The Item Analysis Report

The following plots appear in Item Analysis reports.

Item characteristic curves for each question appear in the top section of the output. Initially, all curves are shown stacked in a single column. They can be rearranged using the Number of Plots Across command, found in the drop down menu of the report title bar. For Component Curves, four plots across are displayed.

Component Curves

A vertical red line is drawn at the inflection point of each curve. In addition, dots are drawn at the actual proportion correct for each ability level, providing a graphical method of judging goodness-of-fit.

Gray information curves show the amount of information each question contributes to the overall information of the test. The information curve is the slope of the ICC curve, which is maximized at the inflection point.

Elements of the ICC Display

Information Curves

Questions provide varying levels of information for different ability levels. The gray information curves for each item show the amount of information that each question contributes to the total information of the test. The total information of the test for the entire range of abilities is shown in the Information Plot section of the report (Information Plot).

Information Plot

Dual Plots

The information gained from item difficulty parameters in IRT models can be used to construct an increasing scale of questions, from easiest to hardest, on the same scale as the examinees. This structure gives information about which items are associated with low levels of the trait, and which are associated with high levels of the trait.

JMP shows this correspondence with a dual plot. The dual plot for this example is shown in Dual Plot.

Dual Plot

Questions are plotted to the left of the vertical dotted line, examinees on the right. In addition, a histogram of ability levels is appended to the right side of the plot.

This example shows a wide range of abilities. Q10 is rated as difficult, with an examinee needing to be around half a standard deviation above the mean in order to have a 50% chance of correctly answering the question. Other questions are distributed at lower ability levels, with Q11 and Q4 appearing as easier. There are some questions that are off the displayed scale (Q7 and Q14).

The estimated parameter estimates appear below the Dual Plot, as shown in Parameter Estimates.

Parameter Estimates

Item

Identifies the test item.

Difficulty

Is the b parameter from the model. A histogram of the difficulty parameters is shown beside the difficulty estimates.

Discrimination

Is the a parameter from the model, shown only for 2PL and 3PL models. A histogram of the discrimination parameters is shown beside the discrimination estimates.

Threshold

Is the c parameter from the model, shown only for 3PL models.