20141210 - Misinterpretation of the p-value and of the level of significance (2000)

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# 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%).

# Methods

### Research approach

Meta-analysis done on data collated from three exploratory studies.

### Sample

Frequency of responses from 236 users of statistics for six of the items, and from 183 users for the remaining two items4. The users were a mix of university lecturers, researchers and students from three countries: the UK (Oakes, 19863), Israel (Falk & Greenbaum, 19951), and Germany (Haller & Krauss, 20002).

### Materials

Six statements reflecting common misinterpretations of the p-value and tests of significance.

### Analysis

Percentages.

References
1. FALK Ruma & Charles W GREENBAUM (1995). Significance tests die hard: the amazing persistence of a probabilistic misconception. Theory & Psychology, 1995, volume 5, number 1, pages 75-98. DOI 10.1177/0959354395051004.
2. HALLER Heiko & Stefan KRAUSS (2000). Misinterpretations of significance. A problem students share with their teachers. Methods of Psychological Research Online, 2002, volume 7, number 1, pages 1-20.
3. OAKES Michael (1986). Statistical inference: a commentary for the social and behavioral sciences. John Wiley & Sons (Chichester, UK), 1986.
+++ Notes +++
4. Those two items were not used by Falk & Greenbaum (19951).

# 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.

## Author

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

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page revision: 2, last edited: 02 Mar 2015 02:41