Stat 502
Homework 4
Assigned 10/23/08
Due 10/30/08
Analyze the experiments described in 1 and 2 by answering (a)-(g) for each.
1. Eggs: A biologist randomly assigned one of three different diet supplements (a=high calorie,
b=medium calorie, c=low calorie) to 30 female lizards, and recorded the number of eggs laid.
The interest is in how the diet supplement might affect clutch size (the number of eggs laid).
The data are in the file egg.dat.
2. Running: This experiment studied metabolic cost of locomotion as a function of a combina-
tion of conditions such as speed, stride, and mass distribution. There were 3 experimental
conditions (A,B,C) which were randomly allocated to 18 male members of a track club, so
that 6 runners got A, 6 got B, and 6 got C. One runner who was supposed to receive treat-
ment B dropped out of the study before it started. The response was time after running
commenced until oxygen consumption leveled off, and are in the file run.dat.
(a) Describe the experimental design (how many treatment levels, how the randomization
was done, the sample sizes, etc.).
(b) Make some plots. Based on the plots, describe evidence of variation due to treatment.
(c) Write out the treatment-effects model for the experiment and find the least-squares
estimates of µ,τ1, . . . , τmand σ2.
(d) Calculate the sample variance for each treatment group, and find the pooled sample
variance. Compute SSTotal, SSTreatment SSError, and write these out in an ANOVA
table.
(e) Discuss the evidence against the null hypothesis of no treatment effects, based on the
F-statistic you compute from the ANOVA table (don’t compare it to a null distribution
just yet). Explain why your statistic is a valid measure of evidence against the null
hypothesis.
(f) Make some assumptions about the data, list the assumptions, and find a normal-theory
p-value for testing against H0: no treatment effect. What assumptions validate the use
of this test? Check any assumptions you can.
(g) You would like to decide if the statistic you calculate in (e) is much larger than would be
observed under the hypothesis of no treatment effect, without making the assumptions
in (f). Find the randomization distribution of your test statistic and give the p-value.
Plot the randomization null distribution against the normal-theory null distribution.
3. Overlapping confidence intervals: Suppose yAand yBare i.i.d. samples from populations A
and Bwith
yA={5.12,5.93,4.91,7.35,6.08,4.93,6.24,6.49}
yB={7.58,6.69,8.51,7.39,6.38,4.79,8.12,6.96}
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