Popup window

Print this page

Calculation of Recommended Performance Levels

For the multiple-choice section the panel-based recommended performance level was calculated as follows:

  1. Find the median value of all panelists' ratings for each scorable multiple-choice item on the test form.
  2. Sum the median values for all scorable items on a form and divide by 100. The results were rounded to the nearest integer to provide a panel-based, multiple-choice section performance level.

For the open-response section the recommended performance level was calculated as follows:

  1. Find the median value of all panelists' Round II ratings for the open-response section.
  2. Round to the nearest integer to obtain a score point value on the scale 2 through 8, 2 through 16, or 2 through 40, depending on the scale for the field.

The item median was computed using the following formula.

  1. The following formula was used:

    Md equals Lm plus w times n over 2 minus cumf divided by function M

  2. where LM is the lower limit of the category that contains the middle score, w is the width of the category that contains the middle score, n is the total number of scores, cumf is the total number of scores that fall below the score category that contains the middle score, and fM is the number of scores in the score category that contains the middle score.
  3. For open-response items, the input to the formula are the ratings (e.g., 2, 3, 4...16) given by the raters for the set of open-response items.
  4. For multiple-choice items, the input to the formula are the ratings (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) given by the raters for the multiple-choice item. The median is calculated for each item using the formula above, rounded to one decimal place, and then translated to the 0–100 scale using the following transformation formula: Md Tran = 10Md − 5
  5. For example, an item with a median rating of 7.2 would have a transformed median of 67 on the 0–100 scale.