(For this problem, you'll need to use JASP, SPSS, or an online ANOVA calculator. Use the data in the file 'Beatles-spring2020'.) An investigator wonders if slow-tempo music is more complex than fast-tempo music - since with slower music, the listener has more time to process the incoming musical information. To study this, he examines three samples of pop songs by the Beatles that differ in tempo: slow (group 1), moderate (group 2), and fast (group 3). 20 Beatles songs are sampled in each category (so, 60 songs total). As a measure of musical complexity, the investigator counts the number of different chords that appear in each song (a chord is a group of notes played at the same time). He then compares the three tempo groups to see if they differ in average number of chords each song contains. Analyze the data using JASP, SPSS, or an online calculator, and answer the following questions:

A. (2 pts) What is the independent variable? What is the dependent variable?

B. (4 pts) What is the omnibus null hypothesis? What is the alternative hypothesis?

C. (3 pts) Report the mean and standard deviation for each condition.

D. (4 pts) Report the full ANOVA table for this analysis (including the p value from the computer).

E. (3 pts) What is the critical value for this F-test for a = 0.05? (Be sure to state the degrees of freedom.)

F. (3 pts) Based on this critical value, should you reject or fail to reject the omnibus null hypothesis? Why or why not? In plain English, say substantively what the omnibus result means.

G. (7 pts) By hand, perform a planned comparison (a = 0.05_2-tailed) between the slow songs (group 1) and fast songs (group 3). State the null and alternative hypotheses, calculate t_obt by hand (show your work!), report |t_crit| (including df), and your decision about the null hypothesis.

H. (6 pts) In JASP, SPSS, or the online calculator, do post hoc comparisons using Tukey's HSD with a = 0.05. Report which means are reliably different, and what the basis for that decision is (in terms of the decision rule).

I. (3 pts) By hand, calculate and interpret the effect size, omega-squared, for the omnibus F test. (In JASP, you can get this number automatically, but please also do it by hand.)