Obtain the test characteristic curve for a test with five items using the following item difficulty and item discrimination parameters:

b1 D 1:0 b2 D 1:0 b3 D 1:0 b4 D 1:0 b5 D 1:0 a1 D 1:6 a2 D 1:9 a3 D 1:6 a4 D 1:9 a5 D 1:6 The majority of the test characteristic curve is compressed into a rather small section of the ability scale. Up to an ability level of 1 the true score is nearly zero. Beyond an ability level of 2:5, the true score is approaching a value of J.

Between these two limits, the curve has a definite S-shape and the steep slope reflects the high values of the item discrimination parameters. The mid true score of 2:5 occurs at an ability level of 1:0. Notice how the difference in average level of item discrimination parameters in these last two problems shows in the difference of the steepness of the two curves.