Item analysis2

Item Analysis

• When analyzing the test item, we have several questions
about the performance of each item. Some of these
questions include :
•Are the item congruent with the test objectives?
•Are the item valid? Do they measure what they supposed to
measure?
•Are the item reliable? Do they measure consistently?
•How long does it take an examinee to complete each item?
•What item are most difficult to answer correctly?
•What item are easy?
•Are they any poor performing items that need to be discarded?

Types Of Item Analysis for CTT
• Three major types :

1. Assess quality of the distracters

2. Assess difficulty of the items

3. Assess how well an item differentiates between high and
low performers

Purposes and Elements of item Analysis

To select the best available items for the final
form of the test.
To identify structural or content defects in the
items.
To detect learning difficulties of the class as a
whole
To identify the areas of weakness of students
in need of remediation

Three elements of item analysis

1. Examination of the difficulty level of the items.

2. Determination of the discriminating power of each
item, and

3. Examination of the effectiveness of distractors in a
multiple choice or matching items.

The difficulty level of an item is known as index of
difficulty.
Index of difficulty is the percentage of students answering
correctly each item in the test
Index of discrimination refer to the percentage of high-scoring
individuals responding correctly versus the number of low-
scoring individuals responding responding correctly to an
item.
This numeric index indicates how effectively an item
differentiates between the students who did well and those
who did poorly on the test.

Preparing Data for Item Analysis

1. Arrange test score from highest to lowest.

2. Ger one-third of the papers from the highest scores
and the other third from the lowest scores.

3. Record separately the number of times each
alternative was chosen by the students in both
groups.

4. Add the number of correct answers to each item
made by the combined upper and lower groups.
5. Compute the index of difficulty for each item,
following formula :
IDF = (NRC/TS)100

Where IDF = index of difficulty
NRC = number of students responding correctly to an item
TS = total number of an students in the upper and lower groups.

6. Compute thee index of discrimination, based
on the formula :
IDN = (CU – CL)
NSG
Where IDN = index of discrimination
CU = number of correct responses of the upper group
CL = number of correct responses of the lower group
NSG = number of student per group

Using information about Index of Difficulty

The difficulty index of a test items tells a teacher
about the comprehension of or performance on
material or task contained in an item.

For an item to be considered a good item, its difficulty
index should be 50%. An item with 50% difficulty
index is neither easy nor difficult.
If an item has a difficulty index of 67.5%, this means
that it is 67.5% easy and 32.5% difficult.
Information on the index of difficulty of an item can
help a teacher decide whether a test should be
revised, retained or modified.

Interpretation of the Difficulty Index

Range Difficulty Level

20 & below Very difficult
21-40 Difficult
41-60 Average
61-80 Easy
81 & above Very easy

Using Information About Index Of
Discrimination
• The Index Of Discrimination tells a teacher the degree to
which a test item differentiates the high achievers from the
low achievers in is class. A test item may have positive or
negative discriminating power.
• An item has a positive discriminating power when more
student from the upper group got the right answer than those
from the lowest group.
• When more student from the upper group got the correct
answer on an item than those from the upper group, the item
has a negative discriminating power.

There are instance when an item has zero
discriminating power – when equal number of
students from upper and lower group got the right
answer to a test item.
In the given example, item 5 has the highest
discriminating power. This means that it can
differentiate high and low achievers.

Interpretation of the Difficulty Index

Range Verbal Description

.40 & above Very Good Item
.30 - .39 Good Item
.20 - .29 Fair Item
.09 - .19 Poor Item

When should a test item be rejected? Retained?
Modified or revised

A test item can be retained when its level of difficulty is
average and discriminating power is positive.
It has to rejected when it is either easy / very easy or
difficult / very difficult and its discriminating power is
negative or zero.
An item can be modified when its difficulty level is
average and its discrimination index is negative.

Examining Distracter Effectiveness

An ideal item is one that all student in the upper group
answer correctly and all students in the lower group
answer wrongly. And the responses of the lower
group have to be evenly distributed among the
incorrect alternatives.

Developing an Item Data File

 Encourage teachers to undertake an item analysis as often as
practical
 Allowing for accumulated data to be used to make item
analysis more reliable
 Providing for a wider choice of item format and objectives
 Facilitating the revision of items
 Accumulating a large pool of items as to allow for some items
to be shared with the students for study purposes.

