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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 the following questions.

In order 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 "rule-of-thumb" 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 high-

performing students would select the correct answer for each question more often than the low

performing 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 low-performing 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 11

Anthony

90 1 0 1

Mike

80 0 0 1

Sharon

80 1 0 1

Charles

70 1 0 1

Bruce

60 1 0 0

Catherine

60 1 0 1

Patricia

50 1 1 0

Kelly

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. 1. 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.

2. 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.

3. 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.

4. The answers for Questions 1-3 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 low performing

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 higher-level skills.