Investigation 6: Comparing popular diets (assigned Thur Jan 28, due Tues Feb 2)

You may work with one other person on this assignment, handing in one report with both names.  Word-processed reports are much preferred to hand-written ones.  Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

 

A recent article in the Journal of the American Medical Association (Dansinger, Griffith, Gleason et al., 2005) reported on a randomized, comparative experiment in which 160 subjects were randomly assigned to one of four popular diet plans: Atkins, Ornish, Weight Watchers, and Zone (40 subjects per diet).  These subjects were recruited through newspaper and television advertisements in the greater Boston area; all were overweight or obese with body mass index values between 27 and 42. Among the variables measured were:

  • which diet the subject was assigned to
  • whether or not the subject completed the twelve-month study
  • the subject’s weight loss after two months, six months, and twelve months (in kilograms, with a negative value indicating weight gain)
  • the degree to which the subject adhered to the assigned diet, taken as the average of 12 monthly ratings, each on a 1-10 scale (with 1 indicating complete non-adherence and 10 indicating full adherence)

Data for the 93 subjects who completed the 12-month study are in the Minitab worksheet ComparingDiets.mtw.

 

a) Examine (submit) comparative boxplots of the weight loss amounts, comparing the four diet plans.  Write a paragraph comparing and contrasting the distributions of weight loss across the four plans.  [Remember to comment on center, spread, shape, and outliers.]

 

b) Report the sample mean and sample standard deviation of the weigh loss amounts within each group.

 

c) Examine whether the technical conditions for ANOVA appear to be satisfied here.  Comment on and justify your conclusion.

 

d) Use Minitab to perform an ANOVA to investigate whether the experimental data provide strong evidence that there is a significant difference in mean weight loss among these four diet plans.  Report the ANOVA table, as well as the hypotheses, test statistic, and p-value.  Summarize your conclusion.

 

e) Now suppose that all of the sample sizes had been ten times larger than they actually were, and that all of the sample means and standard deviations had turned out as they did in the actual experiment.  Produce the ANOVA table for this scenario.  [Hint: You will have to do this by hand, using the sum of squares (SS) expressions introduced in class.]

 

f) How do the test statistic and p-value compare between (d) and (e)?  Explain why this makes intuitive sense.

 

g) For each diet plan, determine the sample proportion of subjects who completed the study.  [Hint: Remember that 40 subjects were assigned at random to each diet plan, and the Minitab worksheet only contains data for the subjects who completed the study.]

 

h) Perform the appropriate test to determine if the proportions in g) differ significantly.  Report the test statistic and p-value.  Also summarize your conclusion.