By Ronald K. Hambleton

ISBN-10: 9048158095

ISBN-13: 9789048158096

ISBN-10: 9401719888

ISBN-13: 9789401719889

In the last decade of the Seventies, merchandise reaction concept turned the dominant subject for research via dimension experts. yet, the genesis of merchandise reaction conception (IRT) may be traced again to the mid-thirties and early forties. in reality, the time period "Item attribute Curve," that is one of many major IRT strategies, will be attributed to Ledyard Tucker in 1946. regardless of those early study efforts, curiosity in merchandise reaction concept lay dormant until eventually the overdue Sixties and took a backseat to the rising improvement of robust actual rating concept. whereas precise rating idea constructed quickly and drew the eye of major psychometricians, the issues and weaknesses inherent in its formula started to elevate matters. Such difficulties because the loss of invariance of merchandise parameters throughout examinee teams, and the inadequacy of classical try systems to notice merchandise bias or to supply a legitimate foundation for size in "tailored testing," gave upward thrust to a resurgence of curiosity in merchandise reaction conception. Impetus for the advance of merchandise reaction conception as we now are aware of it was once supplied by way of Frederic M. Lord via his pioneering works (Lord, 1952; 1953a, 1953b). The growth within the fifties was once painstakingly gradual a result of mathematical complexity of the subject and the nonexistence of laptop programs.

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Notice that there is a spread of test scores about the regression line. The variability is probably due, mainly, to measurement errors in the test scores. The distribution of test scores at each ability level is known as the conditional distribution of test scores for an ability level. N ext, consider the nonlinear regression lines for several subpopulations of examinees. These conditional distributions for the r subpopulations (r = 3 in figure 2-2) will be identical if the test is unidimensional.

Except in the simple and unlikely situation in which 50 percent of the candidates receive each score for each variable, the computational formula for the tetrachoric correlation is very complex and, except in some special cases, involves numerical integration techniques. Tetrachoric correlations have one attractive feature: A sufficient condition for the unidimensionality of a set of items is that the matrix of tetrachoric item intercorrelations has only one common factor (Lord & Novick, 1968).

Even free-response data can be subjected to a dichotomous scoring system. The majority of the presently available item response models handle binary-scored data. To use these models, we sometimes force a binary scoring system on multichotomous response data. This may be done by combining the available scoring categories so that only two are used. Somewhat less common in present measurement practices are multichotomous or polychotomous scoring systems. These systems arise, for example, when scoring weights are attached to the possible responses to multiple-choice test items.

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Item Response Theory: Principles and Applications by Ronald K. Hambleton

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