Comments(1)

Least significant P-value digits are not uniformly distributed

Stephen Senn   (13 August 2007)  University of Glasgow

The authors of this interesting paper assume that the distribution of the least significant digit for a P-value ought to be adequately approximated by the uniform distribution.

In fact my calculations show that for a non-centrality parameter of 2.8 (corresponding to 80% power for a 2.5% type one error rate, one sided) the least significant digit for a one-sided P-value would be far from uniform. The results (further details and details of calculation available on request) for the digit 0 and 9 are as follows.

Digit

Decimal places 0 9

3 0.35 0.042

4 0.21 0.070

5 0.14 0.087

(If I have rounded correctly!)

Of course, things may be rather different for two-sided P-values (which are commonly reported) and of course the above corresponds to only one particular value of the noncentrality parameter. For true null hypotheses the distribution should be, of course, perfectly uniform, whether looking at the P-value as a whole or the least significant digit. Nevertheless, these results show that the uniform distribution cannot be taken as an appropriate model for least significant digits for P-values by default.

(NB my attention was drawn to this paper by a paper I was recently asked to review for Biomed Central. However, the point above was not made in the paper I was asked to review.)

Competing interests

As an academic my career is furthered by publication

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