The Calculus Concept Inventory–Measurement of the Effect of Teaching Methodology in Mathematics

Abstract

This article examines the adequacy of the "rules of thumb" conventional cutoff crite- ria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2-index presentation strategy, which includes using the maximum likelihood (ML)-based standardized root mean squared residual (SRMR) and supple- menting it with either Tucker-Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, Mc- Donald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff crite- ria for the ML-based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true-population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and Gamma Hat; a cutoff value close to .90 for Mc; a cutoff value close to .08 for SRMR; and a cutoff value close to .06 for RMSEA are needed before we can conclude that there is a relatively good fit between the hypothesized model and the observed data. Furthermore, the 2-index presentation strategy is re- quired to reject reasonable proportions of various types of true-population and misspecified models. Finally, using the proposed cutoff criteria, the ML-based TLI, Mc, and RMSEA tend to overreject true-population models at small sample size and thus are less preferable when sample size is small