# How is cut-score grading calculated?

Q: I print off my tests for students to take offline. How do I figure out their cut-­score based grade for a paper and pencil test?

You’ll have 2 different equations to use here, depending on whether the student’s raw score was above the cut score of the test or not.

1) The student scored below the cut score: The equation you’ll use here is (A x B)/C = Cut‐score based grade.

• A = the student's raw score (Let’s say they got a 51%, which you’d plug in as .51)
• B = the passing percentage for the test (If you said a 75% is a passing grade, then you’d enter .75)
• C = The Cut score of the test, which is the displayed average of the cut scores of all questions on the test (Let’s go with a .58)

So, (Raw Score multiplied by Passing Percentage for the test) divided by the cut score. This will result in (.51 x .75)/.58 = 0.659, or a 66%, which would be a failing grade.

2) The student scored above the cut score: The equation you’ll use is ((A ‐ C)/(1 ‐ C)) x (1 ‐ B) + B = Cut ‐ score based grade.

• A = The student's raw score (Let’s say they got an 84%, which you’d plug in as .84)
• B = The passing percentage for the test (If you said a 75% is a passing grade, then you’d enter .75)
• C = The Cut score of the test (Let’s go with a .58)

So, ((Raw Score minus Cut Score) divided by (1 minus Cut Score) multiplied by (1 minus Passing Percentage)) plus the Passing Percentage = Cut-­‐score based grade. This will result in ((.84 ‐ .58)/(1 ‐ .58)) x (1 ‐ .75) + .75 = .904, or a 90% passing grade.

Once you know the passing grade and cut score of your test, you can do some short cuts: ((Raw Score ‐ .58) /( .42)) x (.25) + .75 = Cut Score grade.