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CHAPTER 12: Data Analysis and Interpretation: Part II. Tests of Statistical Significance and the Analysis Story 405FIGURE 12.1Means and 95% confidence intervals for the memory-training experiment.Mean Recall1614121086420Memory-Training ExperimentControl Story Imagery RhymesConditionsKey ConceptResults based on the construction of confidence intervals for the memory experimentare shown in Figure 12.1. You should be able by now to interpret theseresults, but see Box 11.5 in Chapter 11 if you need a refresher.A second approach makes use of NHST and focuses on a small set of twogroupcomparisons in order to specify the source of the overall effect of ourindependent variable. A comparison of two means allows the researcher tofocus on a particular difference of interest. These comparisons can be quitesophisticated, for example, comparing the average of two or more groups inan experiment with the mean of another group or the average of two or moreother groups. However, most of the time we will be interested in the differencebetween just two means that are represented by individual groups. Thesetwo-mean comparisons are usually made after we have determined that ouromnibus F-test is statistically significant.One approach for carrying out comparisons of two means is to use a t-test;however, there is a slight modification in the way that t is calculated whencomparing means in a multiple-group experiment. Specifically, we want to usea pooled variance estimate based on the within-group variation estimate (MS error )found in our omnibus F-test. That is, our variance estimate uses informationobtained from all the groups in our experiment, not just the two groups of interest.Therefore, the formula for this t-test is__Xt 1 _____________________ X 2 MS error n 1__ n 1__1 2The value for the MS error is obtained from the ANOVA Summary Table of ouromnibus F-test, and the degrees of freedom for our comparison t-test are thoseassociated with the MS error [or k(n 1), where k number of groups]. For example,the MS within groups (error) for the analysis reported in Table 12.3 is2.33 with 16 degrees of freedom [4(5 1) 16].