1. Item Analysis,
Test Validity and Reliability
Prepared by:
Rovel A. Aparicio
Mathematics Teacher

2. THERE IS always A
better WAY

3. Stages in Test Construction
I. Planning the Test
A. Determining the Objectives
B. Preparing the Table of Specifications
C. Selecting the Appropriate Item Format
D. Writing the Test items
E. Editing the Test items

4. Stages in Test Construction
II. Trying Out the Test
A. Administering the test
Item analysis
C. Preparing the Final Form of the Test

5. Stages in Test Construction
III. Establishing Test Validity
IV. Establishing Test Reliability
V. Interpreting the Test Scores

6. Item Analysis
GOAL: Improve the test.
IMPORTANCE: Measure the effectiveness of individual test item.
DIFFICULTY INDEX
DISCRIMINATION INDEX
 the percentage
 refers to the degree
of the pupils who
got the items rigth.
interpreted as
how easy or how
difficult an item is.
to which success or
failure of an item
indicates possession of
the acheivement being
measured.

7. ACTIVITY NO.1
COMPUTE THE DIFFICULTY
INDEX AND
DISCRIMINATION INDEX OF
PERIODICAL TEST.

8. U-L INDEX METHOD
(STEPS)
1. Score the papers and rank them from
highest
to lowest according to the total score.
2. Separate the top 27% and the bottom 27%
of the papers.
3. Tally the responses made to each test item
by each individual in the upper 27% group.
4.Tally the responses made to each test item
by each individual in the lower 27% group.

9. U-L INDEX METHOD
(STEPS)
5. Compute the difficulty index.
[d= (U+L)/(nu+nl)]
6. Compute the discrimination index.
[D=(U-L)/nu] or [D=(U-L)/nl]

10. Item
no.
Upper
27%
1
Lower
27%
Difficulty
Index
14
12
0.81
0.13
Revised
2
10
6
0.50
0.25
3
11
7
0.56
0.25
Retained
Retained
4
9
2
0.34
0.44
Retained
5
12
0.56
0.38
Retained
6
6
6
14
0.63
-0.50
Rejected
7
13
4
0.53
0.56
Retained
8
3
10
0.41
-0.44
Rejected
9
13
12
0.78
0.06
Rejected
10
8
6
0.44
0.13
Revised
No. of pupils tested- 60
Discrimination
Index
Remarks

11. Item Analysis
DIFFICULTY INDEX
.00-.20
Very Difficult
.21-.80
Moderately
Difficult
.81-1.00
DISCRIMINATION INDEX
< .09
Poor items
(Reject)
.10-.39
Reasonably
Good (Revise)
.40-1.00
Very Good
items (Retain)
Very Easy

12. Establishing Test Validity
Criterionrelated
Validity
Content
Validity
Types of Test
Validity
Construct
Validity

13. Establishing Test Validity
Types of Validity
Types of Validity
1.Content
Validity
Meaning
Meaning
Procedure
Procedure
Compare test tasks
How well the
with test
sample test bar specifications
tasks represent describing the task
the domain of
domain under
tasks to be
consideration
measured.
(non-statistical)

14. Establishing Test Validity
Types of Validity
Types of Validity
2. Construct
Validity
Meaning
Meaning
Procedure
Procedure
Experimentally
determine what factors
How test
influence scores on test.
performance can
The procedure may be
be described
psychologically. logical and statistical
using correlations and
other statistical
methods.

15. Establishing Test Validity
Types of Validity
Types of Validity
3.
Meaning
Meaning
Procedure
Procedure
Compare test scores
How well test
with measure of
performance
performance(grade)
obtain on later date(for
Criterion- predicts
future performance prediction).or another
related or estimates current
measure of performance
Validity
performance on obtain concurrently(for
some valued
estimating present
measures other
status.( Primarily
than the test
Statistical). Correlate
itself.
test results with
outside criterion.

