Question: A researcher is interested in whether ingroup favoritism varies as a function of task-type categorized participants into novel social groups and randomly assigned them to allocate monetary payment, bonus money, or feelings to an ingroup and outgroup member. The following table contains the responses of 30 participants and displays the amount of the resource each participant allocated to the ingroup member.

A one-factor ANOVA indicated that ingroup favoritism varied as a function of task-type, F(2, 27) = 23.54, p < .0001. The following questions pertain to further contrasts that the researcher might test to determine how task-type affects ingroup favoritism.(Summarize the results of each question using APA format and be sure to report all of the relevant inferential statistics and means).

a. Use Fisher’s Protected Test to determine whether (a) monetary payment task differs from the mean of the bonus and feelings tasks and (b) the bonus task differs from the feelings task.

b. Use Scheffe's method to test the contrasts in 4.a. and specify the appropriate critical value against which each contrast would be compared?

c. Assume the research planned a priori to test whether (a) payment differed from bonus and (b) payment differed from feelings. At what p-value would each contrast be considered significant according to the Bonferroni adjustment?

d. What adjusted test should the researcher use if s/he planned to test all pairwise comparisons. Tukey's Wholly Significant difference?

Use the latter adjusted test to test all pairwise comparisons and specify the appropriate critical against which each contrast would be compared?

e. For this question do not use any adjusted tests. Report the F-value, degrees of freedom, and numerator Mean Square for the comparison of bonus and payment conditions using (a) the standard approach to testing contrasts and (b) the t-test approach to pairwise contrasts (report as an F). Why do the f-values differ? Use Table A.2 in Maxwell and Delaney to determine the critical value for each approach (note that for the standard approach the exact denominator df are not listed and you’ll have to use the next closer but smaller df to estimate the critical value). Based on these critical values, which approach provides an advantage in terms of power?