Browsing by Author "Cohen, Jacob"

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    The cost of dichotomization
    (1983) Cohen, Jacob
    Assuming bivariate normality with correlation r, dichotomizing one variable at the mean results in the reduction in variance accounted for to .647r²; and dichotomizing both at the mean, to .405r². These losses, in turn, result in reduction in statistical power equivalent to discarding 38% and 60% of the cases under representative conditions. As dichotomization departs from the mean, the costs in variance accounted for and in power are even larger. Consequences of this practice in measurement applications are considered. These losses may not be quite so large in real data, but since methods are available for making use of all the original scaling information, there is no reason to sustain them.
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    Problems in the measurement of latent variables in structural equations causal models
    (1990) Cohen, Patricia; Cohen, Jacob; Teresi, Jeanne; Marchi, Margaret L.; Velez, C. Noemi
    Some problems in the measurement of latent variables in structural equations causal models are presented, with examples from recent empirical studies. Latent variables that are theoretically the source of correlation among the empirical indicators are differentiated from unmeasured variables that are related to the empirical indicators for other reasons. It is pointed out that these should also be represented by different analytical models, and that much published research has treated this distinction as if it had no analytic consequences. The connection between this theoretical distinction and disattenuation effects in latent variable models is shown, and problems with these estimates are discussed. Finally, recommendations are made for decisions about whether and how to measure latent variables when manifest variables are potentially available. Index terms: causal models, disattenuation, emergent variables, latent variable measurement, latent variables, structural equations modeling.
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    Set correlation and contingency tables
    (1988) Cohen, Jacob
    Set correlation is a realization of the general multivariate linear model, can be viewed as a multivariate generalization of multiple correlation analysis, and may be employed in the analysis of multivariate data in any form. Set correlation supplements the four methods for analyzing two-way contingency tables described by Zwick and Cramer (1986), and its application to their example is illustrated. It gives the same results for the overall association, and in addition, by the use of nominal scale coding and partialling, it assesses specific hypotheses about the details of the association. Set correlation includes measures of strength of association (including correlations and proportions of variance), significance tests and estimation, power analysis, and computer programs to implement the calculations. Index terms: canonical analysis, contingency table analysis, correspondence analysis, general multivariate linear model, multivariate analysis of variance, Pearson chi-square, set correlation.