A New Index for Measuring Internal Consistency of Multiple-item Instruments

Abstract

This paper introduces a new index for measuring internal consistency of multiple-item instruments designed for assessing only one attribute. The index is based on an intuitive idea that as the homogeneity of a test increases, a test taker with a higher total score should have a greater probability to obtain score on each and every item than a test taker with a lower total score. Accordingly, an approximated sampling distribution of the index is derived by means of an analysis of variance approach. An example is presented and its interpretation is discussed. A sample-based estimator will also be proposed and compared to the model-based estimator by statistical simulation. Finally, its relation to Cronbach's alpha is also indicated.