Chapter 6 Exercise

STAT 3022, section 00110/03/2011

Do Poets Die at a Younger Age?

A sample was taken of 123 female American writers who have died in the past 100 years.Their age of death was recorded, as well as the type of literature they wrote: nonfiction,novels, or poems.

Group n Mean SDNonfiction 24 76.88 14.10Novels 67 71.45 13.05Poems 32 63.19 17.30

The data can be found at

http://www.stat.umn.edu/~graalum/olddata/ch12/ta12_002.txt.

(a) Construct a side-by-side box plot for the age of death of writers in all groups, andcomment on the data distributions. Does a one-way analysis of variance F -test seemappropriate?

(b) State the H0 and Ha for the one-way ANOVA F -test.

(c) Complete the ANOVA table:

Source d.f. Sum of Squares Mean Square F -statistic p-value

Between groups

Within groups

Total

What is your conclusion?

(d) Check your model assumptions with diagnostic plots. Are there any obvious violationsof our assumptions?

(e) Suppose we wish to compare poets to both of the other groups. In other words, we wantto find a contrast between poets and the average of the two other groups. What is thelinear combination for which we should construct a 95% CI?

(f) Find the point estimate for , g, and the standard error SE(g). Then construct theinterval and state your conclusion.

(g) Suppose instead we simply wish to perform simultaneous multiple comparisons. Whatis the Bonferroni multiplier for each pairwise difference? What is the Bonferroni half-width for each pairwise difference?

(h) Using the Bonferroni method, which pairwise differences are significant? Compare theinterval half-widths to the differences:

Difference with...Group Average Poems NovelsNonfiction 76.88 13.68 5.43Novels 71.45 8.26Poems 63.19

(i) Now use R to perform multiple pairwise comparisons using the Tukey-Kramer proce-dure. What are your conclusions? Do they contradict the conclusions based on theBonferroni method?