**Use H rather than F to test the weight change data recorded in Review Question

Question

**Use H rather than F to test the weight change data recorded in Review Question 16.13 on page 381.

16.13 Twenty-three overweight male volunteers are randomly assigned to three different treatment programs designed to produce a weight loss by focus- ing 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 signity a weight drop; negative scores, a weight gain. Note: See the comment in Review Question 16.10 about calculations when sample sizes are unequal. WEIGHT CHANGES DIET EXERCISE BEHAVIOR MODIFICATION 10 18 12 100 12 63

Explanation / Answer

We can quickly answer this using the open source statistical package R , the complete R snippet is as shown below

########################

Diet <- c(3,4,0,-3,5,10,3,0)
Exercise <- c(-1,8,4,2,2,-3)
Behaviour <- c(7,1,10,0,18,12,4,6,5)

data <- list (diet = Diet, exercise= Exercise,behaviour = Behaviour)

kruskal.test(data)

###################

The results are

Kruskal-Wallis rank sum test

data: data
Kruskal-Wallis chi-squared = 4.4705, df = 2, p-value = 0.107

The hypothesis is

H0 : There is no difference in the average weight loss between the groups

H1 : There is a signifcant difference in the average weight loss between the groups

as the p value is 0.107 , which is not less than our assumed alpha of 0.05 , hence we fail to reject the null hypothesis and conclude that There is no difference in the average weight loss between the groups

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