Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 12.4 | Examples of Hypothesis Testing and Effect Size with ANOVA 387
df 5 2, 15
FIGURE 12.8
The distributions of F-ratios with df = 2, 15.
The critical boundary for α = .05 is 3.68.
1 2 3 4
3.68
STEP 3
Compute the F-ratio. The series of calculations for computing F is presented in Figure
12.4 and can be summarized as follows:
a. Analyze the SS to obtain SS between
and SS within
.
b. Use the SS values and the df values (from step 2) to calculate the two variances,
MS between
and MS within
.
c. Finally, use the two MS values (variances) to compute the F-ratio.
Analysis of SS. First, we compute the total SS and then the two components, as indicated
in Figure 12.5.
SS total
is simply the SS for the total set of N = 18 scores.
SS total
5SX 2 2 G2
N
= 1324 – 1152
= 172
SS within
combines the SS values from inside each of the treatment conditions.
SS within
= ΣSS inside each treatment
= 24 + 34 + 30 = 88
SS between
measures the differences among the three treatment means (or treatment totals).
Because we have already calculated SS total
and SS within
, the simplest way to obtain SS between
is
by subtraction (Equation 12.5).
SS between
= SS total
– SS within
= 172 – 88
= 84