Generalized Linear Interactive Modeling: Four Wrongs Don’t Make a Right

Paul R. Yarnold

Optimal Data Analysis, LLC

Several examples used to illustrate generalized linear interactive modeling violate crucial assumptions underlying chi-square, advocate arbitrary parsing of attributes, and conduct statistically unmotivated agglomeration of class categories. Violating assumptions call the validity of the estimated effect and associated Type I error rate into question, and arbitrary parsing and agglomerating procedures can reduce model classification accuracy at best, and mask effects that exist or identify paradoxical effects at worst.

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Chi-Square Corner Cells Test: Two Wrongs Don’t Make a Right

Paul R. Yarnold

Optimal Data Analysis, LLC

For an application involving two ordered attributes the chi-square four corner cells (CSFC) test is described as a “quick preliminary test” in lieu of factorial ANOVA. In this procedure a 2 x 2 contingency table is constructed using only the highest and lowest possible values of both measures: chi-square is used to obtain p, and phi to estimate the correlation between variables. The example used to illustrate this methodology violates two crucial assumptions underlying chi-square.

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UniODA vs. Doubly Incomplete Three- Factor ANOVA: Production Failure Attributable to Acid Corrosion

Paul R. Yarnold

Optimal Data Analysis, LLC

Production units for concentrating dilute acid are subject to failure as a result of corrosion. Seven units were selected from each of nine factories representing three groups according to the type of acid being concentrated. Productivity before failure was compared between type of acid and factory using doubly incomplete three-factor ANOVA that considers mean productivity across units, versus using UniODA that evaluates productivity of individual units.

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UniODA vs. Wilcoxon Rank Sum Test: A Small-Sample Paired Experiment

Paul R. Yarnold

Optimal Data Analysis, LLC

Consumer opinion of two competing brands of frozen dinners was rated by six independent purchasing managers, each using a 10-point Likert-type scale. Comparing ratings using the Wilcoxon rank sum test revealed no statistically significant difference between brands (p > 0.10). Using UniODA there was a statistically marginal (p < 0.072) relatively strong (ESS = 66.7) difference between brands in training analysis, that was stable and statistically significant (p < 0.031) in jackknife (leave-one-out) validity analysis.

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