Test Scores, Norms, and Score Interpretation
Transcript Of Test Scores, Norms, and Score Interpretation
Test Scores, Norms, and Score Interpretation
PSY 721 Scores and Norms
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What We Will Cover in This Section.
• Test scores • Norms
• Types of interpretation
PSY 721 Scores and Norms
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Raw Score
Count or sum of the number of items endorsed
or number of items correctly answered.
PSY 721 Scores and Norms
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1
Norms
Norm Norms Norming
Behavior that is usual or typical for members of a group.
Reference scores against which an individual’s scores are compared.
Process of establishing norms for a test.
Norman
A fat guy who drinks beer in Cheers.
PSY 721 Scores and Norms
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Establishing Norms
1. Target population. 2. Standardization sample. 3. Norm Group.
- Size. - Geographic representation. - Socioeconomic level. - Ethnic composition.
PSY 721 Scores and Norms
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PSY 721 Scores and Norms
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2
PSY 721 Scores and Norms
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Types of Norms
PSY 721 Scores and Norms
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Reference Groups
• National norms. • Regional norms. • Local norms. • Sub-group norms.
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3
Table 2. Word, raw score: Total Sample
Valid
Missing Total
5 6 7 8 9 10 11 12 13 14 Total System
Frequency 1 9
24 31 40 12 19 15
1 1 153 11 164
Percent .6
5.5 14.6 18.9 24.4
7.3 11.6
9.1 .6 .6
93.3 6.7
100.0
Valid Percent .7
5.9 15.7 20.3 26.1
7.8 12.4
9.8 .7 .7
100.0
Cumulative Percent .7 6.5 22.2 42.5 68.6 76.5 88.9 98.7 99.3 100.0
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Valid
Table 6. Word, raw score: Undergraduate Students
6 7 8 9 11 12 Total
Frequency 3
14 11
7 1 1 37
Percent 8.1
37.8 29.7 18.9
2.7 2.7 100.0
Valid Percent 8.1
37.8 29.7 18.9
2.7 2.7 100.0
Cumulative Percent 8.1 45.9 75.7 94.6 97.3 100.0
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Valid
Table 9. Word, raw score: Graduate Students
5 6 7 8 9 10 11 12 13 14 Total
Frequency 1 6
10 20 33 12 18 14
1 1 116
Percent .9
5.2 8.6 17.2 28.4 10.3 15.5 12.1
.9 .9 100.0
Valid Percent .9
5.2 8.6 17.2 28.4 10.3 15.5 12.1
.9 .9 100.0
Cumulative Percent .9 6.0 14.7 31.9 60.3 70.7 86.2 98.3 99.1 100.0
PSY 721 Scores and Norms
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4
Developmental: Age Norms
• Uses.
– Initially for establishing ‘mental age’.
– BASAL AGE highest age at and below which all tests are passed.
• Issues.
– Mental age units are not constant with chronological age.
– Rapid growth spurts.
– Not an interval scale.
– Cannot be interpreted as overall performance.
PSY 721 Scores and Norms
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Developmental: Grade Norms
• Uses.
– Educational achievement tests.
– May be expressed in years and months.
• Issues.
– Instructional content varies from school to school.
– Not really relevant at high school level.
– Interpretation.
PSY 721 Scores and Norms
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Developmental: Ordinal Scales
• Uses.
– Behavioral and cognitive development.
– Piaget. – Gesell.
• Issues.
– Assume one level is prerequisite to the next.
PSY 721 Scores and Norms
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5
Major Issue
1. How do you compare performance of different people across different forms of a test?
2. How to compare performance of people on the same test across different administration techniques?
PSY 721 Scores and Norms
16
Equating
Process of establishing the relationship
between scores on alternate forms of a test or the same test across
time.
