Stat 301
HW 9
Due: 20 Nov / 30 Nov 2015
Reading:
On qualitative variables: 5.7, 5.8, skim: 12.3 - 12.5
On outliers and influence: 8.6
On variable selection (coming up in lecture): 6.1, 6.3, 6.4
1. Chimpanzees have been taught to communicate in American Sign Language. The data in
chimp.csv come from a study of whether some words were more difficult to learn than others.
Four chimps were taught to use the same 10 words. The response variable is how long, in
minutes, it took before each chimp could reliably use the word. That variable should be
log transformed before analysis. Chimps should be considered as a blocking variable in your
analysis.
You do not need to backtransform any responses in this problem. All answers can be left as
log-transformed values.
(a) Test the null hypothesis that all 10 words take the same amount of time to learn. Report
the F statistic and p-value.
(b) Write a one-sentence conclusion from that test
(c) Estimate the average (log tranformed) time to learn each word. No need to report those
averages. Instead: which word takes the longest to learn? which word is the fastest to
learn? Report the average log-transformed time and a 95% confidence interval for those
mean for each of those two words.
(d) Report the standard error of the mean time to learn one word. (It should be the same
value for all words).
(e) Reanalyze the data omitting Chimp (the blocking variable) from the model. Report the
standard error of the mean time to learn one word when blocks are omitted.
(f) This approximates the standard error of the mean if the study was done with 40 chimps,
each of which learned one of the 10 words. Was blocking a good idea? Briefly explain
why or why not.
2. The data in iridium.csv come from a geological study of rocks across the Cretaceous-Tertiary
boundary. A large meteor is suspected to have impacted the earth at this boundary. One
of the potential signatures of a meteor impact is elevated levels of the trace element Iridium.
Iridium is naturally present on the earth, but at low concentrations. The data here are the
concentrations of Iridium in two types of rock (shale and limestone) at six depth categories.
The goal of the study is to examine whether there is an elevated concentration of Iridium
at one or more depths, and whether the change in Iridium concentration across depths was
similar in both types of rock.
(a) The two-way ANOVA model for these data will include main effects for type and depth,
and the interaction effect between rock and depth. Which of these three effects tells you
whether the increase was similar in both types of rock? Which tells you whether the
difference between shale and limestone is the same at each depth?
1
Fit the two-way ANOVA model to these data and use that and related output to answer the
questions.
Note: Depthcat is a number, so JMP will treat that as a continuous variable by default. You
want depthcat to define categories (with a separate mean for each category). You need to
change depthcat from a blue ramp to a red bar variable. Either:
right click on the blue ramp by depthcat and change the modeling type to nominal
or right click on the column name, choose modeling type, and change to nominal
or do something else (e.g., in the column info dialog box) to change it to nominal
(b) Is the change in Iridium across depths similar in the two types of rock? Report the
appropriate test statistic, p-value, and your conclusion.
(c) Plot the interaction profile plots.
(d) Look at the interaction profile plot with two lines, one for each type of rock. Explain
why this plot is generally consistent with the conclusion of the test in part b.
(e) Averaged over rock types, do all six depth categories have the same mean concentration
of Iridium? Report the appropriate test statistic, p-value, and your conclusion.
(f) Report the LSMEAN Iridium concent8ration for each depth category.
(g) Report the 95% confidence interval for the difference between the LSMEAN for depth
category 3 and the LSMEAN for depth category 5.
3. Problem 8.28 (p. 423) Book’s questions with the following amendments:
a) no answer needed.
d) Use Cook’s D to describe influence.
2