
C. Item Analysis
After you create your objective assessment items and give your test,
how can you be sure that the items are appropriate  not too difficult
and not too easy? How will you know if the test effectively differentiates
between students who do well on the overall test and those who do
not? An item analysis is a valuable, yet relatively easy, procedure
that teachers can use to answer both of these questions.
To determine the difficulty level of test items, a
measure called the Difficulty Index is used. This measure
asks teachers to calculate the proportion of students who answered
the test item accurately. By looking at each alternative (for multiple
choice), we can also find out if there are answer choices that should
be replaced. For example, let's say you gave a multiple choice quiz
and there were four answer choices (A, B, C, and D). The following
table illustrates how many students selected each answer choice
for Question #1 and #2.
Question 
A 
B 
C 
D 
#1 
0 
3 
24* 
3 
#2 
12* 
13 
3 
2 
* Denotes correct answer.
For Question #1, we can see that A was not a very
good distractor  no one selected that answer. We can also compute
the difficulty of the item by dividing the number of students who
choose the correct answer (24) by the number of total students (30).
Using this formula, the difficulty of Question #1 (referred to as
p) is equal to 24/30 or .80. A rough "ruleofthumb" is
that if the item difficulty is more than .75, it is an easy item;
if the difficulty is below .25, it is a difficult item. Given these
parameters, this item could be regarded moderately easy  lots
(80%) of students got it correct. In contrast, Question #2
is much more difficult (12/30 = .40). In fact, on Question #2, more
students selected an incorrect answer (B) than selected the correct
answer (A). This item should be carefully analyzed to ensure that
B is an appropriate distractor.
Another measure, the Discrimination Index, refers to how
well an assessment differentiates between high and low scorers.
In other words, you should be able to expect that the highperforming
students would select the correct answer for each question more
often than the lowperforming students. If this is true,
then the assessment is said to have a positive discrimination
index
(between 0 and 1)  indicating that students who received a high
total score chose the correct answer for a specific item more
often than the students who had a lower overall score. If, however,
you find that more of the lowperforming students got a specific
item correct, then the item has a negative discrimination
index
(between 1 and 0). Let's look at an example.
Table 2 displays the results of ten questions on a quiz. Note that
the students are arranged with the top overall scorers at the top
of the table.
Student 
Total
Score (%) 
Questions 
1 
2 
3 
Asif 
90 
1 
0 
1 
Sam 
90 
1 
0 
1 
Jill 
80 
0 
0 
1 
Charlie 
80 
1 
0 
1 
Sonya 
70 
1 
0 
1 
Ruben 
60 
1 
0 
0 
Clay 
60 
1 
0 
1 
Kelley 
50 
1 
1 
0 
Justin 
50 
1 
1 
0 
Tonya 
40 
0 
1 
0 





"1" indicates the answer was correct; "0"
indicates it was incorrect.
Follow these steps to determine the Difficulty Index
and the Discrimination Index.

After the students are arranged with the highest
overall scores at the top, count the number of students in the
upper and lower group who got each item correct. For Question
#1, there were 4 students in the top half who got it correct,
and 4 students in the bottom half.
 Determine the Difficulty Index by dividing the number who got
it correct by the total number of students. For Question #1, this
would be 8/10 or p=.80.
 Determine the Discrimination Index by subtracting the number
of students in the lower group who got the item correct from the
number of students in the upper group who got the item correct.
Then, divide by the number of students in each group (in this
case, there are five in each group). For Question #1, that means
you would subtract 4 from 4, and divide by 5, which results in
a Discrimination Index of 0.
 The answers for Questions 13 are provided in Table 2.
Item 
# Correct (Upper group) 
# Correct (Lower group) 
Difficulty (p) 
Discrimination (D) 
Question 1 
4 
4 
.80 
0 
Question 2 
0 
3 
.30 
0.6 
Question 3 
5 
1 
.60 
0.8 
Now that we have the table filled in, what does it mean? We can
see that Question #2 had a difficulty index of .30 (meaning it was
quite difficult), and it also had a negative discrimination index
of 0.6 (meaning that the lowperforming students were more likely
to get this item correct). This question should be carefully
analyzed, and probably deleted or changed. Our "best"
overall question is Question 3, which had a moderate difficulty
level (.60), and discriminated extremely well (0.8).
Another consideration for an item analysis is the cognitive level
that is being assessed. For example, you might categorize
the questions based on Bloom's taxonomy (perhaps grouping questions
that address Level I and those that address Level II). In this manner,
you would be able to determine if the difficulty index and discrimination
index of those groups of questions are appropriate. For example,
you might note that the majority of the questions that demand higher
levels of thinking skills are too difficult or do not discriminate
well. You could then concentrate on improving those questions
and focus your instructional strategies on higherlevel skills.
