Norris Anne E, Aroian Karen J
William F Connell School of Nursing, Boston College, Chestnut Hill, Massachusetts 02467, USA.
Nurs Res. 2004 Jan-Feb;53(1):67-71. doi: 10.1097/00006199-200401000-00011.
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.
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.
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.
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.
尽管通常建议进行数据转换，但其益处尚未得到广泛研究。本报告回顾了关于在心理测量分析中常用的两个统计量（克朗巴哈系数和皮尔逊积矩相关系数）方面对偏态数据进行转换的成本和效益的证据。
使用描述758名前苏联移民的数据，这些移民完成了俄语版的症状自评量表90修订版（SCL - 90 - R），以证明转换的效果。超过一半（55%）的SCL - 90 - R项目存在问题性偏态。对原始项目反应以及这些反应的平方根和对数转换计算克朗巴哈系数和皮尔逊积矩相关系数。操纵样本量（完整样本、30%、20%）、转换类型（平方根或对数转换）和转换方法（先对项目求和然后转换、先对项目进行转换然后求和）来评估这些因素与转换的相关性。
无论样本量如何，克朗巴哈系数和皮尔逊积矩相关系数在原始数据和转换后的数据之间均未显示出差异，但有一个例外。在计算皮尔逊积矩相关系数时，当项目先进行转换然后求和时，相对于不同样本量下未转换数据得到的值，观察到不一致的较高值（+.05）或略低的值（-.01）。
这些发现表明，当对具有偏态项目反应的工具计算克朗巴哈系数或皮尔逊积矩相关系数时，数据转换并非总是必要或可取的。
