Dangers Inherent in Correlating Averages

Halliwell, Joseph W.

doi:10.1080/00220671.1962.10882826

Cited by 3 publications

(2 citation statements)

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“…The only accessible discussion of within versus between versus total correlation coefficients in the educational literature between 1939 and 1970 appeared in a short paper on the correlation between intelligence and grades by Halliwell (1962). The topic has received a great deal of attention in the seventies but the focus has switched from correlation coefficients to regression coefficients (simple and multiple), with the previously-cited works by Burstein (1975), Cronbach (1976, and Hannan (1971) as the principal contributions.…”

Section: The Inter-relationships Of Within-aggregate Between-aggmentioning

confidence: 99%

The Unit-of-Analysis Problem in Applications of Simple Correlation Analysis to Educational Research

Knapp

1977

Journal of Educational Statistics

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Section: The Inter-relationships Of Within-aggregate Between-aggmentioning

confidence: 99%

The Unit-of-Analysis Problem in Applications of Simple Correlation Analysis to Educational Research

Knapp

1977

Journal of Educational Statistics

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“…The relationship between the Pearson R and regression coefficients computed from individual scores and the Pearson R and regression coefficients computed from grouped averaged or aggregate scores has been the subject of many papers [4,6,8]. Ecological studies and epidemiology often need to use group averaged data to make inferences about individual patterns [14].…”

Section: Introductionmentioning

confidence: 99%

Describing the Pearson 𝑅 distribution of aggregate data

Torres

2020

Monte Carlo Methods and Applications

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Ecological studies and epidemiology need to use group averaged data to make inferences about individual patterns. However, using correlations based on averages to estimate correlations of individual scores is subject to an “ecological fallacy”. The purpose of this article is to create distributions of Pearson R correlation values computed from grouped averaged or aggregate data using Monte Carlo simulations and random sampling. We show that, as the group size increases, the distributions can be approximated by a generalized hypergeometric distribution. The expectation of the constructed distribution slightly underestimates the individual Pearson R value, but the difference becomes smaller as the number of groups increases. The approximate normal distribution resulting from Fisher’s transformation can be used to build confidence intervals to approximate the Pearson R value based on individual scores from the Pearson R value based on the aggregated scores.

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