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

396 CHAPTER 12 | Introduction to Analysis of Variance
freedom between treatments. Therefore, df between
= 3 – 1 = 2, and the MS between treatments
is
MS between
5 SS between
df between
5 3 2 5 1.5
Finally, the Scheffé procedure uses the error term from the overall ANOVA to compute the
F-ratio. In this case, MS within
= 5.87 with df within
= 15. Thus, the Scheffé test produces an
F-ratio of
F 5 MS between
MS within
5 1.5
5.87 5 0.26
With df = 2, 15 and α = .05, the critical value for F is 3.68 (see Table B.4). Therefore,
our obtained F-ratio is not in the critical region, and we conclude that these data show no
significant difference between treatment B and treatment C.
The second largest mean difference involves treatment A (T = 30) vs. treatment B (T =
54). This time the data produce SS between
= 48, MS between
= 24, and F(2, 15) = 4.09 (check
the calculations for yourself). Once again the critical value for F is 3.68, so we conclude
that there is a significant difference between treatment A and treatment B.
The final comparison is treatment A (M = 5) vs. treatment C (M = 10). We have already
found that the 4-point mean difference between A and B is significant, so the 5-point difference
between A and C also must be significant. Thus, the Scheffé posttest indicates
that both B and C (answering prepared questions and creating and answering your own
questions) are significantly different from treatment A (simply rereading), but there is no
significant difference between B and C.
■
In this case, the two post-test procedures, Tukey’s HSD and Scheffé, produce exactly
the same results. You should be aware, however, that there are situations in which
Tukey’s test will find a significant difference but Scheffé will not. Again, the Scheffé
test is one of the safest of the posttest techniques because it provides the greatest protection
from Type I errors. To provide this protection, the Scheffé test simply requires
a larger difference between sample means before you may conclude that the difference
is significant.
LEARNING CHECK
1. Under what circumstances are posttests necessary?
a. reject the null hypothesis with k = 2 treatments.
b. reject the null hypothesis with k > 2 treatments.
c. fail to reject the null hypothesis with k = 2 treatments.
d. fail to reject the null hypothesis with k > 2 treatments.
2. Which of the following accurately describes the purpose of posttests?
a. They determine which treatments are different.
b. They determine how much difference there is between treatments.
c. They determine whether a Type I Error was made in the ANOVA.
d. They determine whether a complete ANOVA is justified.