Test-Retest-Reliabilty-Presentation.pptx

Presentation by: Jerson D. Jocutan, MASE
Test-Retest Reliability
EDF 204: Advanced Statistics

Reliability
EDF 204: Advanced Statistics: Test-retest Reliability

Reliability and Validity are related
concepts. If an instrument is unreliable,
it cannot yet valid outcome, as reliability
improves validity may improve (or may
not). However, if an instrument is shown
scientifically to be valid then it is almost
certain that it is also reliable.

Types of Reliability Measures
Measure of Internal
Consistency
Measure of Stability
with Equivalence
Measure of
Equivalence
Measure of Stability

Measure of
Internal
Consistency

Test-Retest with Equivalent
Forms
PROCEDURE:
Give parallel form of test, with increased time
interval between forms.
STATISTICAL MEASURE:
Pearson r
Measure of
Stability and
Equivalence

Measure
of Stability
PROCEDURE:
Give a test twice to the same group with any time
interval between sets, from several minutes to several years
STATISTICAL MEASURE:
Pearson r
Test-Retest

Test-Retest Reliability
Description:
Measures the stability of score between two
points of time within the same participants.
How it is Measured:
The Correlation between response in Time 1
and Time 2.

Pearson Product
Moment
Correlation
• FORMULA:
𝑟 =
𝑁 ∑𝑋𝑌−(∑𝑋)(∑𝑌)
𝑁∑𝑋2−(∑𝑋)2 𝑁∑𝑌2−(∑𝑌)2
Whereas;
N = number of
respondents/examinee
X = score in the test (Test 1)
Y = score in the retest (Test
2)

Test-Retest:Measure
of Stability using
Pearson r
• Example:
This test is for the reliability
of teacher made test using
the statistical measure
Pearson R.
STUDENTS N X Y 𝑿𝟐 𝒀𝟐 XY
1 50 51
2 43 42
3 48 48
4 45 44
5 40 41
6 47 47
7 52 51
8 39 38
9 44 43
10 43 42
11 41 41
12 46 45
13 39 39
14 51 50
15 49 48
SUMMATION (∑)
X Y 𝑿𝟐
𝒀𝟐 XY

1 50 51
2 43 42
3 48 48
4 45 44
5 40 41
6 47 47
7 52 51
8 39 38
9 44 43
10 43 42
11 41 41
12 46 45
13 39 39
14 51 50
15 49 48
SUMMATION (∑)
X Y 𝑿𝟐
𝒀𝟐 XY
• FORMULA:
𝑟 =
𝑁 ∑𝑋𝑌−(∑𝑋)(∑𝑌)
𝑁∑𝑋2−(∑𝑋)2 𝑁∑𝑌2−(∑𝑌)2
Whereas;
N = number of respondents/examinee
Y = score in the retest (Test 2)

1 50 51 2500 2601 2550
2 43 42 1849 1764 1806
3 48 48 2304 2304 2304
4 45 44 2025 1936 1980
5 40 41 1600 1681 1640
6 47 47 2209 2209 2209
7 52 51 2704 2601 2652
8 39 38 1521 1444 1482
9 44 43 1936 1849 1892
10 43 42 1849 1764 1806
11 41 41 1681 1681 1681
12 46 45 2116 2025 2070
13 39 39 1521 1521 1521
14 51 50 2601 2500 2550
15 49 48 2401 2304 2352
SUMMATION (∑)
677 670 30817 30184 30495
X Y 𝑿𝟐
𝒀𝟐 XY
• FORMULA:
𝑟 =
𝑁 ∑𝑋𝑌−(∑𝑋)(∑𝑌)
𝑁∑𝑋2−(∑𝑋)2 𝑁∑𝑌2−(∑𝑌)2
Whereas;
N = number of respondents/examinee
Y = score in the retest (Test 2)

1 50 51 2500 2601 2550
2 43 42 1849 1764 1806
3 48 48 2304 2304 2304
4 45 44 2025 1936 1980
5 40 41 1600 1681 1640
6 47 47 2209 2209 2209
7 52 51 2704 2601 2652
8 39 38 1521 1444 1482
9 44 43 1936 1849 1892
10 43 42 1849 1764 1806
11 41 41 1681 1681 1681
12 46 45 2116 2025 2070
13 39 39 1521 1521 1521
14 51 50 2601 2500 2550
15 49 48 2401 2304 2352
SUMMATION (∑)
677 670 30817 30184 30495
X Y 𝑿𝟐
𝒀𝟐 XY
• FORMULA:
𝑟 =
𝑁 ∑𝑋𝑌−(∑𝑋)(∑𝑌)
𝑁∑𝑋2−(∑𝑋)2 𝑁∑𝑌2−(∑𝑌)2
• SOLUTION:
𝑟 =
(15) (30495) − (677)(670)
(15)(30817) − 6772 (15)(30184) − 6702

