1. 1. What are the assumptions of a correlated-groups t-test?
Solution
Level of measurement. The criterion variable should be assessed on an interval-or
ratio-level of measurement. The predictor variable should be a nominal-level variable that
includes just two categories (i.e., two groups). Independent observations. A given observation
should not be dependent on any other observation in either group. In an experiment, you
normally achieve this by drawing a sample and randomly assigning each participant to only one
of the two treatment conditions. This assumption would be violated if a given participant
contributed scores on the criterion variable under both treatment conditions. The independence
assumption is also violated when one participant’s behavior influences another’s behavior within
the same condition. For example, if participants are given experimental instructions in groups of
five and are allowed to interact in the course of providing scores on the criterion variable, it is
likely that their scores will not be independent. That is, each participant score is likely to be
affected by the others in that group. In these situations, scores from participants constituting a
given group of five should be averaged and these average scores should constitute the unit of
analysis. None of the tests discussed in this text are robust against violations of the independence
assumption. Random sampling. Scores on the criterion variable should represent a random
sample drawn from the populations of interest. Normal distributions. The distribution of
observed values for all continuous variables should approximate normal distributions.
Homogeneity of variance. To use the equal-variances t test, you should draw the samples from
populations with equal variances on the criterion. If the null hypothesis of equal population
variances is rejected, you should use the unequal-variances t test.