Illustrating How 95% Confidence Intervals Indicate Model Redundancy

Paul R. Yarnold

Optimal Data Analysis, LLC

In novometric analysis exact 95% confidence intervals (CIs) are computed for overall model performance and for model endpoints. When CIs overlap for two or more endpoints a model is said to be redundant, meaning that the domain of the outcome cannot be distinguished between overlapping endpoints. This research note provides an illustration of model redundancy.

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What Most Dissatisfies Emergency Department Patients?

Paul R. Yarnold

Optimal Data Analysis, LLC

Novometric analysis is used to determine aspects of care which induce greatest dissatisfaction among Emergency Department (ED) patients. Data were obtained from a satisfaction survey on which responses were obtained using five-point Likert-type scales. The first analysis discriminated 131 strongly dissatisfied and 114 moderately dissatisfied patients, and the second analysis discriminated 182 patients who were very unlikely and 92 patients who were moderately unlikely to recommend the ED to others. Maximum dissatisfaction was associated with perceived inadequacy of physician explanation of one’s illness or injury, and minimum likelihood of recommending the ED to others was associated with extreme dissatisfaction with time spent in the treatment area waiting to see the physician.

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Increasing the Likelihood of an Ambivalent Patient Recommending the Emergency Department to Others

Paul R. Yarnold

Optimal Data Analysis, LLC

Novometric analysis is used to discriminate 239 ambivalent versus 584 discharged patients who are likely to recommend the Emergency Department (ED) to others. Findings reveal the critical factors are physician explanation of tests and treatment, and attention paid to the patient by the nurse.

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What Influences Patients to Recommend an Emergency Department to Others?

Paul R. Yarnold

Optimal Data Analysis, LLC

Recent research reported that an Emergency Department (ED) patient’s ratings of how well the physician explained one’s illness or injury is the best discriminator of extreme satisfaction versus extreme dissatisfaction ratings regarding care received in the ED. The present study uses novometric analysis to discriminate 1,012 ED patients who are highly likely, versus 182 who are highly unlikely, to recommend the ED to others. Although ratings of satisfaction and likelihood to recommend are nearly perfectly related, novometry reveals that the best discriminator of ratings of extreme likelihood to recommend versus not to recommend the ED to others is waiting time in the treatment area before being seen by one’s physician.

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Globally Optimal Statistical Models, II: Unrestricted Class Variable, Two or More Attributes

Paul R. Yarnold & Robert C. Soltysik

Optimal Data Analysis, LLC

Novometrics—meaning new (Latin: novo) measurement, connotes a newly discovered theoretically-motivated algorithm that explicitly identifies the globally-optimal (GO) statistical model underlying any random statistical sample, indicated as S. Originating from the field of operations research, “optimal” denotes explicitly maximized (weighted) classification accuracy for S: that is, predicting the class category (“dependent variable”) of (weighted) observations in S as accurately as is theoretically possible for S. Novometry identifies the nature and strength of the GO relationship between a class variable and one or more attributes (“independent variables”) for S, where nature and strength are characterized by the number and homogeneity of discrete sample strata which are identified by the GO statistical model. Models maximizing ESS (a normed index of effect strength) and efficiency (ESS/number of strata, a normed index of parsimony) prevent over-fitting and promote cross-generalizability when using the model to classify an independent random S. The present article demonstrates novometry for two applications involving multiple attributes. The first study models a binary measure of patient satisfaction with care received in the Emergency Department (ED) using survey ratings of administration, nurse, physician, lab, and care of family and friends, for 2,198 ED patients. The second study ascertains the effect of atmospheric pressure on fibromyalgia symptoms recorded by a single individual over 297 sequential days.

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Globally Optimal Statistical Classification Models, I: Binary Class Variable, One Ordered Attribute

Paul R. Yarnold & Robert C. Soltysik

Optimal Data Analysis, LLC

Imagine a random sample S consisting of a class variable (“dependent measure”), one or more attrib­utes (“independent measures”), a weight (unit-weighted obser­vations are equally-valued), and a number of observations N yielding at least minimally ade­quate statistical power for testing the a priori or post hoc hypothesis that the attributes predict the class variable. The null hypothesis is the attributes can’t predict the class varia­ble. A statistical model is identified for S that optimally (most accurately) predicts the (weighted) class variable on the basis of the attributes. This is the first axiom underlying novometrics—meaning new (Latin: novo) measure­ment, and connoting a newly dis­covered theoretically-motivated algorithm that explicitly identifies the globally-optimal (GO) statistical model(s) underlying S. Originating from operations research, “optimal” as used here denotes explicitly maximized (weighted) classification accuracy for S: that is, predicting the class category of (weighted) observations in S as accurately as is theoreti­cally possible for S. Novometry identifies the nature and strength of the GO relation­ship(s) between a class variable and one or more at­trib­utes for S, where nature and strength are char­acter­ized by the number and homo­geneity of discrete sample strata identified by GO statistical model(s). Models maximizing ESS (a normed index of effect strength) and efficiency (ESS/number of strata, a normed index of parsimony) prevent over-fitting and promote cross-generalizability when using the model to classify an independent random S. This article demonstrates novometry for elemental applications involving one binary class variable and one ordered attribute. Using data from the Surveillance, Epidemiology, and End Results (SEER) Program, cancer incidence is parsed separately by sex (male, female) and by race (white, African American) to ascertain whether these class variables identify dis­crete patient strata dif­fering in cancer in­cidence.

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