2. Purpose of Item Analysis
– Evaluates the quality of each item
– Rationale: the quality of items determines the
quality of test (i.e., reliability & validity)
– May suggest ways of improving the
measurement of a test
– Can help with understanding why certain
tests predict some criteria but not others
3. Item Analysis
When analyzing the test items, we have several
questions about the performance of each item. Some
of these questions include:
Are the items congruent with the test objectives?
Are the items valid? Do they measure what they're
supposed to measure?
Are the items reliable? Do they measure consistently?
How long does it take an examinee to complete each
item?
What items are most difficult to answer correctly?
What items are easy?
Are there any poor performing items that need to be
discarded?
4. Types of Item Analyses for CTT
Three major types:
1. Assess quality of the distractors
2. Assess difficulty of the items
3. Assess how well an item
differentiates between high and low
performers
5. DISTRACTOR ANALYSIS
A. Multiple-Choke
B. Multiply-Choice
C. Multiple-Choice
D. Multi-Choice
6. Distractor Analysis
First question of item analysis: How many
people choose each response?
If there is only one best response, then all
other response options are distractors.
Example from in-class assignment (N = 35):
Which method has the best internal consistency? #
a) projective test 1
b) peer ratings 1
c) forced choice 21
d) differences n.s. 12
7. Distractor Analysis (cont’d)
A perfect test item would have 2 characteristics:
1. Everyone who knows the item gets it right
2. People who do not know the item will have
responses equally distributed across the wrong answers.
It is not desirable to have one of the distractors chosen
more often than the correct answer.
This result indicates a potential problem with the
question. This distractor may be too similar to the correct
answer and/or there may be something in either the stem
or the alternatives that is misleading.
8. Distractor Analysis (cont’d)
Calculate the # of people expected to choose each of the
distractors. If random same expected number for each
wrong response (Figure 10-1).
# of Persons N answering incorrectly 14
Exp. To Choose = = 4.7
Distractor Number of distractors 3
9. Distractor Analysis (cont’d)
When the number of persons choosing a distractor
significantly exceeds the number expected, there are 2
possibilities:
1. It is possible that the choice reflects partial knowledge
2. The item is a poorly worded trick question
unpopular distractors may lower item and test difficulty
because it is easily eliminated
extremely popular is likely to lower the reliability and
validity of the test
10. Item Difficulty Analysis
Description and How to Compute
ex: a) (6 X 3) + 4 = ?
b) 9 [1n(-3.68) X (1 – 1n(+3.68))] = ?
Itis often difficult to explain or define difficulty in
terms of some intrinsic characteristic of the item
The only common thread of difficult items is that
individuals did not know the answer
12. Item Difficulty
– An item with a p value of .0 or 1.0 does not
contribute to measuring individual differences and
thus is certain to be useless
– When comparing 2 test scores, we are interested in
who had the higher score or the differences in
scores
– p value of .5 have most variation so seek items in
this range and remove those with extreme values
– can also be examined to determine proportion
answering in a particular way for items that don’t
have a “correct” answer
13. Item Difficulty (cont.)
What is the best p-value?
– most optimal p-value = .50
– maximum discrimination between good
and poor performers
Should we only choose items of .50?
When shouldn’t we?
14. Should we only choose items of .50?
Not necessarily ...
When wanting to screen the very top group of
applicants (i.e., admission to university or medical
school).
Cutoffs may be much higher
Other institutions want a minimum level (i.e., minimum
reading level)
Cutoffs may be much lower
15. Item Difficulty (cont.)
Interpreting the p-value...
example:
100 people take a test
15 got question 1 right
What is the p-value?
Is this an easy or hard item?
16. Item Difficulty (cont.)
Interpreting the p-value...
example:
100 people take a test
70 got question 1 right
What is the p-value?
Is this an easy or hard item?
17. Item Difficulty (cont’d)
General Rules of Item Difficulty…
p low (< .20) difficult test item
p moderate (.20 - .80) moderately diff.
p high (> .80) easy item
18. ITEM DISCRIMINATION
... The extent to which an item
differentiates people on the
behavior that the test is designed
to assess.
the computed difference between
the percentage of high achievers
and the percentage of
low achievers who got the item
right.
19. Item Discrimination (cont.)
compares the performance of upper
group (with high test scores) and lower
group (low test scores) on each item--%
of test takers in each group who were
correct
20. Item Discrimination (cont’d):
Discrimination Index (D)
Divide sample into TOP half and
BOTTOM half (or TOP and BOTTOM
third)
Compute Discrimination Index (D)
21. Item Discrimination
D =U-L
U = # in the upper group correct response
Total # in upper group
L = # in the lower group correct response
Total # in lower group
The higher the value of D, the more adequately
the item discriminates (The highest value is 1.0)
22. Item Discrimination
seekitems with high positive numbers (those
who do well on the test tend to get the item
correct)
negative numbers (lower scorers on test more
likely to get item correct) and low positive
numbers (about the same proportion of low and
high scorers get the item correct) don’t
discriminate well and are discarded
23. Item Discrimination (cont’d):
Item-Total Correlation
Correlation between each item (a correct response
usually receives a score of 1 and an incorrect a score
of zero) and the total test score.
To which degree do item and test measures the same
thing?
Positive -item discriminates between high and low
scores
Near 0 - item does not discriminate between high & low
Negative - scores on item and scores on test disagree
24. Item Discrimination (cont’d):
Item-Total Correlation
Item-total correlations are directly
related to reliability.
Why?
Because the more each item correlates
with the test as a whole, the higher all
items correlate with each other
( = higher alpha, internal consistency)
25. Quantitative Item Analysis
Inter-item correlation matrix displays the
correlation of each item with every other
item
provides important information for
increasing the test’s internal consistency
each item should be highly correlated
with every other item measuring the same
construct and not correlated with items
measuring a different construct
26. Quantitative Item Analysis
itemsthat are not highly correlated with
other items measuring the same
construct can and should be dropped to
increase internal consistency
27. Item Discrimination (cont’d):
Interitem Correlation
Possible causes for low inter-item correlation:
a. Item badly written (revise)
b. Item measures other attribute than rest of
the test (discard)
c. Item correlated with some items, but not
with others: test measures 2 distinct
attributes (subtests or subscales)
