Compare the mean, standard deviation, and variance for the data for the Cognitive Behavior condition in Exercise 5.21 with their 20% trimmed and Winsorized counterparts. Why is the Winsorized variance noticeably smaller than the usual variance? (You can do this using R by loading the “psych” library and using the “describe” command.)

Exercise 5.21

Everitt, as reported in Hand et al. (1994), presented data on the amount of weight gained by 72 anorexic girls under one of three treatment conditions. The conditions were Cognitive Behavior Therapy, Family Therapy, and a Control group who received no treatment. The data follow, and are available on the Web as Ex5.21.dat:

a) What would you hypothesize about central tendency and variability?

b) Calculate the relevant descriptive statistics and graphics for each condition separately.

c) What kind of conclusions would you feel comfortable in drawing, and why?

Transcribed Image Text:

Cog. 1.7 10 0.7 -0.1 -0.7 -3.5 14.9 3.5 17.1 -7.6 1.6 11.7 6.1 I.I = -4.0 Behav. 20.9 -9.1 2.1 -1.4 1.4 -0.3 -3.7 -0.8 2.4 126 1.9 3.9 0.1 15.4 -0.7 Family 11.4 11.0 5.5 9.4 13.6 -2.9 -0.1 7.4 21.5 -5.3 -3.8 13.4 13.1 9.0 3.9 5.7 10.7 Control -0.5 -9.3 -5.4 12.3 -2.0 -10.2 -12.2 11.6 -7.1 6.2 -0.2 -9.2 8.3 3.3 11.3 0.0 -1.0 -10.6 -4.6 -6.7 2.8 0.3 1.8 3.7 15.9 -10.2