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Formula for Equating

  1. Define:
    • X = the mean raw score achieved on the new test form's scorable items based on response data from the parent form (Y)
    • sx = the standard deviation of the scorable items on X based on response data from the parent form (Y)
    • Y = the mean raw score achieved on the parent test form's scorable items
    • sy = the standard deviation of the scorable items on Y
    • Xi = a given raw score on the new test form
    • Yi = the raw score equivalent to Xi expressed in the raw score metric of form Y
  2. Set zx = zy

    Xi minus X over Sx equals Yi minus Y over Sy

  3. In order to find the equivalent raw cutscore on the new form, solve for Xi, where Yi = the raw cutscore on the parent form rounded to one decimal place.
    Xi = X + (sx/sy)(YiY)