Scaled scores simplify score reports but are also a regular source of questions from candidates and program directors. ARRT uses scaled scores because they allow us to report the passing score as 75 no matter which items the candidate sees. In this week's article, we will address a couple misconceptions and show you a sample scaled score calculation from start to finish.
First, we determine the raw cut score for an exam by applying a psychometric model to each version of the exam. We determine the number of correct answers required to pass by comparing the standard (see: Setting Cut Scores) to the difficulty of each item on the form and sum the results. This process ensures that candidates must demonstrate the same ability to pass no matter which items are selected. For example, a form full of easy items would require a larger number of correct answers to pass than a form full of difficult items.
Misconception: Some items on ARRT exams are weighted more than others. Correction: Each correct answer contributes equally to a candidate's score. Caveat: For RA, the entire case study section is adjusted to ensure it makes up 25% of the available points. Each item within that section still contributes as much as any other.
Reporting a candidate's raw score is inconvenient because candidates would have to look up the raw cut score for their specific exam form to know whether they passed or failed. Instead, we scale the results so that the raw cut score equals 75 and a perfect score equals 99 by drawing a line between these two points and looking up each scaled score on the line.
As a hypothetical example, assume that the raw passing score is 130 out of 200. We first calculate the slope using the "rise over run" formula. Note that we go down to two decimals for scaled scores to account for rounding.
- slope = (max scaled score - passing scaled score) / (max raw score - passing raw score)
- 0.357 = (99.49 - 74.50) / (200 - 130)
Then, we calculate the intercept for the line with one of the known points.
- y = mx + b
- scaled score = (slope * raw score) + intercept
- 74.50 = (0.357 * 130) + intercept
- 74.50 - (0.357 * 130) = intercept
- 74.50 - (0.357 * 130) = 28.09
Equipped with both the slope (0.357) and intercept (28.09), we can now determine the scaled score:
- (0.357 * raw score) + 28.09 = scaled score
- (0.357 * 128) + 28.09 = 73.786 (rounds up to 74)
- (0.357 * 129) + 28.09 = 74.143 (rounds down to 74)
- (0.357 * 130) + 28.09 = 74.5 (rounds up to 75)
- (0.357 * 131) + 28.09 = 74.857 (rounds up to 75)
- (0.357 * 132) + 28.09 = 75.214 (rounds down to 75)
Misconception: Candidates must answer 75% of the exam items correctly to pass. Correction: Scaled scores are not percentages; the percentage required to pass varies by form.
