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# Ecological Correlations and the Behavior of Individuals

## Details

**Authors** Robinson, W. S.

**Year** 1950

**Publisher** American Sociological Review

**Kind of work** article

**Discipline** Sociology

**Secondary disciplines** Statistics, Political Science

**Applied** false

[Read it at the publisher](https://doi.org/10.2307/2087176) 
10.2307/2087176

## In authors' words

### What they set out to do (purpose)

To examine whether correlations computed between percentages across geographic areas (ecological correlations) can stand in for correlations between the properties of individuals, and to show what the two depend on.

### Who or what was studied (sample)

U.S. Census of 1930, population aged 10 and over (about 97.3 million persons). Ecological correlations were computed over the nine Census divisions and over the 48 states.

### How they did it (methods)

Derivation of the algebraic relation between an ecological correlation and the corresponding individual correlation, followed by comparison of both for two pairs of variables: percent Negro with illiteracy, and percent foreign-born with illiteracy.

### What they found (results)

Percent Negro and illiteracy: individual correlation .203, ecological correlation .946 across divisions and .773 across states. Percent foreign-born and illiteracy: individual correlation .118, ecological correlations -.619 across divisions and -.526 across states, so the sign reverses. The individual correlation depends on the cell frequencies within each area, while the ecological correlation depends only on the marginal totals, which do not determine those cells. Robinson concludes that an ecological correlation is almost certainly not equal to its corresponding individual correlation, and that ecological correlations should not be used as substitutes for individual ones.

## Commentary

### In short

Using 1930 U.S. Census data, the paper shows that correlations computed across areas can differ greatly from, and even reverse the sign of, correlations among the individuals within those areas. It derives why this happens.

### Response

The finding bears on the systems structure: relations measured on aggregates (the whole) need not hold among the members (the parts), and the study makes this precise by showing that the group-level correlation is fixed by marginal totals that leave the internal cell distribution undetermined. Relationships also carry weight, since the object of study is a correlation, and the sign reversal shows that the same variables stand in different relations at different levels of aggregation. Caveats: the paper is a methodological warning about inference between levels and does not describe parts and wholes in systems terms; the fit to relationships is by way of correlation rather than causal or mechanistic connection; a perspective reading (the aggregate and the individual as two vantage points) is arguable but is not made by the author, so it is not ticked.

**Patterns it shows** S, R

Formal proof or model, Shows the structure is there

**Added** 2026-10-28

**How to cite this** Robinson, W. S. (1950). Ecological Correlations and the Behavior of Individuals. American Sociological Review.