Several authors have suggested that prior to conducting a confirmatory factor analysis it may be useful to group items into a smaller number of item 'parcels' or 'testlets'. The present paper mathematically shows that coefficient alpha based on these parcel scores will only exceed alpha based on the entire set of items if W, the ratio of the average covariance of items between parcels to the average covariance of items within parcels, is greater than unity. If W is less than unity, however, and errors of measurement are uncorrelated, then stratified alpha will be a better lower bound to the reliability of a measure than the other two coefficients. Stratified alpha are also equal to the true reliability of a test when items within parcels are essentially tau-equivalent if one assumes that errors of measurement are not correlated.

中文翻译：

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关于使用alpha和分层alpha来估计由项目包裹组成的测试的可靠性的说明。

几位作者建议，在进行验证性因素分析之前，将项目分组为少量的项目“包裹”或“小样”可能会很有用。本文从数学上表明，如果W（宗地之间的项目平均协方差与宗地中项目的平均协方差之比）W大于1，则基于这些宗地得分的系数alpha仅会超过整个项目集的alpha。 。但是，如果W小于1，并且测量误差不相关，则分层的alpha值将比其他两个系数更好地限制度量的可靠性。如果人们认为测量误差不相关，则当包裹中的物品基本上等于tau时，分层的alpha也等于测试的真实可靠性。