EXERCISES FOR CHAPTER 18
a–c. Exercises for Sections 18.1–18.3.a1. Consider The Mystery of the Missing Cloud Cover
in Section 16.2.2. How does the negative b
weight for fighter opposition bear on the distinction between process and outcome for assessing importance discussed under Understanding Regression
?a2. a. The bigger the real effect, the bigger is the expected F
, and the smaller is the expected p
. Thus, F
might seem good indexes of effect size. Argue instead that F
are poor indexes of effect size because both depend on the number of observations.a3. P and Q do identical experiments, each using different random samples from the same population. P gets p
=.009; Q gets p
=.032. Who is better off if:a. H0
is true? b. H0
is false?a4. Multiple regression has been used to assess relative importance of stimulus informers. Mebrabian (1972) showed photographs of women's facial expressions intended to communicate liking, neutrality
, or disliking
, paired with recorded voices of women saying “maybe” intended to communicate the same three feelings. The three levels of each variable were assigned values of −1, 0, 1, and used in a two-variable regression analysis. The b
weights were 1.50 for face, 1.03 for voice. These b
weights were treated as indexes of importance; facial expression was thus considered 50% more important than voice tone.
|a. ||What is the argument to treat the b weights as measures of importance?|
|b. ||What is the fatal flaw in the argument of (a)?|
|c. ||With a 3 × 3 design, could Anova measure relative importance?|
a5. Suppose the additive model holds so that each cell mean can be written as α j + β k (ignoring error and the overall mean). Show that the row means may be written as α j + β. Show that the sum of the ranges for the row and column means equals the range of the cell means. Relate this to the relative range index of Equation 4.
a6. a. From Equation 1, show that ¦μ1 − μ2¦ = 2σA for two groups.
b. From (a) and Equations 2–3, show that d = 2 f.
a7. P and Q have been independently funded by an international pharmaceutical corporation to develop a chemical intended to decrease family quarreling and increase family happiness. Both report success, but the development costs, especially getting FDA approval, are so huge that only one can be developed.