2.(15 points) A research was interested in testing the effects of caffeine on word recall. For the study the researcher recruited 24 males and 24 females. Within each gender, 6 participants were randomly assigned to one of 4 doses of caffeine, either a placebo, 1 cup of coffee, 2 cups of coffee or 3 cups of coffee. So we end with a 2(gender) x 4(Caffeine) design with 6 people in a group. The data for the study is listed below.

Females Males

Placebo 1 cup 2 cups 3 cups Placeb 1 cup 2 cups 3 cups

6.50 7.40 8.00 7.5 7.10 7.40 8.20 13.20

7.30 6.80 7.70 7.90 7.90 8.10 8.50 13.50

6.60 6.70 7.10 6.90 8.20 8.20 9.50 14.50

7.40 7.30 7.60 7.80 7.70 8.00 8.70 16.70

7.20 7.60 6.60 6.70 7.50 7.60 9.60 14.60

6.80 7.40 7.20 7.30 7.60 8.00 9.40 14.40

1. Copy and paste the analysis of variance below here.

1. What number is the average variance for all the 8 groups?_________
2. What number is the variance among the gender main effect means? _______

c) What number is the variance among the main effect means of dose.________

d) What number is the variance among the 8 group means that remains after we subtract the variance due to the main effects of Gender and Dose?_________

e) how many df are in any one group (cell)?________

f) what number is the denominator for all of the F tests? ______

A=Dose, B=gender

s²_{main effect dose} = (a-1)(MSa-MSe)/nab

• s²_{main effects of gender} = (b-1)(MSb-MSe)/nab
• s²_{interaction d x gender}= (a-1)(b-1)(MSab-MSe)/nab

• s²_total = s²_A + s²_B + s²_AB + s²_e

g) Report the Omega squared for the Main effect of Gender

h) Report the Omega squared for the Main effect of Dose

i) Report the omega squared for the interaction of gender and Dose

j) Report the Cohen ffor the Main effect of gender

k) Report the Cohen f for the Main effect of Dose

l) Report the Cohen f for the interaction of gender and Dose

m) Copy and paste the output for the test of homogeneity of variance below,--Do you have heterogeneity of variance? Why or why not?