ABSTRACT
In the previous chapter, we used inferential techniques with a single mean or proportion. We dealt with claims about a population mean, seeing how likely the claim was to be true given what we had found in our sample. We also covered confidence intervals, developing an interval within which we could confidently claim that the population mean is likely to fall. Notice that, in both of these procedures, we are dealing with only a single sample mean (or a single proportion). This chapter applies our inferential ideas to situations where we have more than one sample mean and are seeking to make claims about more than one population mean. For example, rather than stating where a
single population mean falls, we want to be able to say whether or not two population means differ significantly. Or we want to be able to say whether three or more population means differ significantly. To answer these questions, respectively, we use two additional inferential techniques: the difference-of-means test (or the t-test for short) and the analysis of variance (or ANOVA for short). Because we’ll be talking about differences among groups, you will see some similarities to the chi-square test. And just as the last two chapters were based on probability distributions (the chi-square distribution and the sampling distribution of sample means), in this chapter, we start with another sampling distribution.
