Quantitative Psychology Research Laboratory


Meta Analysis

Meta-analysis is becoming very popular in behavioral and medical research. We are interested in using the method in applied research to solve real problems.

So, S. H.-W., Siu, N. Y.-F., Wong, H.-L., Chan, W., & Garety, P. A. (2016).  ‘Jumping to conclusions’ data-gathering bias in psychosis and other psychiatric disorders — Two meta-analyses of comparisons between patients and healthy individuals.  Clinical Psychology Review, 46, 151-167.

Measurement Invariance

The chi-square difference test plays a key role in multiple-group structural equation modeling (SEM) for testing invariance.  We argue that the traditional approach of using the chi-square test for comparing two nested models sequentially would fail to control either type I or type II errors.  Analysis and example show why chi-square-difference tests are easily misused in the context of multi-group analysis, and Monte Carlo results support the analysis.  To overcome this issue, our study further proposes a test of equivalence as an alternative.

Yuan, K.-H., & Chan, W. (2016).  Measurement invariance via multigroup SEM: Issues and solutions with chi-square-difference tests.  Psychological Methods, 21, 405-426.

Yuan, K.-H., Chan, W., Marcoulides, G. A., & Bentler, P. M. (2016).  Assessing structural equation models by equivalence testing with adjusted fit indices.  Structural Equation Modeling, 23, 319-330.


Different indices have been proposed for measuring reliability of a test, including coefficient alpha, coefficient omega, the greatest lower bound reliability, and others. Among these, the coefficient alpha has been most widely used.  However, it is known that coefficient alpha under-estimates the true reliability unless the items are tau-equivalent, and coefficient omega is deemed as a practical alternative to coefficient alpha in estimating measurement reliability of the total score.  To see if the difference between alpha and omega is practically ignorable, we developed a method to examine the difference of coefficient alpha alpha and omega omegastatistically.

The R codes for testing the difference between reliability coefficients alpha and omega (Deng & Chan, 2017)

Deng, L., & Chan, W. (2017).  Testing the difference between reliability coefficients alpha and omega.  Educational and Psychological Measurement, 77, 185-203.

Computer Programs

  • An SAS/IML program for evaluating the statistical significance of congruence coefficients with Procrustes rotation (Chan, Ho, Leung, Chan, & Yung, 1999)
  • A Fortran program for performing the exact unconditional test for linear trend in dose-response studies (Tang, Chan, & Chan, 2000)