1. Item Analysis

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 C. Multiple-Choice 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
b) peer ratings
c) forced choice
d) differences n.s

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).
N answering incorrectly
Number of distractors
# of Persons Exp. To Choose Distractor
= 4.7 =

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))] = ?
It is 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

11. Percentage of test takers who respond correctly
Item Difficulty
Percentage of test takers who respond correctly
What if p = .00
What if p = 1.00? ?

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 ( ) 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
seek items 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
items that 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)