### When would I use an independent samples t-test?

### When is it useful?

An independent samples t-test is the most useful when you are comparing two separate groups (based on something you've measured about them). Here are some examples of research designs for which an independent samples t-test might be appropriate:

- You want to know which of two potting soils results in the tallest tomato plants. You do an experiment, planting tomatoe seeds in each kind of soil and measuring the heights of the resulting plants.
- You want to compare the average family size of U.S. Catholics and U.S. Mormons. You survey a random sample of Catholics and Mormons, and ask them the size of their families.
- You want to compare the average income of men and women employed by small businesses in the intermountain west. You survey a random sample of men and women in your target population and ask their income.

The design of an independent samples t-test includes one categorical independent variable with two levels (that is, two samples distinguished by something like gender, treatment group, etc.), and one continuous dependent variable (that is, something measured about each sample, such as test scores, number of sick days, plant height, etc.).

Perhaps a different statistical test will suit your needs better. Some options might include:

- Paired samples t-test (often used for pre-post comparisons)
- One-way ANOVA (for when you have more than two groups)

Return to the home page for more options.

### How does an independent samples t-test work?

The independent samples t-test is a hypothesis test. The null hypothesis is usually that the samples means are the same — that is, the true difference between means is zero. The independent samples t-test gives you the likelihood of getting your sample means if this hypothesis is true.

In other words, when we perform an independent samples t-test, we are asking: "How likely are we to observe the difference we see between Sample A and Sample B, if the true means of Population A and Population B are really the same?" Another way of putting it is, "What is the likelihood that the differences between my sample means are due purely to random sampling variation, rather than due to differences in the underlying population they represent?"

If the likelihood is very small, you can make an argument that the means of the two populations are probably different (this is what it means to "reject the null hypothesis"). This does not mean that we know for certain that the means of the two underlying populations are different — it just means that if they were the same, our data would be very rare or anamolous.

Here are some resources that might help:

- Resource #1
- Resource #2