# Quality of norms

© Paul Cooijmans

## Explanation

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)/18

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 18 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