# Zach’s facts

Zach’s facts have been extracted from the book to remind you of the key concepts you and Zach have learned in each chapter.

Zach's Facts 15.1  The independent t-test

• The independent t-test compares two means, when those means have come from different groups of entities.

• It is a special case of the linear model in which an outcome variable is predicted from membership of two groups, and these groups are dummy-coded. (That is, one group is represented by the number 0 and the other by the number 1.)

• The b for the predictor variable represents the difference between the two group means.

• The t-statistic, like in any linear model, tests whether the b is different from 0. In this special case, that means it tests whether the difference between group means is zero.

• If the p-value for t is less than 0.05 then we assume that the differences between means is ‘significant’.

Zach's Facts 15.2 Paired-samples t-test

• The paired-samples t-test compares two means, when those means have come from the same entities.

• The logic behind the t-statistic is the same as for the independent t-test, except that we apply it to the differences between scores rather than the scores themselves.

• The paired-samples t-test, therefore, tests whether the mean difference between scores is significantly different from zero.

• The t itself is the mean difference divided by its standard error. It’s a signal-to-noise ratio: it shows how big the mean difference score is relative to how variable mean differences can be across samples (the standard error).

• If the p-value for t is less than 0.05 then we assume that the differences between means is ‘significant’.