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