A conceptual introduction to psychometrics
Chapter 6
Classical analysis of item scores
The conventional way of scoring items is by assigning ordinal numbers to the response categories.
Usually, these item scores are ordered with respect to the attribute that the item is assumed to measure. But, these assignment of these ordinal numbers lacks a theoretical justification.
Usually, the analysis of test scores is supplemented by an analysis of the item scores.
The scores of a given item have a distribution in a population of N persons.
- Location: the place of the scale where item scores are centered
- Dispersion: the scatter of the item scores
- Shape: the form of the distributions
Classical item difficulty and attractiveness
The location of the item score distribution is used to define the classical item difficulty (maximum performance tests) and classical item attractiveness (typical performance tests) concepts.
- Classical item difficulty: a parameter that indicates the location of the item score distribution in a population of persons.
- Classical item attractiveness: a parameter that indicates the location of the item score distribution in a population of persons.
The two definitions are the same.
Classical item difficulty and attractiveness are defined in a population of persons.
Population-dependent and may differ between populations.
The mean in mainly used for this.
The mean of a dichotomously scored item is called the item p-value.
Item score variance and standard deviation
The most common parameters that are used in classical item score analysis are the variance and the standard deviation of the item scores.
Items that have a small item score variance, have little effect on the test score variance.
The variance of dichotomous item scores is a function of the item p-value.
For a given sample size, the variance has its maximum value at p=.5.
Location and dispersion parameters yield useful information on the items of a test.
But, these parameters do not indicate the extent to which an item contributes to the aim of a test to assess individual differences in the attribute that is measured by the test.
Classical item discrimination: a parameter that indicates the extent to which the item differentiates between the true test scores of a population of persons.
Defined in a population of persons, may vary between different populations.
The item-test and item-rest correlations
An appropriate index for discrimination between the true scores would be the product moment correlation between the item score and the true score in the population of persons.
Test taker j’s observed
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