UniODA vs. Wilcoxon Rank-Sum Test: Invariance over Monotonic Transformations

Paul R. Yarnold

Optimal Data Analysis, LLC

A study compared ordinal scores between two groups (Ns = 9 and 8) using the Wilcoxon rank-sum test (p < 0.03). When the scores were compared using UniODA, p < 0.02, ESS = 66.7 (a relatively strong effect). While the Wilcoxon test is performed on ranks, UniODA is conducted using raw data. However, performing UniODA on the ranks yields identical results because UniODA is invariant over any monotonic transformation of the attribute.

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ESS as an Index of Decision Consistency

Paul R. Yarnold

Optimal Data Analysis, LLC

Decision consistency is “…appropriate for describing the degree of consistency that is realized when educational and psychological measures are used to make pass/fail decisions about examinees”. In this method a test or parallel form is administered twice and the pass/fail decision at each testing is cross-classified. The fraction (or percent) of overall agreement, and kappa, are used to index decision consistency, but both of these statistics have limitations overcome by the chance- and maximum-corrected ESS statistic.

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UniODA-Based Structural Decomposition vs. Legacy Linear Models: Statics and Dynamics of Intergenerational Occupational Mobility

Paul R. Yarnold

Optimal Data Analysis, LLC

Analysis assessed structure underlying the cross-classification of occupational category of N = 3,396 sons and fathers. A plethora of linear legacy models have been developed for these data, without a clearly superior solution emerging. Structural decomposition analysis identified four models that together yielded a very strong effect.

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Modeling Religious Mobility by UniODA-Based Structural Decomposition

Paul R. Yarnold

Optimal Data Analysis, LLC

Analysis assessed structure underlying the cross-classification of religious affiliation of N = 1,995 adults, and their religious affiliation when they were 14 years of age. Typically true when using legacy methods to model mobility applications, no satisfactory linear model was identified, encouraging the authors to comment: “It is difficult to conceive of other models that could shed light on this nominal-by-nominal mobility table, or for that matter, on other square tables of a similar kind.” UniODA-based structural decomposition revealed that the stability model (elements fall into the major diagonal of the table) fits the data very well, but the residual sample is too small to justify additional structural models due to insufficient statistical power.

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GO-CTA vs. Logit Models: Gender and Desirability of Divorce

Paul R. Yarnold

Optimal Data Analysis, LLC

In prior reseach a sample of N = 601 male and N = 783 female parents in unhappy relationships used a five-point Likert-type scale ranging from 0 (much better to divorce) to 4 (much worse to divorce) to respond to a survey item: “When a marriage is troubled and unhappy, do you think it is generally better for the children if the couple stays together or gets divorced?” No logit model achieved acceptable fit in modeling the responses of men and women on the desirability of divorce scale. GO-CTA revealed that a single model underlies the data, yielding a statistically significant but relatively weak effect.

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Reverse CTA vs. Five-Factor Factorial ANOVA: Purifying a Crystalline Product

Paul R. Yarnold

Optimal Data Analysis, LLC

A five-factor factorial experiment was conducted to assess aspects of the manufacturing process that affected product quality. All factors were binary, and each of the 32 cells in the design had N = 1. The findings of analyses using factorial ANOVA versus using reverse CTA to identify factors influencing quality are contrasted.

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UniODA-Based Structural Decomposition vs. Log-Linear Model: Statics and Dynamics of Intergenerational Class Mobility

Paul R. Yarnold

Optimal Data Analysis, LLC

Analysis assessed structure underlying the cross-classification of social class of N = 9,434 son’s aged 20-64 years, and their father’s social class when the son was 14 years of age. No satisfactory log-linear model was identified. UniODA-based structural decomposition analysis identified four models that together yielded a strong effect.

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Predicting Divorce: The Role of Gender, and of Pre- and Extra-Marital Sex

Paul R. Yarnold

Optimal Data Analysis, LLC

A survey-based study comparing N = 494 divorcees and N = 542 married people collected binary data for three attributes: respondent gender; if the respondent reported having pre-marital sex (PMS); and if the respondent reported having extra-marital sex (EMS). Analysis via globally-optimal CTA (GO-CTA) identified a moderately strong (ESS = 26.3) model that employed both sexual behavior attributes to correctly classify 83.4% of married and 42.9% of divorced people.

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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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