2. Both the F-ratio and the t statistic are comparing the actual mean difference between samples (numerator) with the difference that would be expected from chance factors such as experimental error (denominator). If the numerator is sufficiently bigger than the denominator, we conclude that there is a significant difference between treatments.
4. With 3 or more treatment conditions you need 2 or more t tests to evaluate all of the mean differences. Each test involves a risk of a Type I error. The more tests you do the more risk there is of a Type I error. The ANOVA performs all of the tests simultaneously with a single, fixed alpha level.
6. a. There is n difference between treatments: Both have T = 8 and Mean = 2. MS-between should be zero.
b. F = 0
c. SS-between = 0 and MS-between = 0
8. a. The null hypothesis states that there are no differences among the treatments, Ho: mu-1, = mu-2 = mu-3. The critical value for alpha is 4.26.
Source SS df MS Between Treatments 56 2 28 F(2,9) = 7.0 Within Treatments 36 9 4 Total 92 11
Reject Ho and conclude that there are significant differences among the three treatments.
b. Tukey's HSD = 3.95. Treatments I and II are both significantly different from treatment III, but there is no significant difference between I and II.
10. a. The null hypothesis states that the size of discrepancy has no effect on attitude change, Ho: mu-1 = mu-2 = mu-3. The critical value of alpha (.01) is 6.36.
Source SS df MS Between Treatments 36 2 18 F(2,15) = 9.0 Within Treatments 30 15 4 Total 66 17
Reject Ho
b. The greatest change in attitude occurs when there is a moderate discrepancy between the persuasive argument and a person's original opinion.
12. a. The null hypothesis states that handedness has no effect on discrimination, Ho: mu-1 = mu-2 = mu-3. The critical value of alpha (.05) is 3.88.
Source SS df MS Between Treatments 30 2 15 F(2,12) = 15.00 Within Treatments 12 12 1 Total 42 14
Reject Ho and conclude that there are significant differences among the three groups.
b. Of the three samples the largest variance is for the righ-handed subjects (variance = 1.5) and the smallest is for the left-handed subjects (variance = 0.50). F-max = 3.00 which is not significant. The homogeneity assumption is satisfied.
14.
Source SS df MS Between Treatments 48 2 24 F(2,27) = 12.00 Within Treatments 54 27 2 Total 102 29
16.
Source SS df MS Between Treatments 30 3 10 F(3,20) = 5.00 Within Treatments 40 20 2 Total 70 23
18. The null hypothesis states that there are no differences among the three treatments, Ho: mu-1 = mu-2 = mu-3. The critical value for alpha (.05) is 3.88.
Source SS df MS Between Treatments 15 2 7.5 F(2,12) = 1.50 Within Treatments 60 12 5 Total 75 14
Fail to reject Ho. No evidence of any significant differences.
20. a. The means and SS values are:
Endormorph Ectomorph Mesomorph
Mean = 22.0 Mean = 17.6 Mean = 15.0
SS = 24.0 SS = 23.2 SS = 30.0
The null hypothesis states that there are no differences in personality among the three body types, Ho: mu-1 = mu-2 = mu-3. The critical value for alpha (.05) is 3.35. The analysis of variance produces,
Source SS df MS Between Treatments 125.2 2 62.6 F(2,12) = 9.74 Within Treatments 77.2 12 6.43 Total 202.4 14
Reject Ho and conclude that there significant differences in language development among the three groups.
22. The means and SS values are
Alphas Betas Gammas
Mean = 44.2 Mean = 47.1 Mean = 36.8
SS = 865.6 SS = 500.9 SS = 325.6
The null hypothesis states that there are no differences in health among the three groups, Ho: mu-1 = mu-2 = mu-3. The critical value for alpha (.05) is 3.35. The analysis of variances produces,
Source SS df MS Between Treatments 564.2 2 282.1 F(2,27) = 9.74 Within Treatments 1692.1 27 62.67 Total 2256.3 29
Reject Ho. There are significant differences among the three groups.
b. Beginning with the largest mean difference, the Scheffe test results are:
Betas versus Gammas: F(2,27) = 4.23 (significant). Alphas versus Gammas: F(2,27) = 2.18 (not significant) The only significant difference is between the Betas and the Gammas. The Alphas are an intermediate group, not significantly different from either extreme.