Objectives

In practice, tests often include multiple sub-content areas. When a secondary form is constructed, equating is used to accommodate differences in difficulty overall, but forms may still differ in difficulty within sub-content areas. This study applies the FIPC method to dataset with confounding difficulty within dimensions, which is likely on an educational test.

Method

The data were constructed via a NEAT data collection design. The two groups had different ability distributions and were simulated for 1,000 examinees at four levels of correlation: 0, .3, .6, and .9.

For the 40 item specifications of the first test form were taken from the ACT Mathematics. Three additional forms had 32 items in common. The difficulty of a set of common items composed of items primarily measuring each dimension was manipulated. Some forms had an unequal total test difficulty, and others had an equal total test difficulty. Additionally, some forms had harder items measuring the first dimension and easier items measuring the second, while others did not have this confounding. The conditions were replicated 500 times. The estimated item parameters and ability were compared across forms using measures of bias.

Results

On forms 2 and 3, as the correlation is increased, RMSE of difficulty decreased, while RMSE of the discrimination tended to increased. The results on form 4 were not as strong. On the all forms, the ability was closer to the true ability on the second dimension. A detailed result will be provided in the full paper.

Significance

This is important because the appropriate linking and equating procedure is needed for operational applications when the test has the sub-content area. Also this study could bring awareness to consequences of FIPC equating on test forms with differences overall or within sub-content areas.