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By: admission.edhole.com B.Tech Admission in India
ReliabilityDefinition: The stability or consistency of a test.
Assumption: True score = obtained score +/- error
Domain Sampling ModelItem Domain
Test
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Overview of Reliability Techniques
1. Test-retest
2. Parallel/Alternate Forms
3. Split-half
T T1 2
A A1 2
TA B
Score Score
1
100
50 pairs
4. Internal Consistency
K-R-20 Coefficient Alpha
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Test-retest method
[error is due to changes occurring due to the passage of time]Some Issues:• Length of time between test administrations if crucial (generally, the longer the interval, the lower the reliability)• Memory • Stability of the construct being assessed • Speed tests, sensory discrimination, psychomotor tests (possible fatigue factor)admission.edhole.com
Parallel/Alternate Forms [error due to test content and perhaps passage of time]
Two types:
1) Immediate (back-to-back administrations)
2) Delayed (a time interval between administrations)
Some Issues:• Need same number & type of items on each test• Item difficulty must be the same on each test• Variability of scores must be the same on each test
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Split-half reliability [error due to differences in item content between the halves of
the test]
• Typically, responses on odd versus even items are employed
• Correlate total scores on odd items with the scores obtained on even items• Need to use the Spearman-Brown correction formula
rttc = nr12
1 + (n – 1) r12
# of times the test is lengthened
correlation between both parts of the test
corrected r for the total test
Person Odd Even
1 36 43
2 44 40
3 42 37
4 33 40
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KR-20 and Coefficient Alpha [error due to item similarity]
• KR-20 is used with scales that have right & wrong responses (e.g., achievement tests)• Alpha is used for scales that have a range of response options where there are no right or wrong responses (e.g., 7-point Likert-type scales)
Rtt = k pi (1 – pi)
k – 1 y2
# of items variance of test scores
% of those getting the item correct
KR-20
= k 1 – i2
k – 1 y2
# of itemsvariance of test scores
variance of scores on each itemAlph
a
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Correlation of items with total test scores
Corr. with
criteria
.00 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50
.50
.45
.40
.35
.30
.25
.20
.15
.10
.05
.00
Possible problem with choosing test items based on their correlations with a criterion
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*Selection zone
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Factors Affecting Reliability
1) Variability of scores (generally, the more variability, the higher the reliability)
2) Number of items (the more questions, the higher the reliability)
3) Item difficulty (moderately difficult items lead to higher reliability, e.g., p-value of .40 to .60)
4) Homogeneity/similarity of item content (e.g., item x total score correlation; the more homogeneity, the higher the reliability)
5) Scale format/number of response options (the more options, the higher the reliability)
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Standard Error of Measurement
[Error that exists in an individual’s test score]
1 - r1 - rSEM =
Standard DeviationReliability
Examples: = 10; r = .90 SEM = 3.16
= 10; r = .60 SEM = 6.32
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-4 -3 -2 -1 Mean +1 +2 +3 +4
Normal Curve
68%
95%
99%
Actual z-score =
1.96
Actual z-score =
2.58
• 3.16 x 1.96 = 6.19 (95% confidence)• 3.16 x 2.58 = 8.15 (99% confidence)
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Other Standard Errors
Standard error of the mean: SX = S
√N
s = standard deviationN = # observations or sample size
Standard error of proportion: SEP = p (1 - p)/Np = proportion
N = sample size
Standard error of difference in proportions:
Standard error of estimate
(validity coefficient):y’ = y 1 - r
2xy
y = standard deviation of y
(criterion)
r2
xy = correlation between x
and y squared
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