1The following data represent the results from an independent-measures study comparing three treatments.
Treatment
I II III
n = 10 n = 10 n = 10
M = 2 M = 3 M = 7
T = 20 T = 30 T = 70
a. Compute SS for the set of 3 treatment means. (Use the three means as a set of n =3 scores and compute SS.)
b. Using the result from part a, compute n(SSmeans). Note that this value is equal to SSbetween.
c. Now, compute SSbetween with the computational formula using the T values.
2 The following data summarize the results from an independent-measures study comparing three treatment conditions.
Treatment
I II III
n = 6 n = 6 n = 6
M = 4 M = 5 M = 6 N = 18
T = 24 T = 30 T = 36 G = 90
SS =30 SS =35 SS =40 ∑X2 = 567
a. Before you begin any calculations, predict how the change in the data should influence the outcome of the analysis. That is, how will the F-ratio and the value of η2 for these data compare with the values obtained in problem 7? (Problem 7’s values are F(2,15) = 6.0 and η2 = 0.444)
b. Use an ANOVA with α = 0.05 to determine whether there are any significant differences among the three treatment means. (Does your answer agree with your prediction in part a?)
Does your answer agree with your prediction in part a?
c. Calculate η2 to measure the effect size for this study.
Does your answer agree with your prediction in part a?
3 The following data summarize the results from an independent-measures study comparing three treatment conditions.
Describe how these sample variances compare with those from problem 9.
b. Predict how the increase in sample variance should influence the outcome of the analysis.
c. Use an ANOVA with α = 0.05 to determine whether there are any significant differences among the three treatment means.
4 A researcher reports an F-ratio with df = 3, 36 from an independent-measures research study.
a. How many treatment conditions were compared in the study?
b. What was the total number of participants in the study?
5 A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n = 10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all. The dependent variable is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: start in the df column.)
6 The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with α = 0.05 to determine whether there are any significant mean differences among the treatments.
Treatment
I II III
2 5 7 N = 14
5 2 3 G = 42
0 1 6 ∑X2 = 182
1 2 4
2
2
T = 12 T = 10 T = 20
SS = 14 SS = 9 SS = 10
7 The structure of a two-factor study can be presented as a matrix with levels of one factor determining the rows and the levels of the second factor determining the columns. With this structure in mind, describe the mean differences that are evaluated by each of the three hypothesis tests that make-up a two-factor ANOVA.
8 For the data in the following matrix:
No Treatment Treatment
Male M = 5 M = 3 Overall M = 4
Female M = 9 M = 13 Overall M = 11
Overall M = 7 Overall M = 8
a. Describe the mean difference that is the main effect for the treatment.
b. Describe the mean difference that is the main effect for the gender.
c. Is there an interaction between gender and treatment? Explain your answer.