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4. The Paired t-Test (A.K.A. Dependent Samples t-Test, or t-Test for Correlated Groups)
When to use the paired t-test
In many research designs, it is helpful to measure the same people more than once. A common example is testing for performance improvements (or decrements) over time. However, in any circumstance where multiple measurements are made on the same person (or “experimental unit”), it may be useful to observe if there are mean differences between these measurements. The paired t-test will show whether the differences observed in the 2 measures will be found reliably in repeated samples.
Example 4.1
In this next example, we will look at the throwing distance for junior varsity javelin toss (in meters). Five players are selected at random from the entire league. We are interested in the following research question: Do players improve on their distance between the pre and post season? The average throwing distance, in both pre and post season, is recorded in columns 1 and 2 below for each of 5 people (P1-P5):
Unlike the independent samples t-test, on each row the numbers in columns 2 and 3 come from the same people. Person 1, for example, threw an average of 1 meter pre-season, but improved to an average of 2 meters in the post-season (after all competition was completed). It appears that this player may have improved through practice. How can we find if the league has improved overall from the pre to the post season?
The paired t-test will allow us to see if the improvement that we see in this sample is reliable. If we selected another 5 players at random from the league, would we still see an improvement? Without having to go through the trouble and expense of repeated sampling (called replication), we can estimate whether the difference in the 2 means is so large in magnitude that we would likely find the same result if we chose another 5 persons.
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