Question 1
A two-way ANOVA model was used to analyze an experiment with two levels of one factor, three levels of a second factor, and 6 observations per treatment combination.
(a) For each of the main effects and the interaction, give the degrees of freedom for the corresponding F statistic.
(b) Using Table E or statistical software, find the value that each of these F statistics must exceed for the result to be significant at the 5% level.
(c) Answer part (b) for the 1% level.
Question 2
Ile Chapin Social Insight Test measures how well people can appraise others and predict what they may say or do. A study administered this test to different groups of people and compared the mean scores. (This exercise is based on results reported in H. G. Gough, The Chapin Social Insight Test, Consulting Psychologists Press, 1968.) Some of the results are given in the table below. Means for males and females who were psychology graduate students (PG) and liberal arts undergraduates (LU) are presented. The two factors are labeled Gender and Group.
|
|
Group
|
|
Gender
|
PG
|
LU
|
|
Males
|
27.56
|
25.34
|
|
Females
|
29.25
|
24.94
|
Plot the means and describe the essential features of the data in terms of main effects and interactions.
Question 3
A partial ANOVA for the data above is given below:
(a) There were 150 individuals tested in each of the groups. Fill in the missing values in the ANOVA table.
(b) What is the value of the F statistic to test the null hypothesis that there is no interaction? What is its distribution when the null hypothesis is true? Using Table E, find an approximate P-value for this test.
(c) Answer the questions in part (b) for the main effect of Gender and the main effect of Group.
(d) What is s?„ the within-group variance? What is sp?