On the Correlation of Death-Rates

Pearson, Karl; Lee, Alice; Elderton, Ethel M.

doi:10.2307/2340173

Cited by 17 publications

(7 citation statements)

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“…Using, for example, income measured by per capita income and education measured by average education, even if this condition is met and per capita income is related to average education, the inference that person's income is causally dependent upon education drops one into the ecological fallacy (Robinson, 1950). Similarly, inferences made from per capita income or average education (referring to individual statuses) to income or education in general (referring to the aggregate) result in overgeneralizations (see also Blalock, 1964: 95-100; Bollen and Ward, 1979;Firebaugh, 1978;Burstein, 1978;Yule, 1910;and Pearson, 1910 for discussions related to these conditions).…”

Section: Discussionmentioning

confidence: 99%

“…The problem of correlating ratios was first debated at the turn of the century by Pearson (1897Pearson ( , 1910 and Yule (1910) and most recently has been called to the attention of sociologists and demographers by Freeman and Kronenfeld (1973), Schuessler (1973Schuessler ( , 1974, and Fuguitt and Lieberson (1974). All agree that correlated denominators present a difficulty, but the problem and solutions remain ambiguous.'…”

Section: Ratio Variables and The Problem Of Correlated Denominatorsmentioning

confidence: 99%

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Correlated Denominators in Multiple Regression and Change Analyses

Pendleton

Warren

Chang

1979

Sociological Methods & Research

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Sociological and demographic research often uses variables computed as ratios.When the denominators are highly correlated, or identical, and the ratios are used in correlation or regression analysis, a statistical dependency is formed. Interpretations and inferences may be difficult to make and misleading. This article has two basic purposes. The first is to show how this problem expands from bivariate correlation and regression to partial correlation and multiple regression. The second purpose is to review advantages and disadvantages of selected alternative change models, focusing on path analysis and the problem of correlated denominators in change and path analyses. It is suggested that, when an identical denominator exists, it can be used as an independent control variable in standard leastsquares regression equations constructed from the numerators. When, however, the denominators are highly correlated but not identical, as is found in most crosssectional research and is virtually inescapable in longitudinal research, the use of residual analysis is suggested as a solution to the problem of correlated denominators. ociological and demographic research often uses variables computed as ratios or rates. Usually, the denominator of the ratio is used for control purposes, as when population size is used in the calculation of per capita income or the birthrate (Schuessler, 1974). When two ratios with highly correlated, or the same, denominators are correlated, a statistical depend-

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Section: Discussionmentioning

confidence: 99%

Section: Ratio Variables and The Problem Of Correlated Denominatorsmentioning

confidence: 99%

Correlated Denominators in Multiple Regression and Change Analyses

Pendleton

Warren

Chang

1979

Sociological Methods & Research

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show abstract

“…Most of the discussions of the problem of ratio variables begin with the work of Pearson (1897Pearson ( , 1910. Pearson devised a formula to approximate the correlation between ratios that is based on the correlations (r) and coefficients of variation (V = standard deviation/ mean) for the individual components:…”

Section: The Nature Of the Ratio Problemmentioning

confidence: 99%

“…According to Fuguitt and Lieberson (1974), Logan's suggestion is related to solutions proposed by Pearson (1910), Brown et al (1914), Neifeld (1927), and Fleiss and Tanur ( 1971 ). Fuguitt and Lieberson discuss the Logan solution and conclude that more work is necessary on the rationale for part or partial correlations before this approach is adopted as an unambiguous solution.…”

Section: Ratios As Variables Of Theoretical Interestmentioning

confidence: 99%

Ratio Variables in Aggregate Data Analysis

Bollen

Ward

1979

Sociological Methods & Research

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This article discusses three different uses of ratio variables in aggregate data analysis: (1) as measures of theoretical concepts, (2) as a means to control an extraneous factor, and (3) as a correction for heteroscedasticity. In the use of ratios as indices of concepts, a problem can arise if it is regressed on other indices or variables that contain a common component. For example, the relationship between two per capita measures may be confounded with the common population component in each variable. Regarding the second use of ratios, only under exceptional conditions will ratio variables be a suitable means of controlling an extraneous factor. Finally, the use of ratios to correct for heteroscedasticity is also often misused. Only under special conditions will the common form ofregression with ratio variables correct for heteroscedasticity. Alternatives to ratios for each of these cases are discussed and evaluated. he controversy over the use of ratios in correlation or regression analyses has a long history. The issue has been commented on by statisticians,

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“…He coined the term 'spurious correlation' to describe the apparent statistical relationship between any two such 'mathematically coupled' ratio variables [3]. To tackle this problem, Pearson suggested that analysts should calculate the partial correlation between the numerators while 'adjusting' for the denominator, rather than assessing the correlation between the two ratios [4]. For example, if one were investigating the relationship between the incidence rates of two diseases, such as cancer and diabetes, the analyst should calculate the partial correlation between the counts of each disease while adjusting for population size.…”

Section: Introductionmentioning

confidence: 99%

Ratio index variables or ANCOVA? Fisher's cats revisited

Law

Ellison

et al. 2009

Pharmaceutical Statistics

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Over 60 years ago Ronald Fisher demonstrated a number of potential pitfalls with statistical analyses using ratio variables. Nonetheless, these pitfalls are largely overlooked in contemporary clinical and epidemiological research, which routinely uses ratio variables in statistical analyses. This article aims to demonstrate how very different findings can be generated as a result of less than perfect correlations among the data used to generate ratio variables. These imperfect correlations result from measurement error and random biological variation. While the former can often be reduced by improvements in measurement, random biological variation is difficult to estimate and eliminate in observational studies. Moreover, wherever the underlying biological relationships among epidemiological variables are unclear, and hence the choice of statistical model is also unclear, the different findings generated by different analytical strategies can lead to contradictory conclusions. Caution is therefore required when interpreting analyses of ratio variables whenever the underlying biological relationships among the variables involved are unspecified or unclear.

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On the Correlation of Death-Rates

Cited by 17 publications

References 0 publications

Correlated Denominators in Multiple Regression and Change Analyses

Correlated Denominators in Multiple Regression and Change Analyses

Ratio Variables in Aggregate Data Analysis

Ratio index variables or ANCOVA? Fisher's cats revisited

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