At Aberdeen, we had a program written for item analysis back in
1973 by J Houston and J Mitchell, with advice from people then
working with Alex Johnstone. The program has been modified for use
with omr forms, but we still use it now. This is what the manual
says about facility and discrimination:
After scoring and sorting into merit order the lists are searched and
the following quantities are calculated for each question in the
1. The facility value, i.e. the fraction of the class with the
correct answer. 2. The discrimination value, computed as the point
biserial correlation coefficient between response and total scores,
gives a measure of how effective the question is in discriminating
between high scorers and low scorers.
Note: The point biserial correlation coefficient for a particular
question is calculated as:
( Mr - Mt ) * sqrt( Nr / Nw ) / SD
Mr = Mean score of candidates giving CORRECT answer.
Mt = Mean score of the whole class.
Nr = Number of candidates giving CORRECT answer.
Nw = Number of candidates giving WRONG answer.
SD = Standard deviation of scores for whole class:
sqrt( N * S1 - S2 ) / N
where: N = Number of candidates in class.
S1 = Sum of squares of scores.
S2 = Sum of scores squared.
This is stated to be the correct measure (Guilford, J.P., Fundamental
Statistics in Psychology and Education, 4th edition, 1965 p322) and
other methods, such as comparing top and bottom thirds of the class,
are short cut manual methods to approximate the same figures.)
Dr Mary Masson
Department of Chemistry
University of Aberdeen
Meston Walk, Aberdeen AB24 3UE
Tel 01224 272931 Fax 01224 272921
email [log in to unmask]