2. For an independent measures design, the variability within treatments is the appropriate error term. For repeated measures, however, you must subtract individual differences from the variability within treatments to obtain a measure of experimental error.
4. a. k = 4 b. n = 13 subjects.
6. The null hypothesis states that the mean number of errors does not change across sessions, Ho: mu-1 = mu-2 = mu-3 = mu-4. The critical value is 4.76.
Source SS df MS ___________________________________________________________________ Between Treatments 18 3 6.00 F(3,6) = 8.96 Within Treatments 12 8 Between Subjects 8 2 Error 4 6 0.67 Total 30 11
Reject Ho and conclude that there is a significant practice effect.
8. a. The null hypothesis states that there is no difference between treatments, Ho: u-1 = u-2. For an independent-measures design, the critical value is 4.26.
Source SS df MS _____________________________________________________________________ Between Treatments 8 2 4 F(2,9) = 1.06 Within Treatments 34 9 3.78 Total 42 11
Fail to reject Ho. There are no significant differences with the independent ANOVA.
b. The null hypothesis states that there is no difference between treatments, Ho: mu-1 = mu-2. For a repeated-measures design, the critical value is 5.14.
Source SS df MS ___________________________________________________________________ Between Treatments 8 2 4 F(2,6) = 5.97 Within Treatments 34 9 Between Subjects 30 3 Error 4 6 0.67 Total 42 11
c. The repeated measures design removes error variability due to individual differences and therefore is more likely to detect a treatment effect.
10. a. First mean is equal 3, second mean is equal to 5, and third mean is equal to 1.
b. The null hypothesis states that the position in the list has no effect on the number of errors, Ho, mu-1 = mu-2 = mu-3. The critical value is 5.14.
Source SS df MS ___________________________________________________________________ Between Treatments 32 2 6 F(2,10) = 8.00 Within Treatments 24 9 Between Subjects 12 3 Error 12 6 2 Total 56 11
Reject Ho and conclude that the number of errors differes significantly with the position in the list. Most errors are made in the middle of the list, with fewer errors at the beginning, and fewest errors on the last items in the list.
12. a. The null hypothesis states that there is no difference between the two treatments, Ho: mu-D = 0. The critical region consists of t values beyond plus/minus 3.182. The mean difference is +4. SS for the difference scores is 48, and t(3) = 2.00. Faile to reject Ho.
b. The null hypothesis states that there is no difference between treatments, Ho: mu-1 = mu-2. The critical value is F = 10.13.
Source SS df MS ___________________________________________________________________ Between Treatments 32 1 32 F(1,3) = 4.00 Within Treatments 36 6 Between Subjects 12 3 Error 24 3 8 Total 68 7
Fail to reject Ho. Note that F = t-squared.
14. a. k = 3
b. n = 15
16. Answer found below
Source SS df MS ___________________________________________________________________ Between Treatments 48 2 24 F(2,28) = 8.00 Within Treatments 120 42 Between Subjects 36 14 Error 84 28 3 Total 168 44
18. Answer below
Source SS df MS ___________________________________________________________________ Between Treatments 270 3 90 F = 9.00 Within Treatments 410 28 Between Subjects 200 7 Error 210 21 10 Total 680 31
20. a. Means are 6, 4, and 2.
b. The null hypothesis states that there is no change in motivation across the three grade levels, Ho: mu-1 = mu-2 = mu-3. The critical value is 4.46.
Source SS df MS ___________________________________________________________________ Between Treatments 40.00 2 20 F(2,8) = 0.79 Within Treatments 240.00 12 Between Subjects 37.33 4 Error 202.67 8 25.33 Total 280.00 14
Fail to reject Ho. There are no significant differences among the three grade levels.
c. The date in problem 9 have substantially more variability within treatments which increases the error variability. As a result, the sample mean differences are not significant.
22. The null hypothesis states that there are no differences in adaptation among the four regions, Ho: mu-1 = mu-2 = mu-3 = mu-4. The critical value is 8.65.
Source SS df MS ___________________________________________________________________ Between Treatments 225.96 3 75.32 F(3,18) = 215.20 Within Treatments 20.22 24 Between Subjects 13.91 6 Error 3.31 18 0.35 Total 246.19 27