Question

The National Crime Victimization Survey estimates that there were over 400,000 violent crimes committed against women by their intimate partner that resulted in physical injury. An intervention study designed to increase safety behaviors of abused women compared the effectiveness of six telephone intervention sessions with a control group of abused women who received standard care. Fifteen different safety behaviors were examined. One of the variables analyzed was the total number of behaviors (out of 15) that each woman performed. Here is a summary of the means of this variable at baseline (just before the first telephone call) and at follow-up 3 and 6 months later.

	Time
Group	Baseline	3 months	6 months
Intervention	10.4	12.5	11.9
Control	9.6	9.9	10.4

(a) Find the marginal means. (Round your answers to three decimal places.)

	Time
Group	Baseline	3 months	6 months	Mean
Intervention	10.4	12.5	11.9
Control	9.6	9.9	10.4
Mean

Are they useful for understanding the results of this study?

The row means suggest that the intervention group showed more improvement than the 6 months group.

The row means suggest that the control group showed more improvement than the 3 months group.  

  The row means suggest that the intervention group showed less improvement than the control group.

The row means suggest that the control group showed more improvement than the baseline group.

The row means suggest that the intervention group showed more improvement than the control group.

(b) Plot the means. Do you think there is an interaction? Describe the meaning of an interaction for this study.

Yes there is an interaction, it means that the mean number of actions changes differently over time for the two groups

.Yes there is an interaction, it means that the mean number of actions does not change over time for the two groups.   

Yes there is an interaction, it means that the mean number of actions changes consistently over time for the two groups.

No there is not an interaction, meaning that the mean number of actions does not change over time for the two groups.

(Note: This exercise is from a repeated-measures design, and the data are not particularly normal because they are counts with values from 1 to 10. Although we cannot use the methods in this chapter for statistical inference in this setting, the example does illustrate ideas about interactions.)

Answer 1

Answer:

a)

The marginal means are:

	Time
Group	Baseline	3 months	6 months	Mean
Intervention	10.4	12.5	11.9	(10.4+12.5+11.9)/3 = 11.6
Control	9.6	9.9	10.4	(9.6+9.9+10.4)/3 = 9.967 (rounded)
Mean	(10.4+9.6)/2= 10	(12.5+9.9)/2 = 11.2	(11.9+10.4)/2 = 11.15

The row means suggest that the intervention group showed more improvement than the control group

b)

Yes there is an interaction, it means that the mean number of actions changes differently over time for the two groups.