Statistics 8052
Spring 2017
B. Grund
Assignment #2
(Due: Monday, February 6, 2017)
Reading: Oehlert, Chapters 5 – 7.
Written Assignment:
1. Perform a simulation study that estimates the “comparisonwise” and “strong familywise” error rates,
and the FDR for all pairwise comparisons in ANOVA problems with g=2, …, 10 treatments. Investigate
the following methods: LSD (preceeded by F-test for protection against the inflation of type I error due
to multiple comparisons), Tukey’s HSD, Scheffé, SNK, REGWR. Use the following parameters to
generate data: n=20 observations per treatment; =1;
Case 1: 1= …= g =0 (null hypothesis for ANOVA)
Case 2: 1=1, 2= …= g =0 (one mean is different from the others).
Choose B=200 or higher (B is the number of simulated data sets for each value of g for Case 1 or 2).
Produce 2 graphs for each case:
(1) plot of the estimated strong familiywise error rate over g, with one line for each method,
(2) plot of the estimated FDR over g
(3) plot of the estimated comparisonwise error rate for the comparison H0: 1-2 = 0 over g.
2. Q 5.1.
3. E6.3
Remember to check whether your ANOVA assumptions hold; if not, transform your data. If you use a
transformation, assess whether your assumptions hold for your final model. Be careful when wording
your conclusions.
Remark : For your pairwise comparisons, use a method that provides simultaneous 95% confidence
intervals. Provide an underline diagram.
Additionally: b) Which drugs are equivalent to the most effective drug ? Use a method that ensures
an error rate of 0.05 for the subset [of equivalent drugs] selection.
4. E6.5
5. P6.1
Instructions for ANOVA analyses:
1. Always check whether the assumptions for your linear model are fulfilled. Use a transformation if
appropriate.
2. When you work with transformed data, always check that the model assumptions hold for the
transformed data (residuals vs. predicted values, normal probability plot for residuals).
3. Compare treatment means using an underline diagram or a similar graphical representation, for a
method that controls the simultaneous Type I error in multiple comparisons. Always give an
interpretation of your underline diagram! You don’t need to compare treatment means when the
homework problem clearly does not ask for it – but do include pairwise comparisons (or whatever
comparisons are appropriate) in open-ended analyses (e.g., “analyze the data and draw conclusions”).
4.
5.
Write a short summary of your findings (e.g., necessary transformations, results of hypothesis tests,
results of other analyses, etc.)
For open-ended problems, start your report with an executive summary stating conclusions. Then
present your supporting materials with interpretation. Use sub-headings in your supporting materials
for longer problems.