“Topsy-turvy” seasons in college football. Each week during the college football season the Associated Press

(AP) ranks the top 25 Division I college football teams based on voting by sportswriters. Many recent upsets of top-rated teams have led to major changes in the weekly AP Poll over the past several seasons. Statisticians have created a formula for determining a weekly “topsy-turvy”

(TT) index, designed to measure the degree to which the LO4 top 25 ranked teams changed from the previous week

(Chance, Summer 2009). The greater the TT index, the greater the changes in the ranked teams. The statisticians calculated the TT index each week of the 15-week college football season for 6 recent seasons. In order to determine whether any of the 15 weeks in a season tends to be more or less topsy-turvy than others, they conducted an ANOVA on the data using a randomized block design.

Here, weeks were considered the treatments and seasons were the blocks. The ANOVA summary table is shown below.

Source df SS MS F p-Value Weeks 14 3,562.3 254.4 2.57 .0044 Seasons 5 2,936.5 587.3 5.94 .0001 Error 70 6,914.4 98.8 Total 89 13,413.1 Source: Kaw, A. K., and Yalcin, A. “A metric to quantify college football’s topsy-turvy season.” Chance, Vol. 22, No. 3, Summer 2009 (Table 2). Reprinted with permission from Chance. Copyright 2009 by the American Statistical Association. All rights reserved.

a. Is there a significant difference (at a = .01) in the mean TT index across the 15 weeks of the college football season?

b. Is there evidence (at a = .01) that blocking on seasons was effective in removing an extraneous source of variation in the data?

c. Tukey’s multiple comparisons method was applied to compare the mean TT index across the 15 weeks.

How many pairwise comparisons are involved in this analysis?

d. Using an experimentwise error rate of .05, Tukey’s analysis revealed that the last week of the regular season

(week 14), when only conference championships are played, had a significantly smaller mean TT index than week 6. All other pairs of means were not significantly different. Use this result to make a comment about whether any of the 15 weeks in a college football season tend to be more or less topsy-turvy than others.