Difficulty and discrimination

2. The difficulty index of a test item is indicated by the
proportion or percentage of students who got the item
correct.
Example: If 20 out of 25 students in a class
answered an item correctly, the difficulty of that item
would be (20/25) x 100 = 80 percent. Thus, somewhat
confusing, the higher the “ difficulty” the easier the
item.

3.  When the difficulty of test items is around 50 percent,
meaning that about half the students pass and half fail
each item, the resulting test scores will be maximally
spread out from low to high. This is an important result
for the construction of commercial standardized Norm-
referenced test, which are intended to compare the
relative achievement of the students. The more students
score differ, the better for making comparisons and
distinctions among them.

4.  Criterion-referenced focuses on individual student
mastery (not differentiation among students), item
difficulty is not a major concern. Classroom
assessments usually have higher difficulties (i.e.,are
easier) than the standardized, norm-referenced test
items. This would be expected as long as classroom
tests reflect classroom instruction.

5.  A test items discrimination index compares the
difference in performance of high and low test scores on
an item.
 An item is said to have positive discrimination if more
students who do well on the test as a whole answer it
correctly than students who do poorly on the test as
a whole.
Example: If 85 % of the class with the highest overall
test scores got the item correct compared to only 55%
of those with the lowest overall test scores, the item
discrimination would be
85% - 55% = 30%
 The higher the discrimination, the greater the
difference between the high and low tests scores on
that item.

6.  Notice that it is possible to get negative discriminations
For example, If 40 % of the top scorers and 60% of the
bottom scorers got the item correct, the discrimination
index would be 40% - 60% = -20%. In such a case, one
might one to check the scoring key or look at the
options in the item to try to identify the ones that the
top group is selecting incorrectly.

7.  Item discrimination, like item difficulty, is important in
the construction of commercial standardized tests. It is
necessary that each item in such tests have high
positive discrimination. While it is also desirable for
classroom tests to have items with positive
discrimination, it is less important than the commercial
tests because classroom tests are usually scored in a
criterion-referenced way and their higher item
difficulties reduce the differences between the high and
low scores.