Solution:
𝑟 =
(15) (30495) − (677)(670)
(15)(30817) − 6772 (15)(30184) − 6702
𝑟 =
457425 − 453590
(3926)(3860)
r = 0.99

INTERPRETATION
• Note:
To pass a reliability test
for a teacher-made test result
should be 0.85 and above.
VALUE DESCRIPTIVE
EQUIVALENCE
0.00 = zero correlation
0.01 – 0.20 = negligible correlation
0.21 – 0.40 = low correlation
0.41 – 0.70 = moderate correlation
0.71 – 0.90 = high correlation
0.91 – 0.99 = very high correlation

RESULTS
𝑟 =
(15) (30495) − (677)(670)
(15)(30817) − 6772 (15)(30184) − 6702
𝑟 =
457425 − 453590
(3926)(3860)
r = 0.99
INTERPRETATION:
The r value is 0.99 denotes a
very high relationship. This implies
that the students who got a very
high scores in the first administration
of the test, got a very high score in
the second administration of the
test. Likewise, those who got low
scores in the first administration of
the test got low scores in the second
administration of the test. Hence, the
test is highly reliable

Important Notes
A typical assessment would
involve giving participants the
same test on two separate
occasions. If the same or similar
results are obtained, then
external reliability is established.

Important Notes
The timing of the test is important; if the
duration is to brief then participants may recall
information from the first test which could bias
the results.

Important Notes
Alternatively, if the duration is too
long it is feasible that the
participants could have changed in
some important way which could
also bias the results.

Potential Bias
in Test-Retest
Reliability
Practice Effect
A practice effect occurs when participants
simply gets better at some test due to practice.
This means they’re likely to show better results
during later tests because they’ve had time to
practice and improve.
The way to prevent this type of bias is to give
individuals tests that are of equal difficulty but
have a different variety of questions so that
they can’t memorize the answers to the types
of questions asked on the first test.

Potential Bias
in Test-Retest
Reliability
Fatigue Effect
A fatigue effect occurs when participants gets
worse at some test because they get mentally
drained or fatigued from taking previous tests.
The way to prevent this type of bias is to
provide plenty of time in between tests (ideally
weeks or even months) so that participants are
fresh when taking both tests.

Potential Bias
in Test-Retest
Reliability
Differences in Conditions
When participants take the two tests under
different conditions (i.e. different lighting,
different time of day, different time allowed to
complete the test, etc.) it’s possible that they
score differently on the tests simply due to
differences in the testing environment.
The way to prevent this type of bias is to
ensure that participants take both tests under
identical conditions, i.e. during the same time
of day, with the same general lighting and
environment, and given the same amount of
time to complete the test.

STUDENTS N X Y 𝑿𝟐
𝒀𝟐 XY
1 50 35
2 43 32
3 48 45
4 45 36
5 40 49
6 47 43
7 52 44
8 39 42
9 44 45
10 43 43
11 41 44
12 46 35
13 39 37
14 51 48
15 49 45
16 51 52
17 42 43
18 48 47
19 44 43
20 41 42
21 47 48
22 51 50
23 38 42
24 43 43
25 42 45
26 41 39
27 45 43
28 39 38
29 50 50
30 48 45
SUMMATION (∑)
X Y 𝑿𝟐
𝒀𝟐 XY
Let’s Practice!
Teacher Rica prepared a teacher-
made test. She administered the
test twice with 2 weeks interval and
gathered the data as shown on the
table. Determine the reliability of
the test made by Teacher Rica.

References
• Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of
Statistics, Cambridge University Press.
• Lindstrom, D. (2010). Schaum’s Easy Outline of Statistics, Second
Edition (Schaum’s Easy Outlines) 2nd Edition. McGraw-Hill Education
• Vogt, W.P. (2005). Dictionary of Statistics & Methodology: A
Nontechnical Guide for the Social Sciences. SAGE.
• Wheelan, C. (2014). Naked Statistics. W. W. Norton & Company

Thank You
for Listening!
Presentation By:
JERSON D. JOCUTAN, LPT
For inquiries please contact the following:
E-mail: jjocutan9151@student.dmmmsu.edu.ph
Facebook/Messenger: https://www.facebook.com/jrxnjc.tan/

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