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A Two-interval Forced-choice Task for Multisensory Comparisons

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A cautionary note on exact unconditional inference for a difference between two independent binomial proportions.

Devan V Mehrotra¹, Ivan S F Chan, Roger L Berger

¹Merck Research Laboratories, UN-A102, 785 Jolly Rd., Bldg. C, Blue Bell, Pennsylvania 19422, USA. devan_mehrotra@merck.com

|August 21, 2003

Summary

Fisher's exact test can be overly conservative in randomized experiments. Exact unconditional tests are often more powerful, especially Boschloo's test and the score statistic test.

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Area of Science:

Biostatistics
Statistical inference
Clinical trial design

Background:

Fisher's exact test is commonly used for comparing proportions in randomized experiments.
The test can be overly conservative with small sample sizes or extreme proportions due to a discrete null distribution.

Purpose of the Study:

To evaluate the performance of Fisher's exact test and alternative exact unconditional tests.
To identify the most powerful and reliable exact test for comparing proportions in randomized experiments.

Main Methods:

Comparison of exact test size and power using a real-world example.
Evaluation of Fisher's exact test, exact unconditional tests using difference in proportions, difference divided by standard error under alternative, and score statistic.
Analysis of Boschloo's test, which uses Fisher's p-value as a test statistic.

Main Results:

Fisher's exact test was outperformed by some exact unconditional tests.
Exact unconditional tests using the difference in proportions or difference divided by standard error under the alternative were less powerful than Fisher's test.
The exact unconditional test using the score statistic and Boschloo's test demonstrated superior power compared to Fisher's exact test.

Conclusions:

The score statistic and Boschloo's test are recommended for exact unconditional inference in randomized experiments.
Researchers should carefully select the test statistic for exact unconditional tests to avoid reduced statistical power.
Exact unconditional procedures can offer increased power over Fisher's exact test when appropriate test statistics are employed.