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Termination criterion Calibrated item pool[ edit ] A pool of items must be available for the CAT to choose from. The pool must be calibrated with a psychometric model, which is used as a basis for the remaining four components. Typically, item response theory is employed as the psychometric model.
Starting point[ edit ] In CAT, items are selected based on the examinee's performance up to a given point in the test. However, the CAT is obviously not able to make any specific estimate of examinee ability when no items have been administered.
So some other initial estimate of examinee ability is necessary. If some previous information regarding the examinee is known, it can be used,  but often the CAT just assumes that the examinee is of average ability - hence the first item often being of medium difficulty.
Item selection algorithm[ edit ] As mentioned previously, item response theory places examinees and items on the same metric. Therefore, if the CAT has an estimate of examinee ability, it is able to select an item that is most appropriate for that estimate.
Scoring procedure[ edit ] After an item is administered, the CAT updates its estimate of the examinee's ability level.
If the examinee answered the item correctly, the CAT will likely estimate their ability to be somewhat higher, and vice versa. This is done by using the item response function from item response theory to obtain a likelihood function of the examinee's ability. Two methods for this are called maximum likelihood estimation and Bayesian estimation.
The latter assumes an a priori distribution of examinee ability, and has two commonly used estimators: This will continue until the item pool is exhausted unless a termination criterion is incorporated into the CAT.
Often, the test is terminated when the examinee's standard error of measurement falls below a certain user-specified value, hence the statement above that an advantage is that examinee scores will be uniformly precise or "equiprecise. This includes the common "mastery test" where the two classifications are "pass" and "fail," but also includes situations where there are three or more classifications, such as "Insufficient," "Basic," and "Advanced" levels of knowledge or competency.
For example, a new termination criterion and scoring algorithm must be applied that classifies the examinee into a category rather than providing a point estimate of ability.
There are two primary methodologies available for this. The more prominent of the two is the sequential probability ratio test SPRT. Note that this is a point hypothesis formulation rather than a composite hypothesis formulation  that is more conceptually appropriate.
A composite hypothesis formulation would be that the examinee's ability is in the region above the cutscore or the region below the cutscore. A confidence interval approach is also used, where after each item is administered, the algorithm determines the probability that the examinee's true-score is above or below the passing score.
This approach was originally called "adaptive mastery testing"  but it can be applied to non-adaptive item selection and classification situations of two or more cutscores the typical mastery test has a single cutscore. Otherwise, it would be possible for an examinee with ability very close to the cutscore to be administered every item in the bank without the algorithm making a decision.
The item selection algorithm utilized depends on the termination criterion.
Maximizing information at the cutscore is more appropriate for the SPRT because it maximizes the difference in the probabilities used in the likelihood ratio. For example, CAT exams must usually meet content specifications;  a verbal exam may need to be composed of equal numbers of analogies, fill-in-the-blank and synonym item types.
CATs typically have some form of item exposure constraints,  to prevent the most informative items from being over-exposed.We carry a wide selection of diagnostic equipment for your every need, including products from Noregon, Nexiq, and other brands.
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