ExplanationPaired or Independent t-test?
There are two types of t-test, the paired t-test and the independent t-test. This page tells you how to pick the right one for your data.
We have already seen that when comparing two samples, it is important to know whether or not the samples are paired. The section on experimental design covers this in more detail, but here is a quick recap:
- With paired (dependent) samples, it is possible to take each measurement in one sample and pair it sensibly with one measurement in the other sample. This might be because measurements were taken from the same group twice (repeated measures) or because there is some other way to join measurements, for example, comparing the IQ of older and younger brothers;
- With independent samples, there is no sensible way to pair off the measurements.
One of the reasons that you need to identify the type of experimental design that you are dealing with is that you need to use the right t-test for the right design:
That's easy enough.
- The paired t-test is used when you have a paired design
- The independent t-test is used when you have an independent design
The other thing you need to decide at this point is easy to decide, but can be slightly harder to understand. You need to decide which of the following types of effect you expect to find:
You will see this choice referred to in literature and textbooks as the number of tails of the test. The tail is the extreme end of the distribution of the data and your experiment can be one of two types:
- The first mean to be larger than the second
- The first mean to be smaller than the second
- The first mean to be different from the second in either direction
If you have stated your experimental hypothesis with care, it will tell you which type of effect you are looking for. For example, the hypothesis that "Coffee improves memory" is one tailed because you expect an improvement. The hypothesis, "Men weigh a different amount from women" suggests a two tailed test as no direction is implied. So remember, don't be vague with your hypothesis if you are looking for a specific effect! Be careful with the null hypothesis too - avoid "A does not effect B" if you really mean "A does not improve B".
- One tailed tests expect the effect to be in a certain direction, so the first two points above are examples of 1 tailed experiments
- Two tailed tests are used when you have no idea which sample will be larger than the other, but you are looking for any difference. The third point above is such a case.
Level 3 of this topic explains why you need to make this choice. The pages on interpreting t values explain what practical effects the choice has on the results of a t-test.