Prism offers seven related tests that compare two groups. To choose among these tests, answer three questions in the Experimental Design tab of the t test parameters dialog:

Experimental design: unpaired or paired

Choose a paired test when the columns of data are matched. That means that values on the same row are related to each other.

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.

Distribution assumption

Many statistical analyses have certain assumptions about the populations from which the data being analyzed were sampled. One of the common assumptions that tests will make will relate to the distributions of these populations from which the data were sampled. Prism offers three choices:

1.Normal (Gaussian) - assume sampling from a normal distribution. Compare the means of the groups

2.Lognormal - assume sampling from a lognormal distribution. Compare the geometric means of the groups

3.Nonparametric - do not assume that the data were sampled from a specific distribution. Instead, use a nonparametric tests. This often equates to comparing the ranks of the data within the groups

The choice to assume sampling from a lognormal distribution as an explicit choice was introduced with Prism version 10.5, and introduces lognormal variants of the unpaired t test and Welch's t test. The ratio paired t test also assumes sampling from a lognormal distribution, but was available in earlier versions of Prism.

Nonparametric tests are not based on the assumption that the data are sampled from a Gaussian distribution (or any other specific distribution for that matter). This may make them seem more desirable. However, nonparametric tests have less power. Deciding when to use a nonparametric test is not straightforward.

Choose test

After defining the experimental design, and specifying the distribution assumption for the sampled data, you need to decide exactly what test you want Prism to perform.

Unpaired, normal (Gaussian) distribution

Prism offers two choices:

1.Welch's t test. This test does not assume that the variances (standard deviations) of the two populations from which the data were sampled are equal.

2.Unpaired t test. This test does assume that the variances (standard deviations) of the two populations from which the data were sampled are equal.

Many statisticians recommend using Welch's t test as a default over the Unpaired t test as it performs well when variances are equal, and provides greater protection against type I errors when variances are unequal. More importantly, the equal variances assumption is often violated in real-world data.

Paired, normal (Gaussian) distribution

For this experimental design and distribution assumption, there is only one choice. The paired t test is standard in this case, and should be used when you expect the differences between paired values to be a consistent measure of treatment effect. If you expect the ratio of paired values to be a consistent measure of treatment effect, then it's quite possible that your data are actually sampled from a lognormal distribution and you should choose the ratio paired t test.

Unpaired, lognormal distribution

Prism offers two choices:

1.Lognormal Welch's t test. This test does not assume that the geometric standard deviations of the populations are the same

2.Lognormal t test. This test does assume that the two populations from which the data were sampled have the same geometric standard deviation.

As with their normal (Gaussian) counterparts, Prism recommends using the Lognormal Welch's t test as a default when assuming sampling from a lognormal distribution. The arguments for its use over the lognormal t test are the same with respect to its protection against type I errors when geometric standard deviations are unequal, and reasonable performance when the geometric standard deviations are equal.

Paired, lognormal distribution

For this experimental design and distribution assumption, there is only one choice. The ratio paired t test is standard in this case, and should be used when you expect the ratio of paired differences to be a consistent measure of treatment effect.

Unpaired, nonparametric test

Prism offers two choices: The Mann-Whitney test and the Kolmogorov-Smirnov test. It is hard to offer guidelines for choosing one test vs. the other except to follow the tradition of your lab or field. The main difference is that the Mann-Whitney test has more power to detect a difference in the median, but the Kolmogorov-Smirnov test has more power to detect differences in the shapes of the distributions.

Paired, nonparametric test

In this case there is only one choice. Prism will perform the Wilcoxon matched-pairs signed rank test.