Stat209/Ed260 D Rogosa 2/27/19
Assignment 8. Matching review: Randomized Block Designs
Problem 1. Matching and Paired t-test
Example from lecture
Stat 141 exam problem (circa 2005)
An experiment on treating depression by Imipramine, an anti-
depressant drug, employed a matched-pairs design. A total of 60
patients were paired on a combination of age, sex, and time of
entry in study to form 30 matched pairs. That is, each pair
consisted of patients who entered the study within a month of
each other, were of the same sex and were similar in age. One
member of each pair was randomly assigned to receive Imipramine
and the other to receive a placebo. The outcome measure was the
score on the Hamilton rating scale for depression (higher score =
more severe depression) after 5 weeks of treatment.
The file http://web.stanford.edu/~rag/stat209/depressdata
contains the outcome scores for each of the
30 pairs (Imipramine vs Placebo).
a. Carry out a statistical test of the equality of treatment outcomes.
That is, test null hypothesis that Imipramine and Placebo produce equivalent
outcomes versus a non-directional alternative. Use Type 1 error rate .05.
State the result of the statistical test.
b. Pretend that an erstwhile graduate assistant lost all records of the
matched pairs before the data analysis could be completed. Consequently, all the
investigator has available is the 30 scores for the patients receiving
Imipramine and the 30 scores for the patients receiving Placebo (but not the
information on the matching). Carry out a statistical test of the
hypothesis in part a using the available information. Is the result of the
test the same? Explain why or why not.
c. Regard part (b) as a bad dream and return to the data
set with full matching information. But now you are told that
the differences between Hamilton scale scores shouldn't be
regarded as having numerical value. Comparing two Hamilton scores
only indicates relative standing, that is which of the two
patients in the matched pair is showing greater symptoms of
depression. Under that limitation of the data carry out an appropriate
statistical test of the hypothesis in part (a). Explain why the
result is the same or different from the result in part (a).
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Problem 2. background & review
Matching to increase precision: Factorial Randomized blocks designs
Example from lecture
From Neter-Wasserman problem DENTAL PAIN.
An anesthesiologist made a comparative study of
the effects of acupuncture and codiene on
postoperative dental pain in male subjects. The
four treatments were (1) placebo treatment-- a
sugar capsule and two inactive acupuncture
points, (2) codiene treatment only--a codeine
capsule and two inactive acupuncture points; (3)
acupucture only--a sugar capsule and two active
acupuncture points (4) both codeine and
acupuncture. These 4 conditions have a 2x2
factorial structure.
Thirty-two subjects were grouped into 8 blocks
of four according to an initial evaluation of
their level of pain tolerance. The subjects in
each block were then randomly assigned to the 4
treatments. Pain relief scores were obtained 2
hours after dental treatment. Data were
collected on a double-blind basis.
Data in file
http://www-stat.stanford.edu/~rag/stat209/dental.dat
c1 is pain relief score (higher
means more pain relief), c2 is block c3 is
codiene c4 is acupuncture--for c3 and c4, 1=no.
a. obtain cell means for the 2x2 factorial design
b. carry out the randomized blocks analysis of variance,
factors are Block, main effects for Codeine Acup and
interaction term Codeine*Acup,
c. Give a measure for the relative efficiency of the blocking
on pain tolerance--how much better in terms of precision
or number of subjects needed is the analysis using blockings
versus a 2x2 factorial design design that ignores pain tolerance?
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end homework 8 part 1