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**1 - 3**of**3**### COMPUTING GAUSSIAN & EXPONENTIAL MEASURES OF SEMI-ALGEBRAIC SETS

, 2015

"... HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

### Measuring an Effect Size From Dichotomized Data: Contrasted Results Whether Using a Correlation or an Odds Ratio

"... It is well known that dichotomizing continuous data has the effect to decrease statistical power when the goal is to test for a statistical association between two variables. Modern researchers however are focusing not only on statistical sig-nificance but also on an estimation of the ‘‘effect size’ ..."

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It is well known that dichotomizing continuous data has the effect to decrease statistical power when the goal is to test for a statistical association between two variables. Modern researchers however are focusing not only on statistical sig-nificance but also on an estimation of the ‘‘effect size’ ’ (i.e., the strength of asso-ciation between the variables) to judge whether a significant association is also clinically relevant. In this article, we are interested in the consequences of dichotomizing continuous data on the value of an effect size in some classical settings. It turns out that the conclusions will not be the same whether using a correlation or an odds ratio to summarize the strength of association between the variables: Whereas the value of a correlation is typically decreased by a factorffiffiffiffiffiffiffiffi =2 p after each dichotomization, the value of an odds ratio is at the same time raised to the power ffiffiffi 2 p. From a descriptive statistical point of view, it is thus not clear whether dichotomizing continuous data leads to a decrease or to an increase in the effect size, as illustrated using a data set to investigate the relationship between motor and intellectual functions in children and adolescents.