Tools and resources

Software procedures and tools developed or used by Quant-DARE presenters and researchers for carrying out statistical analyses.

Gamma Hat

This document and spreadsheet explain how to calculate the Gamma Hat fit index for use in Confirmatory Factor Analysis and Structural Equation Modeling.

The Akaike Information Criterion

The Akaike Information Criterion can be used to evaluate whether the best fitting model is better than the comparison model. The AIC Evaluation Procedure spreadsheet allows you to enter two AIC values and determine whether one model has better fit than the comparison model. Small differences in AIC will not be defensibly better than comparison models. This helps you determine if the difference is sufficiently large to prefer one model over another.

Equating PAT and e-asTTle scores

We have been asked how to equate PAT and e-asTTle scores. To the best of our knowledge no formal equivalence study has been published. This note provides rationale for using stanines as basis of equating and provides stanine tables for e-asTTle reading and mathematics scores.

Coefficient H

This protocol replaces coefficient alpha in determining the robustness or reliability of a factor when determined with confirmatory factor analysis. It uses the standardised beta regression weights from the factor to the item to determine the proportion of variance explained by the factor as a measure of robustness. The protocol was developed and explained in:

Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In R. Cudeck, S. Du Toit, & D. Sörbom (Eds.), Structural Equation Modeling: Present and Future - A Festschrift in Honor of Karl Jöreskog (pp. 195–216). Scientific Software International Inc.

Download the xlsx ‘coefficient H calculator’. Insert the standardised loading for each item in the factor using the values from your CFA analysis. Coefficient H is automatically calculated using the formula provided by Hancock & Mueller. 

coefficient H Calculator  (16.7kB, EXCEL)

Nmax

Nmax is a new protocol for estimating the number of participants required in a study. It focuses on how strongly multicollinear all predictors in a model are. The procedure is described in:

Hancock, G. R., & Feng, Y. (2026). nmax and the quest to restore caution, integrity, and practicality to the sample size planning process. Psychological Methods, 31(1), 174–199. https://doi.org/10.1037/met0000776

The downloadable xlsx file ‘nmax calculator’ already has the lamda noncentrality parameter for alpha=.05, power=.80 inserted as = 7.849. You can only change gamma (the effect size estimate) and rho c (the estimate of multicollinearity among predictors). Once you set those values, the calculator provides your sample required. The example file is set at gamma=.25 (a small effect) and rho c=.70 (a modest intercorrelation among predictors) and gives a maximum sample = 244. Make changes based on your goals and literature. 

nmax calculator (20 kB, EXCEL) 

 

 

 

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