Mice experiment: lifetime versus diet
The data for this discussion comes from the book The Statistical
Sleuth, by Ramsey and Schafer (Duxbury, 1997). An experiment was
conducted on female mice, which were randomly assigned to one of the
following six treatment groups (as described by Ramsey and Schafer):
- NP: Mice in this group ate as much as they pleased of a
nonpurified, standard diet for laboratory mice.
- N/N85: This group was fed normally both before and after
weaning. (The slash distinguishes the two periods.) After weaning, the
ration was controlled at 85 kcal/wk. This, rather than NP, serves as the
control group because caloric intake is held reasonably constant.
- N/R50: This group was fed a normal diet before weaning and
a reduced-calorie diet of 50 kcal/wk after weaning.
- R/R50: This group was fed a reduced-calorie diet of 50
kcal/wk both before and after weaning.
- N/R50 lopro: This group was fed a normal diet before weaning,
a restricted diet of 50 kcal/wk after weaning, and had dietary protein
content decreased with advancing age.
- N/R40: This group was fed normally before weaning and was
given a severely reduced diet of 40 kcal/wk after weaning.
NOTE: This data comes from R. Weindruch, R.L. Walford, S. Fligiel, and
D. Guthrie, "The Retardation of Aging in Mice by Dietary Restriction:
Longevity, Cancer, Immunity and Lifetime Energy Intake," Journal of
Nutrition 116(4) (1986): 641-54.
Generally the researchers' questions concerned comparisons of lifetimes
between the various diets. There were specifically these questions:
lifetime for the 50 kcal/wk diet exceed that for the 85 kcal/wk diet, and,
if so, by how much, (This calls for a comparison of the N/R50 group to the N/N85group.)
- Is lifetime affected by providing a reduced calorie
diet before weaning, given that a 50 kcal/wk diet is provided after
weaning? (This calls for a comparison of the R/R50 group to the N/R50
- Does lifetime on the 40 kcal/wk diet exceed the lifetime on
the 50 kcal/wk diet? (This calls for a comparison of the N/R40 group to
the N/R50 group.)
- Given a reduced calorie intake diet of 50 kcal/wk,
is there any additional effect on lifetime due to decreasing the protein
intake? (This calls for a comparison of the N/R lopro diet to the N/R50
- Is there an effect on lifetime due to restriction at 85
kcal/week? This would indicate the extent to which the 85 kcal/wk diet
served as a proper control and possibly whether there was any effect of
restricting the diet, even with a standard caloric intake. (This calls for
a comparison of the N/N85 group to the NP group.)
These data are available as the data frame mice.df which should be
available to you automatically from my account. The data frame contains
two variables: Lifetime, which gives the lifetime of each mouse in months,
and Treatment, whose values are described above.
One-way ANOVA with R
Get the data and do basic descriptive statistics:
boxplot(Lifetime ~ Treatment)
nn <- tapply(Lifetime, Treatment, length)
mm <- tapply(Lifetime, Treatment, mean)
ss <- tapply(Lifetime, Treatment, sd)
Do the one-way ANOVA:
fm1 <-aov(Lifetime ~ Treatment) #Fit the one-way ANOVA model.
anova(fm1) #Obtain the ANOVA table.
pairwise.t.test(Lifetime, Treatment, p.adj="bonferroni")