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To the Editor:—
Doctor Menaker has pointed out a defect inherent in the correlation coefficient, which relates two progressively changing variables, but does not indicate magnitude of change. Conceivably a high coefficient can be calculated when changes are very small but progressive. Analysis of death rates from coronary heart disease by state shows similar results, the mean death rate in the highest quartile being 525.3 (which is lower than the national average) and that in the lowest 436.1 per 100,000 population, an increase of 20 per cent. Giving equal weight to each state, large or small, however, and comparing means of quartiles with the national average neglects the factor of the size of the population affected. One must use other methods with the data in the smallest valid units such as states or cities. The correlation coefficients and distribution by the chi-square method suggest that the differences found are not
Schroeder HA. CARDIOVASCULAR DISEASE AND HARDNESS OF WATER-Reply. JAMA. 1960;174(10):1347–1348. doi:10.1001/jama.1960.03030100114034