PSY 721 Scores and Norms
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Equating: Same Sample Technique
1. Get a large representative sample of examinees.
2. Give half the sample form A and the other half form B.
3. Compute the mean and standard deviation for each form.
4. Compute the z-scores for the raw scores for each test.
5. For ease of interpretation transform the z-scores to some common transformed score.
PSY 721 Scores and Norms
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6
Equating: Different Sample Technique
1. Identify a sample of key questions from the earlier test version.
2. Insert these items in the current version of the test.
3. Compare the performance on the key questions across the two groups.
PSY 721 Scores and Norms
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National Anchor Norms
• Uses
– Compare performance on different tests.
• Issues.
– Does not imply that the tests are interchangeable.
– Different psychometric properties.
PSY 721 Scores and Norms
20
Within Group Comparisons
PSY 721 Scores and Norms
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7
Percentile
Percent of people in the standardization sample
who fall at or below a given score.
PSY 721 Scores and Norms
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PSY 721 Scores and Norms
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Percentiles: Benefits & Issues
• Benefits.
– Easy to compute.
– Easy to understand.
– Suitable to all tests.
– Widely used.
– Good if the distribution is normal.
• Issue.
– Inequality of units at extremes of the normal curve.
– Problem if the distribution is not normal.
PSY 721 Scores and Norms
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8
Quartiles
Divides the distribution into four groups each containing
25% of the sample.
PSY 721 Scores and Norms
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Q1 Q2 Q3
PSY 721 Scores and Norms
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Standard Scores
A score that has been converted
from one scale into another scale.
PSY 721 Scores and Norms
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9
Concept
µ
-2σ -1σ -2z -1z
0σ +1σ +2σ 0z +1z +2z
PSY 721 Scores and Norms
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z-Scores
z= X− M s
PSY 721 Scores and Norms
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Example
Mean = 50 SD = 10
What is the z score for a raw score of 65?
What is the z score for a raw score of 45?
Z = (65 –50)/10 Z = 15/10 Z = 1.5
Z = (45 – 50)/10 Z = -5/10 Z = -.5
PSY 721 Scores and Norms
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PSY 721 Scores and Norms
1
What We Will Cover in This Section.
• Test scores • Norms
• Types of interpretation
PSY 721 Scores and Norms
2
Raw Score
Count or sum of the number of items endorsed
or number of items correctly answered.
PSY 721 Scores and Norms
3
1
Norms
Norm Norms Norming
Behavior that is usual or typical for members of a group.
Reference scores against which an individual’s scores are compared.
Process of establishing norms for a test.
Norman
A fat guy who drinks beer in Cheers.
PSY 721 Scores and Norms
4
Establishing Norms
1. Target population. 2. Standardization sample. 3. Norm Group.
- Size. - Geographic representation. - Socioeconomic level. - Ethnic composition.
PSY 721 Scores and Norms
5
PSY 721 Scores and Norms
6
2
PSY 721 Scores and Norms
7
Types of Norms
PSY 721 Scores and Norms
8
Reference Groups
• National norms. • Regional norms. • Local norms. • Sub-group norms.
PSY 721 Scores and Norms
9
3
Table 2. Word, raw score: Total Sample
Valid
Missing Total
5 6 7 8 9 10 11 12 13 14 Total System
Frequency 1 9
24 31 40 12 19 15
1 1 153 11 164
Percent .6
5.5 14.6 18.9 24.4
7.3 11.6
9.1 .6 .6
93.3 6.7
100.0
Valid Percent .7
5.9 15.7 20.3 26.1
7.8 12.4
9.8 .7 .7
100.0
Cumulative Percent .7 6.5 22.2 42.5 68.6 76.5 88.9 98.7 99.3 100.0
PSY 721 Scores and Norms
10
Valid
Table 6. Word, raw score: Undergraduate Students
6 7 8 9 11 12 Total
Frequency 3
14 11
7 1 1 37
Percent 8.1
37.8 29.7 18.9
2.7 2.7 100.0
Valid Percent 8.1
37.8 29.7 18.9
2.7 2.7 100.0
Cumulative Percent 8.1 45.9 75.7 94.6 97.3 100.0
PSY 721 Scores and Norms
11
Valid
Table 9. Word, raw score: Graduate Students
5 6 7 8 9 10 11 12 13 14 Total
Frequency 1 6
10 20 33 12 18 14
1 1 116
Percent .9
5.2 8.6 17.2 28.4 10.3 15.5 12.1
.9 .9 100.0
Valid Percent .9
5.2 8.6 17.2 28.4 10.3 15.5 12.1
.9 .9 100.0
Cumulative Percent .9 6.0 14.7 31.9 60.3 70.7 86.2 98.3 99.1 100.0
PSY 721 Scores and Norms
12
4
Developmental: Age Norms
• Uses.
