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In most contexts, the parameters of the model characterize the proficiency of the respondents and the difficulty of the items as locations on a continuous latent variable. For example, in educational tests, item parameters represent the difficulty of items while person parameters represent the ability or attainment level of people who are assessed.
Difficulty values, in theory, can range from -∞ to +∞; however in practice they rarely exceed ±3. Higher values are indicative of harder test items. Items exhibiting low b parameters are easy test items. [22] Another parameter that is estimated is a discrimination parameter designated a. This parameter pertains to an item's ability to ...
The name item response theory is due to the focus of the theory on the item, as opposed to the test-level focus of classical test theory. Thus IRT models the response of each examinee of a given ability to each item in the test. The term item is generic, covering all kinds of informative items.
The item-total correlation provides an index of the discrimination or differentiating power of the item, and is typically referred to as item discrimination. In addition, these statistics are calculated for each response of the oft-used multiple choice item, which are used to evaluate items and diagnose possible issues, such as a confusing ...
Difficulty level of the items (p), is assumed to be the same for each item, however, in practice, KR-21 can be applied by finding the average item difficulty across the entirety of the test. KR-21 tends to be a more conservative estimate of reliability than KR-20, which in turn is a more conservative estimate than Cronbach's α .
An example of the CPCs for an item with five categories, scored from 0 to 4, is shown in Figure 1. Figure 1: Rasch category probability curves for an item with five ordered categories. A given threshold partitions the continuum into regions above and below its location. The threshold corresponds with the location on a latent continuum at which ...
Weakly correlate with the totality of the remaining items, reflected in an increase in Cronbach's alpha if the item is eliminated from the test; In practical test construction, item analysis is an iterative process, and cannot be entirely automated. The psychometrician's judgement is required to determine whether the emerging set of items to be ...
For example, a 40-item vocabulary test could be split into two subtests, the first one made up of items 1 through 20 and the second made up of items 21 through 40. However, the responses from the first half may be systematically different from responses in the second half due to an increase in item difficulty and fatigue. [7]