Stat209/Ed260A 3/11/19
Week 9 Exercises: time-1, time-2 data
Group Comparisons, Correlates of Change, Lord's Paradox,
Note: Crossover Design analysis using lmer, see Stat222 week 5, Review Question 5 (with solution)
1. Correlates of Change
Repeat the demonstrations in the class handout using instead the
fallible observed score data (the "X"'s instead of the "Xi"'s.
Data are linked from week 9 lecture topics #5.
Compare the amount of change on W regression (W as predictor of change) with
regressions that use W and initial status on X to predict either final status
or change (show that these are equivalent, as in class handout proof).
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2. Lord's paradox example
a. construct a two-group pre-post example with 20 observations in
each group that mimics the description in Lord (1967):
statistician 1 (difference scores) obtains 0 group effect
statistician 2 (analysis of covariance) obtains large group effect
for the group higher on the pre-existing differences in pretest
b. construct second example for which
statistician 1 (difference scores) obtains large group effect
statistician 2 (analysis of covariance) obtains 0 group effect
c. construct a third example (if possible) for which
statistician 1 (difference scores) obtains large postive group effect
statistician 2 (analysis of covariance) obtains large negative group effect
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3. Group Comparisons by repeated measures analysis of variance or lmer
For your example in problem 2, part c, carry out the group
comparison (i.e. is there differential change?) for the artificial
data using a repeated measures anova (one within, one between factor) or
lmer equivalent.
As this is observational data, this could be termed a diffs-diffs analysis.
Demonstrate the equivalence from Brogan-Kutner paper that testing
the groupXtime interaction term is equivalent to a
t-test between groups on individual improvement (i.e. a
statistician 1 analysis).
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end HW9 2019