Tolerance Intervals for True Scores

1985 ◽  
Vol 10 (1) ◽  
pp. 1-17 ◽  
Author(s):  
David Jarjoura
Keyword(s):  
Confidence Intervals ◽  
Practical Implication ◽  
Educational Measurement ◽  
True Score ◽  
Tolerance Intervals ◽  
Observed Score ◽  
True Scores

Issues regarding tolerance and confidence intervals are discussed within the context of educational measurement and conceptual distinctions are drawn between these two types of intervals. Points are raised about the advantages of tolerance intervals when the focus is on a particular observed score rather than a particular examinee. Because tolerance intervals depend on strong true score models, a practical implication of the study is that true score tolerance intervals are fairly insensitive to differences in assumptions among the five models studied.

Interpretation of the Standard Error of Measurement when True Scores and Error Scores on Mental Tests are Not Independent

1966 ◽  
Vol 19 (2) ◽  
pp. 611-617 ◽  
Author(s):  
Donald W. Zimmerman ◽  
Richard H. Williams
Keyword(s):  
Standard Deviation ◽  
Standard Error ◽  
Test Score ◽  
Test Reliability ◽  
True Score ◽  
Observed Score ◽  
Standard Error Of Measurement ◽  
True Scores ◽  
Modified Equation ◽  
Error Of Measurement

It is shown that for the case of non-independence of true scores and error scores interpretation of the standard error of measurement is modified in two ways. First, the standard deviation of the distribution of error scores is given by a modified equation. Second, the confidence interval for true score varies with the individual's observed score. It is shown that the equation, so=√[(N−O/a]+[so2(roō−roo)/roō]̄, where N is the number of items, O is the individual's observed score, a is the number of choices per item, so2 is observed variance, roo is test reliability as empirically determined, and roō is reliability for the case where only non-independent error is present, provides a more accurate interpretation of the test score of an individual.

Two Concepts of “True Score” in Test Theory

1975 ◽  
Vol 36 (3) ◽  
pp. 795-805 ◽  
Author(s):  
Donald W. Zimmerman
Keyword(s):  
Probability Space ◽  
Expected Value ◽  
Test Theory ◽  
The Other ◽  
True Score ◽  
Explicit Formulas ◽  
True Variance ◽  
Points Of View ◽  
Observed Score ◽  
True Scores

Two concepts of “true score” in test theory are examined. Under one concept, the true score is identified with the expected value of the observed score, and it follows that reliability is the ratio of true variance to observed variance. Under the other concept, the true score is a constant which is not necessarily equal to the expected value of the observed score, and it follows that reliability is not necessarily equal to the ratio of true variance to observed variance. Axioms are presented which encompass both points of view, and explicit formulas relating the two kinds of true scores are derived by representing all scores and components of scores as random variables with the same associated probability space.

Tolerance Intervals for True Scores

1985 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
David Jarjoura
Keyword(s):  
Tolerance Intervals ◽  
True Scores

scholarly journals Are Measures of Character and Personality Distinct? Evidence From Observed-Score and True-Score Analyses

Assessment ◽  
2017 ◽  
Vol 27 (1) ◽  
pp. 117-135 ◽  
Author(s):  
Robert E. McGrath ◽  
Ashley Hall-Simmonds ◽  
Lewis R. Goldberg
Keyword(s):  
Character Strengths ◽  
Community Sample ◽  
Mechanical Turk ◽  
True Score ◽  
Personality Inventories ◽  
Personality Facets ◽  
Observed Score ◽  
Via Classification ◽  
Criterion Variables

Two studies were conducted to investigate redundancy between the character strengths found in the VIA model of character and familiar personality facets. Study 1 used a community sample ( N = 606) that completed a measure of character strengths, four personality inventories, and 17 criterion measures. The second study used Mechanical Turk workers ( N = 498) who completed measures of the HEXACO and VIA models and 111 criterion variables. Analyses were conducted using both observed scores and true score estimates, evaluating both predictive and conceptual overlap. Eight of 24 VIA scales proved to be largely redundant with one HEXACO personality facet, but only one VIA scale (Appreciation of Beauty) was largely redundant with Five Factor facets. All strength scales except Spirituality overlapped substantially with at least one personality facet. The results suggest the VIA Classification variables are strongly related to commonly measured personality facets, but the two models are not redundant.

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