Tips for Success

These study tips are designed to clarify key points and help you to avoid errors that students commonly make. Review the Tips for Success as you study each chapter and review them again after you have studied each chapter.

1. Be sure that you fully understand the difference between S² and S²M.
• Although these terms look similar, they are quite different: S² is the estimated variance of the population of individuals, and S²_m is the estimated variance of the distribution of means (based on the estimated variance of the population of individuals, S²).
2. Be careful. To find the variance of a distribution of means, you always divide the population variance by the sample size. This is true whether the population’s variance is known or only estimated. It is only when making the estimate of the population variance that you divide by the sample size minus 1. That is, the degrees of freedom are used only when estimating the variance of the population of individuals
3. As in previous chapters, population 2 is the population consistent with the null hypothesis being true.
4. You now have to deal with some rather complex terms, such as the standard deviation of the distribution of means of difference scores. Although these terms are complex, there is good logic behind them. The best way to understand the terms is to break them down into manageable pieces. For example, you will notice that these new terms are the same as the terms for the t test for a single sample, with the added phrase “of difference scores”. This phase has been added, as all of the figuring for the t test for dependent means uses difference scores
5. Step 2 (page 251) of hypothesis testing is very long for the t test for dependent means and it is easy to lose track of the purpose of that step. Step 2 of hypothesis testing determines the characteristics of the comparison distribution. In the case of the t test for dependent means, this comparison distribution is a distribution of means of difference scores. The key characteristics of this distribution are its mean (μ, which is assumed to equal 0), its standard deviation (which is estimated as S_M), and its shape (a t distribution with degrees of freedom equal to the sample size minus 1).
6. Recall from Chapter 6 that power can be expressed as a probability (such as .71) or as a percentage (such as 71%). Power is expressed as a probability in Table 7-9 (page 260) in the text (as well as in power tables in later chapters.