*observed change in average scores*divided by

*the standard deviation (a measure of how spread out the scores are) of the scores*. There are more nuanced and complicated versions of this formula, but they all build on the same principles. So, what effect size tells you is the number of standard deviations that the scores changed by. Let’s unpack that a bit:

- If the group has, on average, increased its average scores a lot, the effect size will be larger.
- The more the group’s scores are spread out, the smaller the effect size.

- from 10, 20, 30, 40, 50
- to 20, 30, 40, 50, 60

- from 18, 19, 20, 21, 22
- to 28, 29, 30, 31, 32

**big**problem with the way many people use the statistics. Every year a class of students would expect to improve their scores on some standard test (assuming they learn something during that year). When researchers have looked at the average Effect Sizes of these year-on-year changes in the USA from a battery of different standard tests they found the following: 1 – 21.522 – 30.973 – 40.64 – 50.365 – 60.406 – 70.327 – 80.238 – 90.269 – 100.2410 – 110.1911 – 120.1912 – 130.06

Year | Effect Size |
---|---|

1 – 2 | 1.52 |

2 – 3 | 0.97 |

3 – 4 | 0.64 |

4 – 5 | 0.36 |

5 – 6 | 0.40 |

6 – 7 | 0.32 |

7 – 8 | 0.23 |

8 – 9 | 0.26 |

9 – 10 | 0.24 |

10 – 11 | 0.19 |

11 – 12 | 0.19 |

12 – 13 | 0.06 |

- School pupils make less improvement each year, and these numbers genuinely reflect a full year of average progress
- As classes progress, their results get more and more spread out (i.e. the slowest-learning pupils’ scores get further and further below the fastest-learning pupils) which makes the standard deviation much, much bigger and therefore Effect Sizes get smaller
- As classes progress, they have less progress to make on these standardised tests. In the first year they go from knowing no answers to a few, whereas in the last year they know nearly everything so there aren’t many more answers they can improve on.

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