Limitations Of Item Analysis
• It cannot be used for essay items.
• Teacher must be cautious about what damage may
be due to the table of specifications when items not
meeting the criteria are deleted from the test. These
items are to be rewritten or replaced.

What is Item Discrimination?
• Generally, student who did well on the exam should
select the correct answer to any given item on the
exam.
• The Discrimination Index distinguishes for each item
between the performance of students who did
poorly.

How does it work?
• for each item, subtract the number in the lower
group who answered correctly from the number of
students in the upper group who answered correctly.
• Divide the result by the number of students in one
group.
• The discrimination Index is listed in decimal format
and ranges between -1 and 1.

Item Discrimination : Examples

Number of correct answers in group Item
Item
Discrimination
no.
Upper 1/4 Lower 1/4 Index

1 90 20 0.7
2 80 70 0.1
3 100 0 1
4 100 100 0
5 50 50 0
6 20 60 -04

Quick Reference
• Use the following table as a guideline to determine
whether an item ( or its corresponding instruction)
should be considered for revision.

Item Discrimination Item Difficulty
(D)
High Medium Low

D = < 0% review review review

0 % < D < 30 % ok review ok

D > = 30 % ok ok ok

Distracter analysis

First question of item analysis : how many people
choose each response?
If there only one best response, then all other response
options are distracters.
Example from in class assignment (N=35):
Which method has best internal consistensy ?
a) Projective test 1
b) Peer ratings 1
c) Forced choice 21
d) Differences n.s. 12

Distracter analysis (cont’d)
• A perfect test item would have 2 characteristics :
1. Everyone who knows the item gets it right
2. People who do know the item will have responses equality distributed
across the wrong answer.

• It is not desirable to have one of the distracters chosen more often then
the correct answer.

• This result indicates a potential problem with the question. This
distracters may be too similar to the correct answer and /or these maybe
something in either the stem or the alternatives that is misleading.

• Calculate the # of people expected to choose each of the
distracters. If random same expected number for each wrong
response (Figure 10-1).

# of Persons N answering incorrectly 14
Exp. To Choose ___________________ = __ =4.7
Distracter number of distracters 3

When the number of person choosing a distracter significantly
exceeds the number expected, these are 2 possibilities:

1. It is possible that choice reflects partial knowledge
2. The item is a poorly worded trick question

• Unpopular distracters may lower item and test difficulty
because it is easily eliminated
• Extremely popular likely to lower the reliability and validity of
the test

Distracter analysis : Definition
• Compare the performance of the highest and lowest
scoring 25% of the student on the distracter option
(i.e. the incorrect answers presented on the exam)
• Fewer of the top performers should choose each of
the distracters as their answer compared to the
bottom performers.

Distracter analysis : Examples
Item 1 A B C D E Omit
% of student in upper 1/4 20 5 0 0 0 0
% of student in middle 15 10 10 10 5 0
% of student in lower 1/4 5 5 5 10 0 0

Item 2 A B C D E Omit
% of student in upper ¼ 0 5 5 15 0 0
% of student in middle 0 10 15 5 20 0
% of student in lower 1/4 0 5 10 0 10 0

Distracter Analysis : Discussion

• What is the purpose of a good distracter?

• Which distracters should you consider throwing out?

Exercise : Interpret Item Analysis

• Review the sample report.
• Identify any exam items that may require revision.
• For each identify item, list your observation and
hypothesis of the nature of the problem.

Knowledge Or Successful Guessing?

Multiple Choice Exam Strategies
-improve odds by eliminating 1 or more infeasible or
unlikely answer options

Description Exam Strategies
-brain dumping
-part marks
-consideration for perfect answers to questions that
were not asked

Possibility of a “Random Pass”

Depends on the number
of answer options per question
and the number of questions!

Percent Pass ( >50%) by Chance
Number of
Questions 2 choice 3 choice 4 choice 5 choice

1 50 33 25 20

2 75 56 44 36

4 69 41 26 18

6 66 32 17 10

10 62 21 8 3

20 59 9.2 1.4 .3

50 56 1 .01 .0004

Item analysis2

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