This exercise uses the Rasch model to illustrate how the item difficulty parameter locates an item along the ability scale.

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

> icccal(b=-2.0)

(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)

(d) This item will function at an ability level of 2:0 and the curve will be moderately steep at that ability level. Study the plot.

(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 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.
(i) Now there will be three item characteristic curves on the graph. The three dotted lines indicate the values of P. / D 0:5 of these curves at the ability levels defined by their values of item difficulty parameters. In the present example the values of the item difficulty parameters are evenly spaced along the ability scale.
(j) At this juncture Exercise 1 is completed.