Editing Ecological fallacy (section)

=== Robinson's paradox ===
A 1950 paper by William S. Robinson computed the illiteracy rate and the proportion of the population born outside the US for each state and for the District of Columbia, as of the [[1930 United States Census|1930 census]].<ref>{{cite journal |last=Robinson |first=W.S. |year=1950 |title=Ecological Correlations and the Behavior of Individuals |journal=[[American Sociological Review]] |volume=15 |issue=3 |pages=351–357 |doi=10.2307/2087176 |jstor=2087176}}</ref> He showed that these two figures were associated with a negative correlation of −0.53; in other words, the greater the proportion of immigrants in a state, the lower its average illiteracy (or, equivalently, the higher its average literacy). However, when individuals are considered, the correlation between illiteracy and nativity was +0.12 (immigrants were on average more illiterate than native citizens). Robinson showed that the negative correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or "ecological" data. In 2011, it was found that Robinson's calculations of the ecological correlations are based on the wrong state level data. The correlation of −0.53 mentioned above is in fact −0.46.<ref>The research note on this curious data glitch is published in {{cite journal |first1=Manfred |last1=Te Grotenhuis |first2=Rob |last2=Eisinga |first3=S.V. |last3=Subramanian |title=Robinson's ''Ecological Correlations and the Behavior of Individuals'': methodological corrections |journal=[[International Journal of Epidemiology|Int J Epidemiol]] |year=2011 |volume=40 |issue=4 |pages=1123–1125 |doi=10.1093/ije/dyr081 |pmid=21596762 |doi-access=free |hdl=2066/99678 |hdl-access=free }} The data Robinson used and the corrections are available at [https://archive.today/20130222172038/http://www.ru.nl/mt/rob/downloads/]</ref> Robinson's paper was seminal, but the term 'ecological fallacy' was not coined until 1958 by Selvin.<ref>{{cite journal |first=Hanan C. |last=Selvin |s2cid=143488519 |title=Durkheim's ''Suicide'' and Problems of Empirical Research |journal=[[American Journal of Sociology]] |volume=63 |issue=6 |year=1958 |pages=607–619 |doi=10.1086/222356 }}</ref>