# Hardness

© Paul Cooijmans

## Explanation

Hardness is the proportion of the possible raw score range that is on average missed; it is computed thus:

Hardness = (maximum possible score - average score) / (maximum possible score - minimum possible score)

As raw scores are almost always non-linear, the median is mostly used rather than the mean.

A disadvantage of this statistic, when computed from the actual scores on a test, is its dependence on the particular population sample of the test in question. This can be counteracted by using not the actual average score, but the raw score that corresponds, according to the test's norm table, to a particular fixed standard score that represents the median of the high-range population on the whole. Hardness indices of different tests become comparable then. This latter form of hardness is called "sample-independent hardness". Interpretation advice for sample-independent hardness:

- .00 to .25 = easy
- .25 to .50 = moderate
- .50 to .75 = hard
- .75 to 1.00 = hardest