Choosing a t test

The t test analysis compares the means (or medians) of two groups. If your goal is to compare the mean (or median) of one group with a hypothetical value, use the column statistics analysis instead.

Prism offers five related tests that compare two groups. To choose among these tests, answer three questions:

Are the data paired?

Choose a paired test when the columns of data are matched. Here are some examples:

•	You measure a variable in each subject before and after an intervention.

•	You recruit subjects as pairs, matched for variables such as age, ethnic group, and disease severity. One of the pair gets one treatment; the other gets an alternative treatment.

•	You run a laboratory experiment several times, each time with a control and treated preparation handled in parallel.

•	You measure a variable in twins or child/parent pairs.

Matching should be determined by the experimental design, and definitely should not be based on the variable you are comparing. If you are comparing blood pressures in two groups, it is OK to match based on age or postal code, but it is not OK to match based on blood pressure.

Nonparametric test?

Nonparametric tests, unlike t tests, are not based on the assumption that the data are sampled from a Gaussian distribution. But nonparametric tests have less power, and report only P values but not confidence intervals. Deciding when to use a nonparametric test is not straightforward.

Equal variances?

If your data are not paired and you are not choosing a nonparametric test, you must decide whether to accept the assumption that the two samples come from populations with the same standard deviations (same variances). This is a standard assumption, and you should accept it unless you have good reason not to. If you check the option for Welch's correction, the analysis will not assume equal variances (but will have less power).

Summary of tests

Test	Paired?	Nonparametric?	Welch correction?
Unpaired t	No	No	No
Welch's t	No	No	Yes
Paired t	Yes	No	N/A
Mann-Whitney	No	Yes	N/A
Wilcoxon matched pairs	Yes	Yes	N/A