ABSTRACT
This chapter covers how to determine whether there is a statistically significant difference between the central tendencies of two samples. The broad type of test depends upon whether the data are matched or unmatched. For normally distributed data statisticians use a t test, and for non-normal or ordinal data they use a Mann-Whitney U test. Large standard deviations make it less likely that a statistically significant difference between means will be found because they imply that there is a lot of variability that is not accounted for by membership of the categories. Many statistical computer programs use the full formula. In all cases, it is the probability which is the important figure for the interpretation of the results, but always records the degrees of freedom and the test statistic as well. There are several versions of the formula for calculating the t statistic, most of which are user-friendly approximations of a quite complex-looking fuller formula.
