Palavering About P-Values

The American Statistical Association’s most recent confused and confusing communication about statistical significance testing has given rise to great mischief in the world of science and science publishing.[1] Take for instance last week’s opinion piece about “Is It Time to Ban the P Value?” Please.

Helena Chmura Kraemer is an accomplished professor of statistics at Stanford University. This week the Journal of the American Medical Association network flagged Professor Kraemer’s opinion piece on p-values as one of its most read articles. Kraemer’s eye-catching title creates the impression that the p-value is unnecessary and inimical to valid inference.[2]

Remarkably, Kraemer’s article commits the very mistake that the ASA set out to correct back in 2016,[3] by conflating the probability of the data under a hypothesis of no association with the probability of a hypothesis given the data:

“If P value is less than .05, that indicates that the study evidence was good enough to support that hypothesis beyond reasonable doubt, in cases in which the P value .05 reflects the current consensus standard for what is reasonable.”

The ASA tried to break the bad habit of scientists’ interpreting p-values as allowing us to assign posterior probabilities, such as beyond a reasonable doubt, to hypotheses, but obviously to no avail.

Kraemer also ignores the ASA 2016 Statement’s teaching of what the p-value is not and cannot do, by claiming that p-values are determined by non-random error probabilities such as:

“the reliability and sensitivity of the measures used, the quality of the design and analytic procedures, the fidelity to the research protocol, and in general, the quality of the research.”

Kraemer provides errant advice and counsel by insisting that “[a] non-significant result indicates that the study has failed, not that the hypothesis has failed.” If the p-value is the measure of the probability of observing an association at least as large as obtained given an assumed null hypothesis, then of course a large p-value cannot speak to the failure of the hypothesis, but why declare that the study has failed? The study was perhaps indeterminate, but it still yielded information that perhaps can be combined with other data, or help guide future studies.

Perhaps in her most misleading advice, Kraemer asserts that:

“[w]hether P values are banned matters little. All readers (reviewers, patients, clinicians, policy makers, and researchers) can just ignore P values and focus on the quality of research studies and effect sizes to guide decision-making.”

Really? If a high quality study finds an “effect size” of interest, we can now ignore random error?

The ASA 2016 Statement, with its “six principles,” has provoked some deliberate or ill-informed distortions in American judicial proceedings, but Kraemer’s editorial creates idiosyncratic meanings for p-values. Even the 2019 ASA “post-modernism” does not advocate ignoring random error and p-values, as opposed to proscribing dichotomous characterization of results as “statistically significant,” or not.[4] The current author guidelines for articles submitted to the Journals of the American Medical Association clearly reject this new-fangled rejection of evaluating this new-fangled rejection of the need to assess the role of random error.[5]

[1]  See Ronald L. Wasserstein, Allen L. Schirm, and Nicole A. Lazar, “Editorial: Moving to a World Beyond ‘p < 0.05’,” 73 Am. Statistician S1, S2 (2019).

[2]  Helena Chmura Kraemer, “Is It Time to Ban the P Value?J. Am. Med. Ass’n Psych. (August 7, 2019), in-press at doi:10.1001/jamapsychiatry.2019.1965.

[3]  Ronald L. Wasserstein & Nicole A. Lazar, “The ASA’s Statement on p-Values: Context, Process, and Purpose,” 70 The American Statistician 129 (2016).

[4]  “Has the American Statistical Association Gone Post-Modern?” (May 24, 2019).

[5]  See instructions for authors at

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