Hypothesis Testing and the Statistics T-Test

The t-test is probably the most commonly used Statistical Data Analysis procedure for hypothesis testing.

Actually, there are several kinds of t-tests, but the most common is the "two-sample t-test" also known as the "Student's t-test" or the "independent samples t-test".

T-Test Example

The two sample t-test simply tests whether or not two independent populations have different mean values on some measure.

For example, we might have a research hypothesis that rich people have a different quality of life than poor people. We give a questionnaire that measures quality of life to a random sample of rich people and a random sample of poor people. The null hypothesis, which is assumed to be true until proven wrong, is that there is really no difference between these two populations.

We gather some sample data and observe that the two groups have different average scores. But does this represent a real difference between the two populations, or just a chance difference in our samples?

T-Test Statistic

The statistics t-test allows us to answer this question by using the t-test statistic to determine a p-value that indicates how likely we could have gotten these results by chance. By convention, if there is a less than 5% chance of getting the observed differences by chance, we reject the null hypothesis and say we found a statistically significant difference between the two groups. See Statistical Data Analysis for more information about hypothesis testing.