Module 3 Lesson 4: Special Case Of Theta Flashcards
What is the IRT score?
The IRT score is a function of the examinee’s responses interacting with the characteristics of the items.
What is the IRT score usually called?
The IRT score is usually called theta (θ).
What is an example with how theta is applied?
Let’s say items are arranged in order of difficulty from left to right. The lower numbered items are very easy; the higher numbered items are very difficult. For example, if this were a test of arithmetic computation for elementary school students, item 1 might be 6 + 3 =, item 10 might be 740 − 698 =, and item 20 might be 0.56 × 1.05. Here we have simply labeled the items as easy, moderate, or hard. In an actual application, exact difficulty values would be used. (The test items need not be arranged in order of difficulty physically, but it is useful to show such an arrangement for our examples.) Each “x” in the figure represents a correct response. Mike is presented with items 1–10 and gets 7 items right. Ned is presented with items 11–20 and also gets 7 items right. Because Ned answered more difficult items, he receives a higher theta score, even though both examinees got 7 items right. Obviously, this procedure will not work unless the items are scaled on difficulty value first.
Theta has properties of which type of score? Raw or normed?
Both. Theta has some properties of a raw score and some properties of a normed score. It is like a raw score in that it is a relatively immediate result of examinee responses. Also, like a raw score, it has little meaning by itself. Theta is like a normed score in that it is not a simple summation of examinee responses. It depends not only on whether the answer is correct (or “Yes” or other such response) but also on the IRT values of the items to which responses are given.
What does theta do?
Theta locates the examinee on a trait or an ability presumed to underlie the total set of items in the test bank. However, the numerical values for the dimension are arbitrary and hence not easily interpreted.
How are theta numerical values established with?
Although theta numerical values are arbitrary, they are usually established with 0.00 as a central value and a range of about −4.0 to +4.0. Hence, they may look like z‐scores. However, they do not refer to a position within a well‐defined norm group.
How are theta values usually interpreted through?
Although theta values may be the immediate result of examinee responses in an IRT environment, in practice they are usually interpreted through use of the normed scores.
How are theta values interpreted through normed scores?
That is, they are converted to percentiles, standard scores, grade equivalents, and so on. In fact, in a test score report, one may be looking at a percentile or T‐score and not even realize that it is a transformation from a theta score rather than from a conventional raw score.
