ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2012, Vol. 44 ›› Issue (12): 1687-1694.doi: 10.3724/SP.J.1041.2012.01687

• 论文 • 上一篇    下一篇



  1. (1江西师范大学心理学院, 南昌 330022) (2华南师范大学心理应用研究中心, 广州 510631)
  • 收稿日期:2011-11-12 出版日期:2012-12-25 发布日期:2012-12-25
  • 通讯作者: 温忠麟, E-mail:
  • 基金资助:


Estimating Homogeneity Coefficient and Its Confidence Interval

YE Baojuan;WEN Zhonglin   

  1. (1 School of Psychology, Jiangxi Normal University, Nanchang 330022, China) (2Center for Studies of Psychological Application, South China Normal University, Guangzhou 510631, China)
  • Received:2011-11-12 Online:2012-12-25 Published:2012-12-25
  • Contact: WEN Zhonglin

摘要: 在决定将多维测验分数合并成测验总分时, 应当考虑测验同质性。如果同质性太低, 合成总分没有什么意义。同质性高低可以用同质性系数来衡量。用来计算同质性系数的模型是近年来受到关注的双因子模型(既有全局因子又有局部因子), 测验的同质性系数定义为测验分数方差中全局因子分数方差所占的比例。本文用Delta法推导出计算同质性系数的标准误公式, 进而计算其置信区间。提供了简单的计算同质性系数及其置信区间的程序。用一个例子说明如何估计同质性系数及其置信区间, 通过模拟比较了用Delta法和用Bootstrap法计算的置信区间, 发现两者差异很小。

关键词: 同质性系数, Delta法, 置信区间

Abstract: Multidimensional tests are frequently applied to the studies of psychology, education, society and management. Before aggregating all item scores to form a composite score of a multidimensional test, we should consider the homogeneity of the test. Homogeneity coefficient which reflects the extent that all test items measure the same trait can be employed to evaluate test homogeneity. If homogeneity coefficient is low, the composite score is meaningless and cannot be used for further analyses. Homogeneity coefficient is the proportion of variability in composite score that is accounted for by the general factor, which is viewed as common to all items. Any multidimensional test can be represented by a bifactor model that contains a general factor and local factors. Hence homogeneity coefficient can be calculated based on a bifactor model. A unidimensional test with positively worded items and negatively worded items can also be represented by a bifactor model, where the assessed construct is the general factor and method factors are local factors. The confidence interval of homogeneity coefficient provides more information than its point estimate. There are three approaches to estimate the confidence interval of composite reliability: Bootstrap method, Delta method and direct use of the standard error generated from an SEM software output (e.g., LISREL). It has been found that the interval estimates that obtained by Delta method and Bootstrap method were almost the same, whereas the results obtained by LISREL software and by Bootstrap method had large differences. Delta method was recommended when estimating the confidence interval of composite reliability. In order to compute the confidence interval of homogeneity coefficient, we deduced a formula by using Delta method for computing the standard error of homogeneity coefficient. Based on the standard error, the confidence interval can be obtained easily. We used an example to illustrate how to calculate homogeneity coefficient and its confidence interval by using the proposed Delta method with LISREL software. We also illustrated how to get the same result with Mplus software that automatically calculates the standard error with Delta method and presents the confidence interval. Before composite scores of a test are aggregated for further statistical analysis, it is recommended to report homogeneity coefficient so that readers could evaluate the extent that the statistical results are reliable.

Key words: homogeneity coefficient, Delta method, confidence interval