothesis. Options include “two.sided”, “less”, or “greater.”**mu:**The value assumed to be the true difference in means.**paired:**Whether or not to use a paired t-test.**var.equal:**Whether or not the variances are equal between the two groups.**conf.level:**The confidence level to use for the test.

In our example above, we used the following assumptions:

- We used a two-sided alternative hypothesis.
- We tested whether or not the true difference in means was equal to zero.
- We used a two sample t-test, not a paired t-test.
- We didn’t make the assumption that the variances were equal between the groups.
- We used a 95% confidence level.

Feel free to change any of these arguments when you conduct your own t-test, depending on the particular test you want to perform.

**Additional Resources**

An Introduction to the Two Sample t-test

Two Sample t-test Calculator