Reconceptualization of Coefficient Alpha Reliability for Test Summed and Scaled Scores

IF 2.7 4区 教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Educational Measurement-Issues and Practice Pub Date : 2022-07-07 DOI:10.1111/emip.12520
Rashid S. Almehrizi
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Abstract

Coefficient alpha reliability persists as the most common reliability coefficient reported in research. The assumptions for its use are, however, not well-understood. The current paper challenges the commonly used expressions of coefficient alpha and argues that while these expressions are correct when estimating reliability for summed scores, they are not appropriate to extend coefficient alpha to correctly estimate the reliability for nonlinearly transformed scaled scores such as percentile ranks and stanines. The current paper reconceptualizes coefficient alpha as a complement of the ratio of two unbiased estimates of the summed score variance. These include conditional summed score variance assuming uncorrelated item scores (gives the error score variance) and unconditional summed score variance incorporating intercorrelated item scores (gives the observed score variance). Using this reconceptualization, a new equation of coefficient generalized alpha is introduced for scaled scores. Coefficient alpha is a special case of this new equation since the latter reduces to coefficinet alpha if the scaled scores are the summed scores themselves. Two applications (cognitive and psychological assessments) are used to compare the performance (estimation and bootstrap confidence interval) of the reliability coefficients for different scaled scores. Results support the new equation of coefficient generalized alpha and compare it to coefficient generalized beta for parallel test forms. Coefficient generalized alpha produced different reliability values, which were larger than coefficient generalized beta for different scaled scores.

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测试求和分数和标度分数的Alpha信度系数的重新定义
信度系数一直是研究中最常用的信度系数。然而,对其使用的假设还没有得到很好的理解。本文对常用的alpha系数表达式提出了质疑,认为虽然这些表达式在估计总分数的信度时是正确的,但不适用于将alpha系数扩展到正确估计非线性转换后的分数(如百分位排名和stanines)的信度。本文将系数alpha重新定义为两个无偏估计的总和分数方差之比的补充。这包括假设不相关的项目得分的条件总和得分方差(给出错误得分方差)和包含相互关联的项目得分的无条件总和得分方差(给出观察到的得分方差)。利用这一重新概念,引入了一个新的系数广义alpha方程。系数alpha是这个新方程的一个特殊情况,因为如果缩放分数本身是求和分数,则后者会降低为系数alpha。两个应用程序(认知和心理评估),以比较性能(估计和自举置信区间)的信度系数对不同的尺度分数。结果支持系数广义α的新方程,并将其与平行检验形式的系数广义β进行了比较。广义alpha系数产生不同的信度值,不同量表分数的信度值大于广义beta系数。
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CiteScore
3.90
自引率
15.00%
发文量
47
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