PEDIATRICS Vol. 83 No. 3 March 1989, pp. A72
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SMALL SAMPLE SIZE SCIENTIST

Student

The believer in the law of small numbers practices science as follows:

1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power.

2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance.

3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals.

4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.