Stat 427/527 Data Analysis I

Homework 4 due Tuesday October 11


An experiment was designed to investigate whether rapid eye movement
(REM) sleep time depends on the amount of ethanol given in an
injection. Four injection concentrations were considered: 0, 1, 2, and
4 grams per kilogram of body weight. Twenty rats were then chosen and
randomly divided into four equal sized groups. Each group was given a
different treatment [concentration of ethanol]. The REM sleep time
during the subsequent 24 hour period was recorded for each rat. The
data are as follows:

          Treatment            REM sleep in minutes
          ------------------------------------------
          0 g/kg            88.6 73.2 91.4 68.0 75.2
          1 g/kg            63.0 53.9 69.2 50.1 71.5
          2 g/kg            44.9 59.5 40.2 56.3 38.7
          4 g/kg            31.0 39.6 45.3 25.2 22.7
          ------------------------------------------

We are interested in comparing the typical amount of REM sleep across
treatments. 

a)  Make boxplots and dotplots of the data to compare the groups.
Compute, in Minitab, the sample means and standard deviations for the
4 treatment groups.

b)  Looking at the graphical and descriptive summaries from part a, do
there appear to be differences in the typical REM levels for the 4
groups?  Describe the differences you see that appear to be most
pronounced.

c)  Do a one-way Analysis of Variance to compare the mean REM levels
for the 4 groups. Are the groups significantly different at the 5%
level?

d)  Compare all possible pairs of groups using Fisher's LSD method,
and summarize the results of the multiple comparison.  Repeat for
Tukey's HSD method, and using Bonferroni comparisons.  Do the three
methods find different groupings?  If so, what accounts for that?

e)  Are the results of the F-test in part c), and the multiple
comparisons in part d) consistent with what you described in part b)?
Briefly discuss.

f)  Looking at the numerical and graphical summaries does it appear
that the distributions of REM levels are reasonably normal,and have
constant variance across groups? Discuss. 

g)  Comment on the Levene's and Bartlett's formal tests of equal 
variances in light of what you see when you look at the data.

h)  Obtain the residuals (or centered values) and generate a normal
probability plot based on them.  This is an overall check on
normality.  Is the normality assumption reasonable here?  Perform a
formal test of normality on the residuals, report the p-value and
comment.  If the test says we did not sample from normally distributed
populations, why does it appear to be saying that?  Do you think there
is a real difficulty here with applying the normal theory methods?


Summarize all your results carefully in a report.  Make certain you 
define all populations and parameters under consideration, and that you 
make clear with each step which parameter(s) you are analyzing.  I am 
particularly concerned that you keep straight the distinction between 
sample and population means, and sample and population variances.