Statistical Methods for Psychology

groups—the data were actually drawn from a normally distributed population. With real

data, however, it is important to examine these distributions first to make sure that they are

not seriously skewed or bimodal and, even more important, that they are not skewed in dif-

ferent directions. Even for this example, it is useful to examine the individual group vari-

ances as a check on the assumption of homogeneity of variance. Although the variances are

not as similar as we might like (the variance for Imagery is noticeably larger than the oth-

ers), they do not appear to be so drastically different as to cause concern. As we will see

later, the analysis of variance is robust against violations of assumptions, especially when

we have the same number of observations in each group.

Table 11.3 shows the calculations required to perform a one-way analysis of variance.

These calculations require some elaboration.

Section 11.4 Calculations in the Analysis of Variance 325

20

15

10

5

Counting Rhyming Adjective Imagery Intention

Table 11.3 Computations for Data in Table 11.2

Summary Table

Source df SS MS F

Treatments 4 351.52 87.88 9.08
Error 45 435.30 9.67

Total 49 786.82

SSerror=SStotal 2 SStreat=786.82 2 351.52=435.30

=10(35.152)=351.52

SStreat=na(Xj 2 X..)^2 =10((7 2 10.06)^21 (6.90 2 10.06)^21... 1 (12 2 10.06)^2 )

=786.82

SStotal= a(Xij 2 X..)^2 =(9 2 10.06)^21 (8 2 10.06)^21... 1 (11 2 10.06)^2

Figure 11.2 Boxplot of Eysenck’s data on recall as a function of level of processing