16. Establishing Test Reliability
Measure of
Stability and
Equivalence
Measure of
Stability
Types of
Reliability
Measure
Measure of
Internal
Consistency
Measure of
Equivalence

17. Establishing Test Reliability
Types of Reliability
Types of Reliability
Measures
Measures
1. Measure of
Stability
Methods of
Methods of
Estimating Reliability
Estimating Reliability
Test- retest
method
Procedure
Procedure
Give a test twice to
the same group with
any time interval
between tests from
several minutes to
several years.
(Pearson r)

18. Establishing Test Reliability
Types of Reliability
Types of Reliability
Measures
Measures
2. Measure of
Equivalence
Methods of
Methods of
Estimating Reliability
Estimating Reliability
Procedure
Procedure
Give two forms of a
Equivalent formstest to the same
group in close
method
succession
(Pearson r)

19. Establishing Test Reliability
Types of Reliability
Types of Reliability
Measures
Measures
3. Measure of
Stability
Methods of
Methods of
Estimating Reliability
Estimating Reliability
Procedure
Procedure
Give two forms of
a test to the same
Test- retest
with equivalentgroup with increased
time intervals
forms
between forms.
(Pearson r)

20. Establishing Test Reliability
Types of Reliability
Types of Reliability
Measures
Measures
4. Measure of
internal
consistency
Methods of
Methods of
Estimating Reliability
Estimating Reliability
Procedure
Procedure
Give a test once.
Kuder-Richarson
Score the total test
method
and apply the Kuder
Richardson formula.

21. Establishing Test Reliability
Types of Reliability
Types of Reliability
Measures
Measures
4. Measure of
internal
consistency
Methods of
Methods of
Estimating Reliability
Estimating Reliability
Split half
method
Procedure
Procedure
Give a test once.
Score equivalent
halves of the test.
(e.g. odd and even
numbered items.
(Pearson r and
Spearman- Brown
formula)

22. ACTIVITY NO.2
TEST THE RELIABILITY OF
PERIODICAL TEST.

23. Pearson r Standard Scores
(Directions)
1. Begin by writing the pairs of scores to be
studied in two columns. Be sure that the pair of
scores for each pupils is in the same row.
Label one set of scores X , the other Y.
2.Get the sum (∑) of the scores for each
column. Divide the sum by the number of
scores (N) in each column to get the mean.
3.Subtract each score in column X from the
mean x. Write the difference in column x. Be
sure to put an algebraic sign.

24. Pearson r Standard Scores
(Directions)
4. Subtract each score in column Y from the
mean y. Write the difference in column y. Don't
forget the sign.
5. Square each score in column X. Enter each
result under X2 .
6. Square each score in column Y. Enter each
result under Y2 .
7. Compute the standard deviation of X and Y
and enter the result under the column of SDx
and SDy respectively .

25. Pearson r Standard Scores
(Directions)
8. Divide each entry in column x and y by the
standard deviation SDx and SDy respectively
and enter the result under Zx and Zy
respectively.
9. Multiply Zx and Zy and enter the result
under ZxZy.
10. Get the sum (∑) ZxZy.
11. Apply the formula r=∑ZxZy
N

26. Interpretation of
Coefficient of Correlation
Correlation is a measure of relationship
between two variables.
Magnitude or size of
Relationship
0.8 and above means
high correlation
0.5 means moderate
correlation
0.3 and below means
low correlation
Direction of Relationship
Negative coefficient
means, as one variable
increases, the other
decreases.
Positive Coefficient
means, as one variable
increases, the other also
increases

27. Interpretation of
Coefficient of Variation
Coeffecient of Variation is defined as the
ratio of the standard deviation and the mean
and usually expressed in percent.
Criteria:
c.v. = (mean/s.d.)x100
less than 10%Homogenous
greater than 10%- Heterogenous

28. REMEMBER:
1. Use item analysis procedures to check the quality
of the test. The item analysis should be interpreted
with care and caution
2. A test is valid when it measures what it is supposed
to measure
3. A test is reliable when it is consistent .