This exercise uses the two-parameter model to illustrate the joint effect of item difficulty and item discrimination upon the shape of item characteristic curve.

(a) Set the values of the item difficulty parameter to b D 2:0 and the item discrimination parameter to 1:0. Type in the following command line:

> icccal(b=-2.0, a=1.0)

(b) The computer will display the table of computations. Study the table for a few minutes to see the relation between the probability of correct response and the ability scores.

(c) The item characteristic curve will be displayed on the screen by typing in the following command line:

> icc(b=-2.0, a=1.0)

(d) The item characteristic curve is located in the low-ability end of the scale and it is moderately steep.

(e) Next, we want to put another item characteristic curve on the same graph.

Type in the following command line:

> par(new=T)

(f) Now set the item difficulty parameter to a value of b D 0:0 and the item discrimination parameter to a value of a D 1:5. Then repeat steps a through c.

(g) This will place a second curve on the graph.

(h) Now repeat steps e through f using the value of b D 2:0 for the item difficulty parameter and the value a D 0:5 for the item discrimination parameter.

(i) You should now have three item characteristic curves displayed on the same graph. It should be clear that the value of b locates the item on the ability scale and that a defines the slope. However, in the present example the curves cross because the values of a are different for each item.
(j) At this juncture Exercise 2 is completed.