CoChat
Sign Up
Cited by 17Advanced Statistical Methods and ModelsStatistical Distribution Estimation and ApplicationsPsychometric Methodologies and Testing

Another Look at the Robustness of the Product-Moment Correlation Coefficient to Population Non-Normality

Open access
Blair, R. Clifford, Bear Lawson, Stephanie·1982·Florida Journal of Educational Research
DOI 10.62798/tzqq1969
Open this paper in CoChat — free accountOpen PDF

Abstract

PerspectiveStudies of the effects of population nonnormality on the sampling distribution of the product-moment correlation coefficient date from the 1920's.For example, E. S. Pearson (1929), after studying samples taken from two "considerably non-normal distributions" concluded that "the normal bivariate surface can be mutilated and distorted to a remarkable degree without affecting the frequency distribution of r." (Quotations taken from Kowalski, 1972).Other studies of the period resulted in essentially the same conclusion.(See Kowalski 1972 for a review of this literature.)Later researchers tend to agree with Pearson's (1929) conclusion provided that IE' Iis near zero.Norris and Hjelm (1961) state, "When there was essentially no correlation in the population, the shape of the sampling distributions for the product-moment correlation coefficients did not vary markedly as a function of nature or extent of nonnorrnality in the bivariate distribution.In general, these obtained sampling distributions conform very closely to their theoretical distributions."This point of view has become so popular that Kowalski (1972), after reviewing the literature, states "Everyone seems to agree that the distribution of r is quite robust to nonnormality when P = 0•••."

Integrity signals

Registry

Crossref · 10.62798/tzqq1969

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Heavily skewed distributions typically result in outliers, which can be problematic in terms of type I error rates depending on the distribution of X.

    “However, heavily skewed distributions typically result in outliers, which, depending on the distribution of X, can be problematic in terms of type I error rates as just explained above (see also Blair & Lawson, 1982).”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Blair & Lawson, 1982

  • Based on the 100 simulated scenarios, p values from Gaussian models are highly robust to even extreme violation of the normality assumption and can be trusted, except when involving X and Y distributions with extreme outliers (distribution D9).

    “Based on the 100 simulated scenarios that we have constructed, p values from Gaussian models are highly robust to even extreme violation of the normality assumption and can be trusted, except when involving X and Y distributions with extreme outliers (distribution D9; see also Blair & Lawson, 1982).”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Blair & Lawson, 1982

Cites

Still being checked.

Cited by

Sorted by citations

Related

Authors
Blair, R. C., & Bear Lawson, S.
Affiliations
University of South Florida (US)
Venue
Florida Journal of Educational Research
Publisher
Florida Educational Research Association
Published
1982-11-11
Volume
24
Issue
1
Pages
11-15
ISSN
  • 0428-7355 (ISSN-L)
  • 2575-6109
DOI
10.62798/tzqq1969
OpenAlex
W3005116162
Cited by
17
References
0
Citations by year
2021: 3 · 2018: 1 · 2017: 2 · 2016: 1 · 2015: 1 · 2014: 1 · 2013: 2 · 2012: 2
FWCI
0.00
Type
journal article
Language
en
Open access
Locations
Florida Educational Research Association (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Keywords
robustness, non-normality, sampling distribution, Pearson correlation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review