ABSTRACT
I. Introduction.......................................................................................... 422
II. Description and Taxonomy of Multiple Comparison
Procedures............................................................................................ 422
A. Terms............................................................................................. 422
B. Descriptions of Multiple Comparison Procedures ....................... 427
1. The Least Significant Difference and Multiple
t Test Procedures ................................................................... 427
2. S Method ............................................................................... 428
3. T Method ............................................................................... 428
4. Orthogonal Contrasts............................................................. 429
5. Comparisons with a Control or Standard ............................. 429
6. Stepwise (Step-down and Step-up) Tests ............................. 430
7. Multiple Range Tests ............................................................ 431
8. Confidence Intervals.............................................................. 432
9. Comparisons with the Best ................................................... 432
10. Nonparametric Procedures .................................................... 433
11. Multiple Comparisons between Dose Levels and
a Zero Dose ........................................................................... 434
12. Multiple Comparisons of Proportions (0-1 Data) ............... 434
13. Other Methods....................................................................... 435
14. Allocation of Observations among the Treatment
Groups ................................................................................... 435
C. Summary Taxonomy..................................................................... 436
D. Common Sources of Tables.......................................................... 436
III. Multiple Comparison Tests in Practice............................................... 437
A. Is a Multiple Comparison Procedure Needed? ............................ 437
1. Testing a Selected Contrast .................................................... 438
2. Comparisons Between a New Drug and Active and
Placebo Controls ..................................................................... 440
3. Combination Drugs ................................................................. 442
4. Data Dredging......................................................................... 443
5. Drug Screening ....................................................................... 444
B. Analysis of a Randomized Trial................................................... 446
References........................................................................................................ 449
In many of the drug experiments performed in the pharmaceutical industry, at
least two drugs or at least two levels of one drug are considered. As a
consequence of these experiments, questions related to picking out drugs or dose
levels which are different from others are often generated. However, it is rare that
some overall test of a null hypothesis provides researchers with specific details to
answer the questions of interest. Because overall tests tend to average out real
effects with negligible effects, they may fail to detect important features. Even if
an overall test is significant, further analyses may be necessary to determine
which specific differences among the treatments are clinically important. These
“further analyses” constitute performing multiple comparisons among the
treatments to detect those effects which are of prime interest to the researchers.
Suppose we have a drug trial with k distinct treatments (different dosage levels,
for example) that are randomly allocated to distinct experimental units
(rats, patients, baboons, etc.). Suppose y
