Question

A PEW Research Center survey concentrated on the issue of weight loss. It investigates how many pounds heavier the respondents were than their perceived ideal weight. It investigated whether these perceptions differed among regions of the country and gender of the respondants. The following data (pounds) reflect the survey results.

Region

Gender               West                  Midwest            South                           Northeast

Men                    14                       18                       15                           16

                           13                       16                       15                           14

Women              16                       20                       17                           17

                           13                       18                       17                           13

1. Determine if there is interaction between Region and Gender. Use the p-value approach and a significance level of 0.05.
2. Given your findings in part a, determine any significant difference among the discrepancy between the average existing and desired weights in the regions.
3. Repeat part b for the Gender factor.

Answer 1

Anova: Two-Factor With Replication
SUMMARY	West	Midwest	South	Northeast	Total
Men
Count	2	2	2	2	8
Sum	27	34	30	30	121
Average	13.5	17	15	15	15.125
Variance	0.5	2	0	2	2.410714
Women
Count	2	2	2	2	8
Sum	29	38	34	30	131
Average	14.5	19	17	15	16.375
Variance	4.5	2	0	8	5.696429
Total
Count	4	4	4	4
Sum	56	72	64	60
Average	14	18	16	15
Variance	2	2.666667	1.333333	3.333333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Gender	6.25	1	6.25	2.631579	0.143415	5.317655
Region	35	3	11.66667	4.912281	0.031947	4.066181
Interaction	2.75	3	0.916667	0.385965	0.766242	4.066181
Within	19	8	2.375
Total	63	15

a. Since P-value corresponding interaction between Region and Gender=0.766242>0.05 so there is no significant  interaction between Region and Gender.

b. Since P-value corresponding region=0.031947<0.05 so there exists significant differences among the discrepancy between the average existing and desired weights in the regions.

c. Since P-value corresponding Gender=0.143415>0.05 so gender factor is insignificant.