# Complete Guide: How to Interpret t-test Results in R

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:

H0: µ1 = µ2 (the two population means are equal)

HA: µ1 ≠µ2 (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.