3. 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 weaknesses of
students in need of remediation.
4. Three Elements in an 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.
5. 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 refers to the
percentage of high-scoring individuals
responding correctly versus the number of
low-scoring individuals 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.
6. Preparing Data for Item Analysis
1. Arrange test scores from highest to
lowest.
2. Get one-third or 27% of the papers
from the highest scores( Upper Group)
and the other third or 27% from the
lowest scores ( Lower Group).
3. Record separately the number of
times each alternative was chosen by
the students in both groups.
7. 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 the formula:
IDF = (NRC
/TS)100
where IDF = index of difficulty
NRC = number of students
responding correctly to an
item
TS = total number of students in the
upper and lower groups
8. 6. Compute the 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 students per group
9. Using Information about Index of
Difficulty
The difficulty index of a test item
tells a teacher about the
comprehension of or performance
on material or task contained in
an item.
10. Item Group Answers
A B C D
Total No.
of
Correct
Answers
Difficulty
Index
H – L Discrimin
ation
Index
1
H 20
L 20
3 14 2 1
10 7 3 0
21 52.5%
or 0.525
7 0.35
2
H 20
L 20
0 0 18 2
0 3 9 8
27 67.5 %
or 0.675
9 0.45
3
H 20
L 20
3 8 4 4
10 2 4 4
10 25.0 %
or 0.25
6 0.30
4
H 20
L 20
3 3 4 10
2 4 10 4
14 35.0 %
or 0.35
6 0.30
5
H 20
L 20
15 2 2 1
1 10 4 5
16 40.0 %
or 0. 40
14 0.70
11. 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.
12. Interpretation of the Difficulty
Index
Range (%) Difficulty Level
20 & below
21 – 40
41 – 60
61 – 80
81 & above
Very Difficult
Difficult
Average
Easy
Very Easy
13. Range of Difficulty Index Description
0.00—0.20 Very Difficult
0.21—0.60 Difficult
0.41—0.60 Moderately Difficult
0.61—0.80 Easy
0. 81—1.00 Very Easy
Interpretation of the Difficulty
Index
14. 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 his
class. A test item may have positive or negative
discriminating power.
An item has a positive discriminating power when
more students from the upper group got the
right answer than those from the lower group
When more students from the lower group got the
correct answer on an item than those from the
upper group, the item has a negative
discriminating power.
15. There are instances 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.
16. Interpretation of the Index of
Discrimination
Range Verbal Description
.40 & above
.30 – .39
.20 – .29
.09 – .19
Very Good Item
Good Item
Fair Item
Poor Item
17. To facilitate the easy interpretation if an item is good or poor let us
use the table below.
Note that acceptable index of difficulty ranges from 0.41—0.60
while acceptable index of discrimination ranges from 0.20 to 1.00.
Type of Item Characteristics
Good( Retained) Both acceptable indexes of
difficulty and discrimination
Fair( Revised) Either unacceptable difficulty
or discrimination index
Poor ( Rejected) Both unacceptable indexes of
difficulty and discrimination
18. 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.
19. Examining Distractor Effectiveness
An ideal item is one that all
students 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.
20. 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
Facilitating the physical construction and
reproduction of the test
Accumulating a large pool of items as to allow
for some items to be shared with the students
for study purposes.
21. Limitations of Item Analysis
It cannot be used for essay items.
Teachers 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.
22. SHAPES , DISTRIBUTION AND
DISPERSION OF DATA
In order to determine the shape of a distribution of scores it is
important that the teacher must understand the different measures of
central tendency. Let us recall how to compute for the mean, median
and mode.
A. MEASURES OF CENTRAL TENDENCY
1. Mean—arithmetic average , used when the distribution is normal.
Most reliable and stable.
23. Example: A group of 16 elementary school graduates
who took the entrance examination test obtained the
following scores on numerical ability test. What is the
mean of the scores obtained by the examinees?
26 21 29 32 24 17 23 29
17 20 26 23 21 7 28 25
Mean = 23
24. Median - Point in a distribution above and below
which are 50% of the scores. Midpoint of the
distribution. It used when the distribution is skewed.
To determine the median arrange first the scores from least
to greatest, then locate the middle value known as the
median.
7 17 17 20 21 21 23 23
24 25 26 26 28 29 29 32
As you have noticed the middle value is between 23 and 24, hence we
have to get the average of 23 and 24 which 23. 5. Therefore, the
median is 23. 5.
25. Mode—Most frequent/ common score in the
distribution. Unreliable and not stable. It is used
as the quick description in terms of typical
performance.
Looking at the problem above there are four scores
with the same frequency, these are 17, 21, 26 and 29.
Hence, the modes are 17, 21, 26 and 29, it is called a
multimodal distribution. A distribution with one mode is
known as unimodal distribution.
26. SHAPE OF THE DISTRIBUTION
Now to determine the shape of distribution, the following
must be the considerations.
1. Normal Distribution—Mean = Median = Mode
2. Positively skewed distribution— Mean > Median > Mode
3. Negatively skewed distribution—Mean < Median < Mode
27. If skewness = 0 , the distribution is normal.
If Skewness > 0 , the distribution is positively skewed.
If skewness < 0, the distribution is negatively skewed.
The value of the skewness determines the symmetry or asymmetry of
the distribution.
28. What to know!
If the difference of mean and median is negative or less
than zero, the distribution is already negatively skewed.
From our first example the mean is equal to 23 and the
median is 23.5 , by subtracting it
Mean—Median = 23—23. 5
= -0.5.
30. MEASURES OF
DISPERSION
While the skewness tells about degree of symmetry and asymmetry
of distribution, the standard deviation is a measure of dispersion
which gives us the idea if the distribution is scattered or not. The
larger the value of the standard deviation the more scattered the scores.
Given the scores in a quiz of two groups of students , let us determine which
group is more consistent.
Group A : 4 6 8 7 10
Group B : 5 6 6 9 9
It measures how far or scattered are the scores from the
other.
32. MEASURE OF RELATIVE POSITION
1. Percentile Ranks —indicate the percentage of scores that fail below a
given score. For example median of a set of scores is 50th percentile.
If a score separates the lower 25% of the distribution and upper
75% of the distribution, this means that the percentile rank of the score is
25th percentile.
2
It indicate where a score is in relation to all other scores in the distribution. It can
also be used to compare the performance of an individual in two or more different
sets.,
33. MEASURE OF RELATIVE POSITION
2. Z—score— known as the standards scores. A z– score expresses how far
a score is from the mean in terms of the standard deviation. For example , a
z—score of 2, means that the score is two standard deviation away from the
mean.
It indicate where a score is in relation to all other scores in the distribution. It can
also be used to compare the performance of an individual in two or more different
sets.,
