4. The Test Characteristic Curve

Item response theory is based upon the individual items of a test, and up to this point the chapters have dealt with the items one at a time. Now, attention will be given to dealing with all the items in a test at once. When scoring a test, the response made by an examinee to each item is dichotomously scored. A correct response is given a score of 1 and an incorrect response a score of 0; the examinee’s raw test score is obtained by adding up the item scores. This raw test score will always be an integer number and will range from 0 to J, where J is the number of items in the test. If examinees were to take the test again, assuming they did not remember how they previously answered the items, a different raw test score would be obtained. Hypothetically, an examinee could take the test a great many times and obtain a variety of test scores. One would anticipate that these scores would cluster themselves around some average value. In measurement theory, this value is known as the true score and its definition depends upon the particular measurement theory. In item response theory, the definition of a true score according to D.N. Lawley is used.