Keywords

Cronbach alpha, data transformation, Pearson product-moment correlation, skew

 

Authors

  1. Norris, Anne E.
  2. Aroian, Karen J.

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.

 

Data transformation is a commonly recommended strategy for dealing with data that are skewed rather than normally distributed (Ferketich & Verran, 1994). A widely used multivariate statistics textbook states that "unless there are compelling reasons not to, it is safer to transform" (Tabachnik & Fidell, 1989, p.79). Transformation aims to normalize the distribution so that parametric statistics can be used without concern about violating assumptions of normality (Bradley, 1978). Moreover, transformation purportedly increases statistical power and minimizes the attenuation of correlations (Dunlap, Burke & Greer, 1995;Grissom, 2000).

 

However, the benefits of transformation for skewed data have not been widely studied, particularly with respect to the use of the Cronbach alpha and the Pearson product-moment correlation coefficients, both of which are frequently used in psychometric analysis. Extant literature, although sparse, suggests that the costs and benefits differ for each of these statistics. A close examination of whether data for psychometric analysis should be transformed is critical for nursing. The types of measures that are central to evidence-based practice (e.g., interval or near interval level measures of symptom distress as well as measures of healthcare cost and utilization) often produce skewed data (Broskowski & Chalk, 1998;Hiscock & Wake, 2001).

 

This report reviews existing literature regarding the costs and benefits of transformation with respect to the calculation of the Cronbach alpha and the Pearson product-moment correlation coefficient. It demonstrates the impact of log and square root transformations on estimates of internal consistency and test-retest reliability using data obtained from a measure of psychological distress. The specific aims of the reported study were to investigate how square root and log transformations affect the Cronbach alpha and Pearson product-moment correlation coefficient for three different sample sizes, and to consider what impact the method of transformation (i.e., transforming items before totaling them or summing items and the transforming the total score) has on the Pearson product-moment correlation coefficient for these different sample sizes.