# Quality of norms

Quality of norms reflects both the number of score pairs used in norming (N) and their mean correlation (r) with the object test; this statistic is in itself the best indicator of quality of norms:

Quality of norms (unscaled) = √N × r2

When selecting other tests for norming the object test, the threshold correlation is set so as to maximize the quality of norms; that is, it is set where the expression √N × r2 has its maximum. The result is that mainly tests with high correlations will be selected, and tests with low correlations will only be included when there are very many of them.

To allow combination of this statistic with other measures of test quality, a scaling from 0 to 1 is also provided as follows:

Quality of norms (scaled) = (Quality of norms (unscaled)) / divider

This method replaces the old one, the scaled values of which were becoming too high, and therefore less informative, as a result of the increasing amount of available norming data. The new scaled values are lower than the old ones. Whenever they become inflated in the future, the divider may be increased to solve this.

## Explanation (previous method)

Quality of norms reflects both the number of score pairs used in norming and their correlations with the object test; the weighted sum of correlations of the used tests is in itself the best indicator of quality of norms. To allow combination of this statistic with other measures of test quality, a scaling from 0 to 1 is also provided as follows:

Quality of norms (scaled) = √(weighted sum of correlations)/25

This method replaces the old one, the scaled values of which were becoming too high, and therefore less informative, as a result of the increasing amount of available norming data. The new scaled values are much lower than the old ones. Whenever they become inflated in the future, the divider may be increased to solve this.

## Explanation (old method)

Quality of norms reflects both the number of score pairs used in norming and their correlations with the object test; if the weighted sum of correlations of tests used in norming is 70 or lower, it is computed thus:

Quality of norms = (weighted sum)/70 × .9

If the weighted sum is larger than 70 but smaller than or equal to 140, it becomes:

Quality of norms = .9 + (weighted sum - 70)/70 × .09

If the weighted sum is larger than 140:

Quality of norms = .99 + (weighted sum - 140)/140 × .01