Estimating true score in the compound binomial error model

Rand R. Wilcox

doi:10.1007/bf02293866

Confidence Intervals for Weighted Composite Scores Under the Compound Binomial Error Model

Journal of Educational Measurement ◽

10.1111/jedm.12168 ◽

2018 ◽

Vol 55 (1) ◽

pp. 152-172

Author(s):

Kyung Yong Kim ◽

Won-Chan Lee

Keyword(s):

Confidence Intervals ◽

Error Model ◽

Compound Binomial ◽

Composite Scores

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Relation of Statistically Significant, Abnormal, and Typical WAIS-R VIQ-PIQ Discrepancies to Full Scale IQs

European Journal of Psychological Assessment ◽

10.1027//1015-5759.16.2.107 ◽

2000 ◽

Vol 16 (2) ◽

pp. 107-114 ◽

Cited By ~ 3

Author(s):

Louis M. Hsu ◽

Judy Hayman ◽

Judith Koch ◽

Debbie Mandell

Keyword(s):

Graphical Method ◽

The United States ◽

Full Scale ◽

True Score ◽

Absolute Value ◽

Normative Population ◽

The Us ◽

The Mean ◽

And Performance ◽

Quadratic Models

Summary: In the United States' normative population for the WAIS-R, differences (Ds) between persons' verbal and performance IQs (VIQs and PIQs) tend to increase with an increase in full scale IQs (FSIQs). This suggests that norm-referenced interpretations of Ds should take FSIQs into account. Two new graphs are presented to facilitate this type of interpretation. One of these graphs estimates the mean of absolute values of D (called typical D) at each FSIQ level of the US normative population. The other graph estimates the absolute value of D that is exceeded only 5% of the time (called abnormal D) at each FSIQ level of this population. A graph for the identification of conventional “statistically significant Ds” (also called “reliable Ds”) is also presented. A reliable D is defined in the context of classical true score theory as an absolute D that is unlikely (p < .05) to be exceeded by a person whose true VIQ and PIQ are equal. As conventionally defined reliable Ds do not depend on the FSIQ. The graphs of typical and abnormal Ds are based on quadratic models of the relation of sizes of Ds to FSIQs. These models are generalizations of models described in Hsu (1996) . The new graphical method of identifying Abnormal Ds is compared to the conventional Payne-Jones method of identifying these Ds. Implications of the three juxtaposed graphs for the interpretation of VIQ-PIQ differences are discussed.

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Testing the Assumption of Uncorrelated Errors for Short Scales by Means of Structural Equation Modeling

Journal of Individual Differences ◽

10.1027/1614-0001/a000135 ◽

2014 ◽

Vol 35 (4) ◽

pp. 201-211 ◽

Cited By ~ 3

Author(s):

André Beauducel ◽

Anja Leue

Keyword(s):

Structural Equation Modeling ◽

Negative Correlation ◽

Structural Equation ◽

Error Score ◽

Classical Test Theory ◽

Test Theory ◽

Equation Modeling ◽

Eysenck Personality Questionnaire ◽

Personality Questionnaire ◽

True Score

It is shown that a minimal assumption should be added to the assumptions of Classical Test Theory (CTT) in order to have positive inter-item correlations, which are regarded as a basis for the aggregation of items. Moreover, it is shown that the assumption of zero correlations between the error score estimates is substantially violated in the population of individuals when the number of items is small. Instead, a negative correlation between error score estimates occurs. The reason for the negative correlation is that the error score estimates for different items of a scale are based on insufficient true score estimates when the number of items is small. A test of the assumption of uncorrelated error score estimates by means of structural equation modeling (SEM) is proposed that takes this effect into account. The SEM-based procedure is demonstrated by means of empirical examples based on the Edinburgh Handedness Inventory and the Eysenck Personality Questionnaire-Revised.

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A Modification of the Payne-Jones Method of Identifying Abnormal Differences in WISC-R Performance and Verbal IQ's

European Journal of Psychological Assessment ◽

10.1027/1015-5759.12.1.27 ◽

1996 ◽

Vol 12 (1) ◽

pp. 27-32 ◽

Cited By ~ 1

Author(s):

Louis M. Hsu

Keyword(s):

Full Scale ◽

True Score ◽

Verbal Iq ◽

Score Difference ◽

The Difference ◽

And Performance

The difference (D) between a person's Verbal IQ (VIQ) and Performance IQ (PIQ) has for some time been considered clinically meaningful ( Kaufman, 1976 , 1979 ; Matarazzo, 1990 , 1991 ; Matarazzo & Herman, 1985 ; Sattler, 1982 ; Wechsler, 1984 ). Particularly useful is information about the degree to which a difference (D) between scores is “abnormal” (i.e., deviant in a standardization group) as opposed to simply “reliable” (i.e., indicative of a true score difference) ( Mittenberg, Thompson, & Schwartz, 1991 ; Silverstein, 1981 ; Payne & Jones, 1957 ). Payne and Jones (1957) proposed a formula to identify “abnormal” differences, which has been used extensively in the literature, and which has generally yielded good approximations to empirically determined “abnormal” differences ( Silverstein, 1985 ; Matarazzo & Herman, 1985 ). However applications of this formula have not taken into account the dependence (demonstrated by Kaufman, 1976 , 1979 , and Matarazzo & Herman, 1985 ) of Ds on Full Scale IQs (FSIQs). This has led to overestimation of “abnormality” of Ds of high FSIQ children, and underestimation of “abnormality” of Ds of low FSIQ children. This article presents a formula for identification of abnormal WISC-R Ds, which overcomes these problems, by explicitly taking into account the dependence of Ds on FSIQs.

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