Chapter 6: Testing Hypotheses About Two Dependent Means

The previous chapters have addressed several issues about samples, means, and standard errors, with the intent to explain the data. It has been pointed out that all differ and that depending on the sample you may get different answers. This chapter will explore these differences based on two dependent means because the real issue is, how much do they differ ? How can you decide whether a difference in sample means can be attributed to their natural variability or to a real difference between groups in the population? And what is significant?

OVERVIEW

Consider another example of testing a hypothesis. We want to see if a difference exists in the average of two groups. When we do a comparison of two groups, we must also be cognizant of the intervening variable(s). An intervening variable is a variable that may explain the difference between the two groups. If that is the case we can minimize this problem by restricting the comparison of that particular variable for that group . By doing that restriction we will no longer affect the comparison as much. As a consequence, the results will be much easier to interpret.

In this case, the null hypothesis is that the groups have the same average. On the other hand, the hypothesis of interest (sometimes called the alternative hypothesis ) is that the average of the two groups is not the same. The groups differ.