Novometrics vs. Yule’s Q: Voter Turnout and Organizational Membership

Paul R. Yarnold

Optimal Data Analysis, LLC

A popular legacy index of association for 2×2 tables that is based on the odds ratio (OR), Yule’s Q=(OR–1)/(OR+1). Yule’s Q ranges between -1.00 and 1.00, with the value 0 indicating no association. Prior research assessing the association between voting behavior (0=not a voter; 1= voter) and the number of one’s organizational memberships (0=no memberships; 1=at least one membership) reported that Q=0.434, and “…the odds of voting among persons belonging to organizations (is) more than 2.5 times greater than the voting odds among those respondents without memberships” (p. 11). These data were analyzed using exploratory novometrics, treating voting behavior as a class variable and number of organizational memberships as an ordered attribute.

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Novometric Analysis Predicting Voter Turnout: Race, Education, and Organizational Membership Status

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled voter turnout (“not voted”=0; “voted”=1) as a function of race (“white”=1; “black”=2), education (“less than high school”=1; “high school graduate”=2; “college”=3), and memberships in organizations (“none”=0; “one or more”=1) via log-linear analysis. Results revealed: “…in the absence of a confirmatory analysis with another sample and in the absence of any compelling theoretical argument for expecting the particular three-variable interaction, (our own preference) would be to choose the more parsimonious model 28, {MER}{MV}{EV}. That model gives a satisfactory fit to the full crosstabulation (L2=4.76, df=5, p<0.45) without resort to a complex three-variable interaction. It also omits the race-turnout effect which is known to be trivial, but which would have to be included in model 34 because it is subsumed in hierarchical relation to the {ERV} term” (p. 40). Exploratory novometric analysis is used to model voter turnout (binary class variable) as a function of race (a categorical attribute), education and number of organizational memberships (both treated as ordered attributes measured on categorical ordinal scales).

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Comparing MMPI-2 F-K Index Normative Data among Male and Female Psychiatric and Head-Injured Patients, Individuals Seeking Disability Benefits, Police and Priest Job Applicants, and Substance Abusers

Paul R. Yarnold

Optimal Data Analysis, LLC

Used as a validity indicator with the MMPI-2, the F-K Index helps to identify people who may over- or under-report psychological issues. Prior research obtained normative data on this index for males and females sampled in a variety of settings, and visual examination of resulting score distributions suggested: “The F-K score distributions appear to differ across the different samples of diagnostic and job applicant samples, as the clinical profiles of these groups would be expected to differ from one another. …Thus, no single set of cutoff scores should be used to judge the motivation or validity of clinical profiles of subjects from different clinical or normative populations” (p. 9). Exploratory novometric analysis is used to predict F-K score as a function of gender and setting in order to establish the existence and assess the strength of the hypothesized inter-sample differences in F-K score distributions.

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Novometrics vs. Polychoric Correlation: Number of Lambs Born Over Two Years

Paul R. Yarnold

Optimal Data Analysis, LLC

This study assesses the agreement between the number of lambs born to 227 ewes over two consecutive years. Polychoric correlation could not be validly used to assess agreement because underlying distributional assumptions were violated. Requiring no such distributional assumptions, prior analysis via ODA identified moderate, statistically significant agreement. Novometric analysis conducted presently identified the globally-optimal model for this application.

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Novometric Analysis vs. MANOVA: MMPI Codetype, Gender, Setting, and the MacAndrew Alcoholism Scale

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research examined scores on the MacAndrew Alcoholism (MAC) scale for three Minnesota Multiphasic Personality Inventory (MMPI) codetypes within three samples: psychiatric inpatients and outpatients; medical outpatients referred for a psychiatric evaluation; and alcoholic inpatients. Analysis via factorial MANOVA revealed: “Mean MAC scores varied drastically as a function of MMPI codetype, gender, and the specific setting in which the MMPI was administered. These large variations in MAC scores suggest that the use of a single cutting score, typically a raw score of 24 or higher, may be inappropriate” (p. 39). These findings obtained by MANOVA are compared with the findings of novometric statistical analysis for this application.

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Using Novometrics to Disentangle Complete Sets of Sign-Test-Based Multiple-Comparison Findings

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior empirical comparison of the timeline follow-back (TLFB, dummy-coded as 1) vs. Drinker Profile (DP, coded as 2) methods of quantifying alcohol consumption in treatment research reported pairwise sign tests comparing these methods separately on four categorical ordinal outcomes: abstinent=1; light=2; moderate=3; heavy=4. It was concluded: “The direction of differences for the abstinent and medium categories approached significance (with unprotected alpha criterion at .05) with the DP more often yielding higher estimates of abstinent days and lower estimates of medium days. The DP significantly more often yielded lower estimates of light days” (p. 27). This example is used to illustrate the use of novometric analysis to disentangle complete sets of sign-test-based pairwise comparison outcomes, including ties.

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