– Initially for establishing ‘mental age’.
– BASAL AGE highest age at and below which all tests are passed.
• Issues.
– Mental age units are not constant with chronological age.
– Rapid growth spurts.
– Not an interval scale.
– Cannot be interpreted as overall performance.
PSY 721 Scores and Norms
13
Developmental: Grade Norms
• Uses.
– Educational achievement tests.
– May be expressed in years and months.
• Issues.
– Instructional content varies from school to school.
– Not really relevant at high school level.
– Interpretation.
PSY 721 Scores and Norms
14
Developmental: Ordinal Scales
• Uses.
– Behavioral and cognitive development.
– Piaget. – Gesell.
• Issues.
– Assume one level is prerequisite to the next.
PSY 721 Scores and Norms
15
5
Major Issue
1. How do you compare performance of different people across different forms of a test?
2. How to compare performance of people on the same test across different administration techniques?
PSY 721 Scores and Norms
16
Equating
Process of establishing the relationship
between scores on alternate forms of a test or the same test across
time.
PSY 721 Scores and Norms
17
Equating: Same Sample Technique
1. Get a large representative sample of examinees.
2. Give half the sample form A and the other half form B.
3. Compute the mean and standard deviation for each form.
4. Compute the z-scores for the raw scores for each test.
5. For ease of interpretation transform the z-scores to some common transformed score.
PSY 721 Scores and Norms
18
6
Equating: Different Sample Technique
1. Identify a sample of key questions from the earlier test version.
2. Insert these items in the current version of the test.
3. Compare the performance on the key questions across the two groups.
PSY 721 Scores and Norms
19
National Anchor Norms
• Uses
– Compare performance on different tests.
• Issues.
– Does not imply that the tests are interchangeable.
– Different psychometric properties.
PSY 721 Scores and Norms
20
Within Group Comparisons
PSY 721 Scores and Norms
21
7
Percentile
Percent of people in the standardization sample
who fall at or below a given score.
PSY 721 Scores and Norms
22
PSY 721 Scores and Norms
23
Percentiles: Benefits & Issues
• Benefits.
– Easy to compute.
– Easy to understand.
– Suitable to all tests.
– Widely used.
– Good if the distribution is normal.
• Issue.
– Inequality of units at extremes of the normal curve.
– Problem if the distribution is not normal.
PSY 721 Scores and Norms
24
8
Quartiles
Divides the distribution into four groups each containing
25% of the sample.
PSY 721 Scores and Norms
25
Q1 Q2 Q3
PSY 721 Scores and Norms
26
Standard Scores
A score that has been converted
from one scale into another scale.
PSY 721 Scores and Norms
27
9
Concept
µ
-2σ -1σ -2z -1z
0σ +1σ +2σ 0z +1z +2z
PSY 721 Scores and Norms
28
z-Scores
z= X− M s
PSY 721 Scores and Norms
29
Example
Mean = 50 SD = 10
What is the z score for a raw score of 65?
What is the z score for a raw score of 45?
Z = (65 –50)/10 Z = 15/10 Z = 1.5
Z = (45 – 50)/10 Z = -5/10 Z = -.5
PSY 721 Scores and Norms
30
10