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COLLEGE OF EDUCATION
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WEEK 7
PED 8: Assessment of Learning 1

LESSON 7:
VII. Item Analysis
The teacher normally prepares a draft of the test. Such a draft is subjected to item analysis and validation
in order to ensure that the final version of the test would be useful and functional. First, the teacher tries out
the draft test to a group of students of similar characteristics as the intended test takers (try-out phase). From
the try-out group, each item will be analyzed in terms of its ability to discriminate between those who know
and those who do not know and also its level of difficulty (item analysis phase). The item analysis will
provide information that will allow the teacher to decide whether to revise or replace an item (item revision
phase). Then, finally, the final draft of the test is subjected to validation if the intent is to make use of the test
as a standard test for the particular unit or grading period. This procedure is known as item analysis. Item
analysis gives information which are as follows:
1) The difficulty of the item.
2) The discriminating power of the item.
3) The effectiveness of each option.

Information from item analysis can assess whether the item is too easy or too difficult. It determines
how well it discriminates between high and low achievers on the test and tells whether all the options function
well.

Item analysis data also help in determining specific technical defect. Furthermore, it gives information
on what improvements the test items need.

Benefits of Item Analysis

Item analysis has many benefits even if there is no intention of revising the test item in the future. The
benefits of item analysis are as follows:
1. It gives useful information for class discussion of a test. For instance, easy items can be treated
lightly, responses of difficult items can be explained comprehensively, and difficult items can be
pointed out to students.
2. It gives data for helping the students to improve their learning strategies. For example, if a learner
commits a number of incorrect responses to several items, this tells that misconception of the
learning tasks which can be taken into consideration for remedial work. Another remedy to improve
the strategy of learning is to tell the students a technique in studying their lessons. i. e, easy lessons
be studied at dawn.
3. It gives insights and skills which lead to the construction of better test items for future use.

There are two important characteristics of an item that will be of interest to the teacher. These are: (a)
item difficulty, and (2) discrimination index. We shall learn how to measure these characteristics and apply
our knowledge in making a decision about the item in question.

The difficulty of an item or item difficulty is defined as the number of students who are able to answer
the item correctly divided by the total number of students. Thus:
 Item difficulty = number of students with correct answer/ total number of students
The item difficulty is usually expressed in percentage.
An easy way to derive such a measure is to measure how difficult an item is with respect to those in the
upper 25% of the class and how difficult it is with respect to those in the lower 25% of the class.
RU + RL
¿ x HYPERLINK tel:100 100
Index of Difficulty 1
T
2
Where:
RU – the number in the upper group who answered the item correctly.
RL – the number in the lower group who answered the item correctly.
T – The total number who tried the item.

Example: What is the item difficulty index of an item if 25 students are unable to answer it correctly
while 75 answered it correctly?
Here, the total number of students is 100, hence, the item difficulty index is 75/100 or 75%.
One problem with this type of difficulty index is that it may not actually indicate that the item is difficult
(or easy). A student who does not know the subject matter will naturally be unable to answer the item
correctly even if the question is easy. How do we decide on the basis of this index whether the item is too
difficult or too easy? The following arbitrary rule is often used in the literature:

Range of Difficulty Index Interpretation Action

0 - 0.25 Difficult Revise or discard
0.26 - 0.75 Right difficulty Retain
0.76- above Easy Revise or discard
Difficult items tend to discriminate between those who know and those who do not know the answer.
Conversely, easy items cannot discriminate between these two groups of students. We are therefore interested
in deriving a measure that will tell us whether an item can discriminate between these two groups of students.
Such a measure is called an index of discrimination.

If the upper 25% of the class found the item easy yet the lower 25% found it difficult, then the item can
discriminate properly between these two groups. Thus:

RU − RL
¿
Index of discrimination = DU – DL or Index of Discrimination 1
T
2
Example: Obtain the index of discrimination of an item if the upper 25% of the class had a difficulty
index of 0.60 (i.e. 60% of the upper 25% got the correct answer) while the lower 25% of the class had a
difficulty index of 0.20.

Here, DU = 0.60 while DL = 0.20, thus index of discrimination=0.60- 0.20 = 0.40.

Theoretically, the index of discrimination can range from -1.0 (when DU =0 and DL = 1) to 1.0 (when
DU = 1 and DL =0). When the index of discrimination is equal to -1 then, it means that all of the lower 25%
of the students got the correct answer while all of the upper 25% got the wrong answer. In a sense, such an
index discriminates correctly between the two groups but the item itself is highly questionable. Why should
the bright ones get the wrong answer and the poor ones get the right answer?

On the other hand, if the index of discrimination is 1.0, then this means that all of the lower 25% failed
to get the correct answer while all of the upper 25% got the correct answer. This is a perfectly discriminating
item and is the ideal item that should be included in the test. From these discussions, let us agree to discard or
revise all items that have negative discrimination index for although they discriminate correctly between the
upper and lower 25% of the class, the content of the item itself may be highly dubious. As in the case of the
index of difficulty, we have the following rule of thumb:

Index Range Interpretation Action

− HYPERLINK tel:1.0%20−%20−.50 1.0 −− 0.50 Can discriminate but item is questionable
Discard
− 0. HYPERLINK tel:55%200.45 55 −0.45 Non – discriminating Revise
0.46 −1.0 Discriminating item Include

Example: Consider a multiple choice type of test of which the following data were obtained:

Item Options
A B* C D
1 0 40 20 20 Total
0 15 5 0 Upper 25%
0 5 10 5 Lower 25%

The correct response is B. Let us compute the difficulty index and index of discrimination:

Difficulty Index = no. of students getting correct response/total

= 40/100 = 40%, within range of a "good item"

The discrimination index can similarly be computed:

DU no. of students in upper 25% with correct response/no. of students in the upper 25%
= 15/20 = 0.75 or 75%

DL = no. of students in lower 75% with correct response/ no. of students in the lower 25%
= 5/20 = 0. 25 or 25%

Discrimination Index = DU - DL = 0. HYPERLINK tel:75%20.25%20.50 75 −0.25=0.50∨50 % .

Thus, the item also has a "good discriminating power".

It is also instructive to note that the distracter A is not an effective distracter since this was never
selected by the students. Distracters C and D appear to have good appeal as distracters.