Question

16.13 Twenty-three overweight male volunteers are randomly assigned to three different treatment programs designed to produce a weight loss by focusing on either diet, exercise, or the modification of eating behavior Weight changes were recorded, to the nearest pound, for all participants who completed the two-month experiment. Positive scores signify a weight drop; negative scores, a weight gain. Note: See the comment in Review Question 16.10 about calculations when sample sizes are unequal. 10 WEIGHT CHANGES DIET EXERCISE BEHAVIOR MODIFICATION 3 -1 7 4 8 1 0 4 -3 2 0 5 2 18 10 -3 12 3 4 0 6 5 22 12 63 8 6 9 EX = G = 97; N = 23 EXP=961 И T n (a) Summarize the results with an ANOVA table. (b) Whenever appropriate, use Tukey's HSD test and estimate all effect sizes, given that the means for diet, exercise, and behavior modification equal 2.75, 2.00, and 7.00, respectively.

Answer 1

(a)

Answer: Let the hypotheis are:

Null Hypothesis: Each of the three methods of weight loss i.e. Diet, Exercise, Behaviour Modification doesn't differ significantly in results.

Alternaitve Hypothesis: Each of the three methods do not provide the same output in terms of weight loss.

The Summary Table and ANOVA table for the data is:

1.    

Summary of Data
	Treatments
Diet	exercise	behaviour Modification	Total
N	8	6	9	23
∑X	22	12	63	97
Mean	2.75	2	7	4.217
∑X2	168	98	695	961
Std.Dev.	3.9188	3.8471	5.6347	5.0087

2.

ANOVA TABLE
Source	SS	df	MSS	F-ratio
Between-treatments	116.413	2	58.2065	F = 2.67309
Within-treatments	435.5	20	21.775
Total	551.913	22

Hence, with an F-Ratio=2.67309 and p-value=0.093578. We do not have suficient evidence to reject the null hypothesis and hence, it can be assumed that alll the three methods of weight loss are same in terms of output.

(b) Since, all the three methods of weight loss do not differ significantly in terms of output. Hence, there is no need of Tukey's HSD test.