*t*-Tests

A *t* test is used either to compare the mean of a sample to the hypothesised mean for a population (e.g. comparing the body temperature of a group of people to an expected 37°C), or to compare the means from two samples (e.g. the weights of two populations of crab). *t* tests should not generally be used for multiple 2-way comparisons when there are more than two samples as this is the realm of ANOVA. A paired *t* test is the *t* test of two samples where there is some relationship between the two samples such that the data occur in pairs (e.g. measuring the hindlimb and forelimb on the same animal) and is therefore unlike the standard *t* test where there is no association between the order of the data in each sample. A multivariate *T ^{ 2}* test compares two samples based on a number of multivariate measures for each sample, or, for a single sample, compares the mean for each measure to a hypothesised mean.

statistiXL’s *t* test module provides for analysis of both univariate and multivariate samples. Both single and two sample tests are provided with the option of analysing paired samples in the univariate two sample test. A test for the equality of variances between samples can be performed in the univariate two sample test with the resulting measure of *t* adjusted appropriately.

Results are presented in tabular form. Descriptive statistics are provided, if this option is selected. The general *t* statistics that are provided are; hypothesised mean, actual mean, standard error of the mean, *t* value, degrees of freedom, and P value. If the variance test option is selected, then the variance is listed for each variable, the F value is given with degrees of freedom, and the P value is given. For multivariate t tests, the *T ^{ 2}* statistic and its degrees of freedom, the F statistic and its degrees of freedom, and the P value are given.

The help file included with statistiXL provides an overview of univariate and multivariate *t* tests, and gives examples including single sample *t* test, variance test, two-sample *t* test, paired *t* test, single sample multivariate *t* test, and two sample multivariate *t* test.