A2. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Survey or PSS) of three groups of people: nonsmokers, smokers, and people who recently quit smoking. Using the following data for PSS scores, do a one-way ANOVA to test the hypothesis that the population means are equal:

Nonsmokers Smokers Quitters 19 26 37 23 29 32 17 22 27 20 30 41 26 23 38 Analysis of variance can be used in a variety of circumstances. A one-way ANOVA is used to compare means for three or more independent groups.

A multifactor ANOVA is used when there are two or more independent variables, called factors in this context. The most common multifactor ANOVA is a two-way ANOVA. Multifactor ANOVA tests for both main effects (i.e., the effects of the independent variables on the dependent variable) and interaction effects (i.e., the effects of the independent variables in combination).

Repeated measures analysis of variance (RMANOVA) is used for within-subjects designs, when means are computed for the same people three or more times. Additional assumptions for RM-ANOVA include compound symmetry and sphericity. These assumptions are usually tested with Mauchly’s test for sphericity. Adjustments to degrees of freedom are used when sphericity is violated.

If an ANOVA yields a significant F, multiple comparison procedures (post hoc tests) must be performed to determine the nature of the relationship between the independent and dependent variable. There are several alternative procedures, such as Tukey’s HSD test and Fisher’s LSD test

(the protected t test), that help to identify the group differences that contributed to the significant F statistic. An effect size statistic called eta-squared (h 2

) can be computed to estimate the strength of the relationship between the independent and dependent variables in ANOVA. This statistic indicates the proportion of variability in a dependent variable accounted for by the independent variable.

Eta-squared is used as the estimate of effect size in power analyses for an ANOVA situation.

What are the means for the three groups? Compute the sums of squares, degrees of freedom, and mean squares for these data. What is the value of F? Using an alpha of .05, is the F statistically significant?