To Transform or Not Transform Skewed Data for Psychometric Analysis

Anne E. Norris · Karen J. Aroian

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Psychometric Methodologies and Testing Health Education and Validation Reliability and Agreement in Measurement

Abstract

BACKGROUND: Although data transformation is generally recommended, its benefits of have not been widely studied. This report reviews evidence regarding the costs and benefits of transforming skewed data with respect to two statistics commonly used in psychometric analyses: the Cronbach alpha and the Pearson product-moment correlation. METHODS: Data describing 758 immigrants from the former Soviet Union who completed a Russian language version of the Symptom Checklist-90-Revised (SCL-90-R) were used to demonstrate the effects of transformation. More than half (55%) of the SCL-90-R items had a problematic skew. The Cronbach alpha and the Pearson product-moment correlation were calculated for original item responses as well as for square root and log transformations of these responses. Sample size (full, 30%, 20%), transformation type (square root or log transformation), and transformation method (sum items first and then transform, transform items first and then sum) were manipulated to evaluate the relevance of these factors to transformation. RESULTS: Regardless of sample size, neither the Cronbach alpha nor the Pearson product-moment correlation showed a difference between original and transformed data, with one exception. When items were transformed first before being summed in the calculation of the Pearson product-moment correlation, inconsistently higher (+.05) or slightly lower values (-.01) were observed relative to those created with the nontransformed data across the different sample sizes. CONCLUSIONS: These findings suggest that data transformation is not always needed or advisable when the Cronbach alpha or Pearson product-moment correlation is calculated for instruments with skewed item responses.

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1957The needless assumption of normality in Pearson's r.

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