Contents

402 PART V: Analyzing and Reporting Researchsystematic variation in our experiments. One approach that is highly recommendedis the use of confidence intervals (see Chapter 11). Confidence intervalscan provide evidence for the pattern of population means estimated byour samples (see especially Box 11.5). Another technique is that of comparingtwo means. We first discuss an effect size measure for the independent groupsANOVA, as well as power analysis for this design, and then turn our attentionto comparisons of two means.Calculating Effect Size for Designs with Threeor More Independent GroupsWe mentioned earlier that the psychology literature contains many differentmeasures of effect magnitude, which depend on the particular research design,test statistic, and other peculiarities of the research situation (e.g., Cohen,1992; Kirk, 1996; Rosenthal & Rosnow, 1991). When we know one measure ofeffect magnitude, we usually can translate it to another, comparable measurewithout much difficulty. An important class of effect magnitude measures thatapplies to experiments with more than two groups is based on measures of“strength of association” (Kirk, 1996). What these measures have in commonis that they allow estimates of the proportion of total variance accounted forby the effect of the independent variable on the dependent variable. A popularstrength of association measure is eta squared, or 2 . It is easily calculatedKey Conceptbased on information found in the ANOVA Summary Table (Table 12.3) for theomnibus F-test (although many computer programs automatically provide etasquared as a measure of effect size). Eta squared is defined asIn our example (see Table 12.3),Sum of squares between groups_____________________________Total sum of squareseta squared ( 2 ) ________________ 54.55[(54.55) + (37.20)] .59Eta squared can also be computed directly from the F-ratio for the betweengroupseffect when the ANOVA table is not available (see Rosenthal & Rosnow,1991, p. 441):or, in our example,eta squared ( 2 ) eta squared ( 2 ) (F)(df effect)_______________________[(F)(df effect)] (df error)(7.80)(3)______________[(7.80)(3)] 16 .59Another measure, designed by J. Cohen, for designs with three or moreindependent groups is f (see Cohen, 1988). It is a standardized measure ofeffect size similar to d, which we saw was useful for assessing effect sizes ina two-group experiment. However, unlike d, which defines an effect in terms