Score Translator

These conversions assume scores follow a normal curve. They hold for normed scores (percentiles, standard scores, T scores, NCEs, stanines, z scores), not raw scores or a publisher's scale score like RIT.

• Percentile to z uses the inverse of the normal curve; z to percentile uses the curve itself. A z of +1.00 is the 84th percentile.
• Standard score = 100 + 15z. T score = 50 + 10z. NCE = 50 + 21.06z, reported from 1 to 99.
• Stanines cut the curve at 4, 11, 23, 40, 60, 77, 89, and 96 percent. A stanine is a band, so it converts to a range.

Percentiles show as whole numbers from the 1st to the 99th. A score past either end shows as below the 1st or above the 99th, never rounded into the scale.

Ranges are fifths of the norm group: 1st to 20th low, 21st to 40th below average, 41st to 60th average, 61st to 80th above average, 81st to 99th high. A 49th and a 51st land in the same range on purpose, because test error is bigger than that gap.

The retest range assumes measurement error of about 0.2 standard deviations. Your test's technical manual lists its own.

Growth percentile ranges follow a common convention: 1 to 34 low, 35 to 65 typical, 66 to 99 high. Your state may use other cut points.

Grade equivalents: skip them. A 5.2 on a third-grade test means the student scored like a typical fifth grader would on the third-grade test. It does not mean the student is ready for fifth-grade work. Use the percentile instead.

A scale score can't be converted here. Percentiles depend on the grade, subject, season, and norm year, so that takes the publisher's own tables.