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Item Analysis,
Test Validity and Reliability
Prepared by:
Rovel A. Aparicio
Mathematics Teacher
THERE IS always A
better WAY
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
Stages in Test Construction
II. Trying Out the Test

A. Administering the test
Item analysis
C. Preparing the Final Form of the Test
Stages in Test Construction
III. Establishing Test Validity

IV. Establishing Test Reliability

V. Interpreting the Test Scores
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.
ACTIVITY NO.1

COMPUTE THE DIFFICULTY
INDEX AND
DISCRIMINATION INDEX OF
PERIODICAL TEST.
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.
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]
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
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
Establishing Test Validity

Criterionrelated
Validity

Content
Validity
Types of Test
Validity

Construct
Validity
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)
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.
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.
Establishing Test Reliability
Measure of
Stability and
Equivalence

Measure of
Stability

Types of
Reliability
Measure

Measure of
Internal
Consistency

Measure of
Equivalence
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)
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)
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)
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.
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)
ACTIVITY NO.2

TEST THE RELIABILITY OF
PERIODICAL TEST.
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.
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 .
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
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
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
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 .
Test validity

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Test validity

  • 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]
  • 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
  • 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 .