Does the black grease beneath football players€™ eyes really reduce glare or does it just make them look intimidating? In a variation of a study actually conducted at Yale University, 46 participants placed one of three substances below their eyes: black grease, black antiglare stickers, or petroleum jelly. The researchers assessed eye glare using a contrast chart for each participant that gives a value on a scale measure. Every participant was assessed with each of the three substances, one at a time. Black grease led to a reduction in glare compared with the two other conditions, antiglare stickers or petroleum jelly (DeBroff & Pahk, 2003).

a. What is the ind ependent variable? What are its levels?

b. What is the dependent variable?

c. What kind of ANOVA is this? 

d. What is the first assumption for ANOVA? Is it likely that the researchers met this assumption? Explain your answer. 

e. What is the second assumption for ANOVA? How could the researchers check to see if they had met this assumption? Be specific. 

f. What is the third assumption for ANOVA? How could the researchers check to see if they had met this assumption? Be specific.

g. What is the fourth assumption, specific to the within-groups ANOVA? What would the researchers need to do to ensure that they meet this assumption? 

h. Perform steps 5 and 6 of hypothesis testing. Be sure to complete the source table when calculating the F ratio for step 5. 

i. If appropriate, calculate the Tukey HSD for all possible mean comparisons. Find the critical value of q and make a decision regarding the null hypothesis for each of the mean comparisons. 

j. Calculate the R2 measure of effect size for this ANOVA. 

k. How could this study be conducted using a between-groups design?

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df Source SS MS A (rows) 0.267 0.267 0.004 B (columns) 3534.008 1767.004 24.432 5.371 2.686 0.037 AXB Within 1157.167 16 72.323 Total 4696.813 21 2.