# 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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# UniODA vs. Point-Biserial Correlation: Marital Status and Need for Achievement

Paul R. Yarnold

Optimal Data Analysis, LLC

Scores of N = 8 single and N = 6 married people on a survey measure of need for achievement were compared by point-biserial correlation: r = 0.82, p < 0.05. Comparing scores of married and single people using UniODA yielded a perfect model: ESS = 100, p < 0.0006.

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# Knowing (ESS) and Not Knowing (D)

Paul R. Yarnold

Optimal Data Analysis, LLC

Taken together the ESS and D statistics elucidate a mystery that began with the discovery of statistical analysis.

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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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