Misinterpretation of 'sig' and 'p'

Oakes (1986³) was the first in exploring the extent to which British academic users misinterpreted inferential statistics, namely 'statistical significance' and the 'p-value'. His research was later replicated by Falk & Greenbaum in Israel (1995¹), and Haller & Krauss (2000²) in Germany. This article offers the results of a meta-analysis done on the collated data.

Results (see illustration 1) show that, overall, about 91% of academic users of statistics (including researchers, teachers and students) misunderstood the concepts of probability and statistical significance in the context of the so-called "null hypothesis testing".

Illustration 1. Collated frequencies and percentages of misinterpretations regarding tests of significance
Common misinterpretations	f	%	(n)
Statistical significance proves the alternative hypothesis	21	8.9%	(236)
Statistical significance disproves the null hypothesis	27	11.4%	(236)

The p-value informs of the probability of the null hypothesis	96	40.7%	(236)
The p-value informs of the probability of the alternative hypothesis	97	41.1%	(236)
The p-value informs of the probability of the results if replicated	90	49.2%	(183)
The p-value informs of the probability of making a wrong decision when rejecting the null	138	75.4%	(183)

(Participants who answered that all of above were false)	20	8.5%	(236)
f = frequencies, or times a misinterpretation was chosen; n = collated sample size

As far as misinterpretations go, misunderstandings regarding the meaning of the p-value appeared more pronounced than those regarding proving or disproving hypotheses. About 9% of academic users thought that achieving statistical significance proved the alternative hypothesis, while a slightly larger percentage (11%) thought achieving statistical significance disproved the null hypothesis.

As per the p-value (or the probability of data given that the null hypothesis is true), 75% of academic users misinterpreted it as the probability of making the so-called 'Type I error' (rejecting the null hypothesis when it is true), and almost half of them misinterpreted it as the probability of obtaining similar results if the study were to be replicated. To a lesser degree, they misinterpreted the p-value as the probability of the null hypothesis being true (41%) or as the probability of the alternative hypothesis being false (41%).

Author

Jose D PEREZGONZALEZ (2014). Massey University, Turitea Campus, Private Bag 11-222, Palmerston North 4442, New Zealand. (JDPerezgonzalez).

Want to know more?

WikiofScience - Null hypothesis significance testing procedure: This WikiofScience page offers an introduction to the pseudoscientific use of the so-called 'null hypothesis testing'.
WikiofScience - Related studies: You can find more information on the studies used for this meta-analysis on WikiofScience: the study done by Oakes in 1986; the replication done by Falk & Greenbaum in 1995; and the replication done by Haller & Krauss in 2000.
WikiofScience - Tests of significance: This page offers a correct procedure for testing the research data against a null hypothesis.