Stanine scores are a way to rescale raw scores into a nine point scale. This nine point scale provides an easy way to compare individuals without worrying about small differences in raw score. Stanine scores are typically used with standardized testing and are often reported on the results along with raw scores.

## Example Data

We will see an example of how to calculate stanine scores for a sample data set. There are 100 scores in the table below that are from a population that is normally distributed with a mean of 400 and a standard deviation of 25. The scores have been ranked in ascending order as

351 | 380 | 392 | 407 | 421 |

351 | 381 | 394 | 408 | 421 |

353 | 384 | 395 | 408 | 422 |

354 | 385 | 397 | 409 | 423 |

356 | 385 | 398 | 410 | 425 |

356 | 385 | 398 | 410 | 425 |

360 | 385 | 399 | 410 | 426 |

362 | 386 | 401 | 410 | 426 |

364 | 386 | 401 | 411 | 427 |

365 | 387 | 401 | 412 | 430 |

365 | 387 | 401 | 412 | 431 |

366 | 387 | 403 | 412 | 433 |

368 | 387 | 403 | 413 | 436 |

370 | 388 | 403 | 413 | 440 |

370 | 388 | 403 | 413 | 441 |

371 | 390 | 404 | 414 | 445 |

372 | 390 | 404 | 415 | 449 |

372 | 390 | 405 | 417 | 452 |

376 | 390 | 406 | 418 | 452 |

377 | 391 | 406 | 420 | 455 |

## Calculation of Stanine Scores

We will see how to determine which raw scores become which stanine scores.

- The first 4% of ranked scores (raw scores 351-354) will be given a stanine score of 1.
- The next 7% of ranked scores (raw scores 356-365) will be given a stanine score of 2.
- The next 12% of ranked scores (raw scores 366-384) will be given a stanine score of 3.
- The next 17% of ranked scores (raw scores 385-391) will be given a stanine score of 4.
- The middle 20% of ranked scores (raw scores 392-406) will be given a stanine score of 5.
- The next 17% of ranked scores (raw scores 407-415) will be given a stanine score of 6.
- The next 12% of ranked scores (raw scores 417-427) will be given a stanine score of 7.
- The next 7% of ranked scores (raw scores 430-445) will be given a stanine score of 8.
- The next 4% of ranked scores (raw scores 449-455) will be given a stanine score of 9.

Now that the scores have been converted to a nine point scale, we can easily interpret them. A score of 5 is the midpoint and is the average score. Each point in the scale is 0.5 standard deviations away from the mean.