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Madde güçlüğü ve birey yeteneği arasındaki matematiksel ilişki

Toplam puana göre değişen madde güçlük indeksleri (p'ler)

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Madde Tepki Kuramının Klasik Test Kuramına göre avantajaları

1.

Assuming the existence of a large pool of items all measuring the same trait, the estimate of an examinee's ability is independent of the particular sample of test items that are administered to the examinee,

2.

assuming the existence of a large population of examinees, thedescriptors of a test item (for example, item difficulty and discriminationindices) are independent of the particular sample of examinees drawn for thepurpose of calibrating the item 

3.

a statistic indicating the precisionwith which each examinee's ability is estimated is provided. This statistic isfree to vary from one examinee to another. Needless to say, the extent towhich the three advantages are gained in an application of an item responsemodel depends on the closeness of the "fit" between a set oftest data and themodel. If the fit is poor, these three desirable features either will not beobtained or will be obtained in a low degree.

4.

(This is more of a side benefit) An additional desirable featureis that the concept of parallel forms reliability is replaced by the concept of statistical estimation and associated standard errors.

Features of Item Response Models


When there is a close fit between the chosen item response model and the test data set of interest:
• Item parameter estimates are independent of the group of examinees used from
the population of examinees for whom the test was designed.
• Examinee ability estimates are independent of the particular choice of test items
used from the population of items which were calibrated.
• Precision of ability estimates are known.