Influence t test

The influence t test compares mean value of a measure in a group with overall mean value for the measure.

The group might be a category or combination of categories. Considering the significance value and effect size, the test identifies influential groups.

The influence t test uses pooled standard deviation estimate that is obtained by combining the measure variation within all the groups. Pooled standard deviation is in turn divided by the square root of the number of rows in the group to obtain the standard error of the group mean. Corresponding t-statistic is computed as the difference between the group mean and the overall mean that is divided by the group standard error.

The t-statistic value is compared to a theoretical t distribution with degrees of freedom equal to the number of rows that are reduced by the number of groups to determine the probability of obtaining the t-statistic value by chance.

This probability is the significance value.
If the significance value after a Bonferroni adjustment is less than the significance level, the group is judged to be influential. The Bonferroni adjustment is necessary because multiple t tests are conducted, one for each group.

The top group has the greatest difference when compared to the expected frequency. The top high group is the group with frequencies that are greater than the expected frequencies. The top low group is the group with frequencies that are less than the expected frequency.

The effect size is influential category strength. It is computed as absolute value of t-statistic divided by the square root of the group count. Meaningful differences highlight the categories with the highest effect size.