# Proportion outscored

© Paul Cooijmans

## Explanation

Proportion outscored is a number between (inclusive) 0 and 1 that is computed for each particular protonorm as follows: Take the number of achieved scores lower than that norm; add to that *half* the number of scores with exactly that norm; divide by the total number of scores. Use just enough decimals to retain the information present in the sample; for instance, if the sample contains in the hundreds of scores, three decimals are needed (round to nearest thousandth) to describe the distribution of the sample.

Proportion outscored is computed by combining the scores of several selected tests, to obtain representative proportions. Proportions outscored of one particular test are not representative, as different tests draw different groups of candidates; the experience is that the harder a test is, the fewer candidates take it, the higher their average intelligence, and the smaller their internal spread.

Proportion outscored is a generalized form of quantile. It can be converted to any quantile; to obtain milliles, round to the nearest thousandth; for centiles, to the nearest hundredth; for vigintiles, to the nearest twentieth; for deciles, the nearest tenth; for quintiles, the nearest fifth; for quartiles, the nearest fourth; for the median, the nearest half.