11/3/2023

See GoogleDrive\Stat216-Nonparametrics-F2023\!Class Notes\Section7.3-7.5-Notes-BH.pdf

Multiple comparisons based on Friedman rank sums

Wilcoxon-Nemenyi-McDonald-Thompson, see cWNMT and pWNMT in R
Exercise 32 on p. 321

More multiple comparisons procedures

Treatment vs. Control - Exercise 37 on p. 327

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Estimating contrasts for block designs

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For each pair of treatments, compute the within block differences and then find the median.

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Obtain an average effect for each treatment.

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Combine these averages, using the contrast coefficients of interest, to obtain the desired estimator.

Where have we seen this idea before?

See GoogleDrive\Stat216-Nonparametrics-F2023\!Class Notes\Section7.9-7.10-Notes-BH.pdf

Testing for General Alternatives when there are Replications

4

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Model

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Hypotheses

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Mack-Skillings Procedure

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L.S.A.

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Exercise 93 on page 338

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Follow-up Multiple Comparisons - After rejecting with Mack-Skillings procedure

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Exercise 104 on page 342

Other Methods in Chapter 7

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Section 7.6 - Balanced Incomplete Block Design (B.I.B.D.) - test is still based on rank sums, but now we only observe s < k treatments in each block

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Section 7.7 - Multiple Comparisons for B.I.B.D - based on differences in rank sums

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Section 7.8 - Arbitrary B.I.B.D.

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Sections 7.11 through 7.15 - discuss the extension of the signed-rank procedures to the randomized complete block design with only one observation per cell. These procedures are competitors with the methods presented in Sections 7.1 through 7.5, but they are not exactly distribution-free.

We will have a problem session on Monday.