1 Test Worthiness Chapter 3. 2 Test Worthiness Four cornerstones to test worthiness: Validity Reliability Practicality Cross-cultural Fairness But first,
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1
Test Worthiness
Chapter 3
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Test Worthiness
Four cornerstones to test worthiness: Validity Reliability Practicality Cross-cultural Fairness
But first, we must learn one statistical concept: Correlation Coefficient
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Correlation Coefficient
Correlation – Statistical expression of the relationship between two sets
of scores (or variables)
Positive correlation Increase in one variable accompanied by increase in other “Direct relationship” - They move in the same direction
Negative correlation Increase in one variable accompanied by decrease in
other “Inverse relationship” – Variables move in opposite
directions
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Examples of Correlation Relationships
What is the relationship between: Gasoline prices and grocery prices? Grocery prices and good weather? Stress and depression? Depression and job productivity? Partying and grades? Study time and grades?
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Correlation (Cont’d)
Correlation coefficient (r ) A number between -1 and +1 that
indicates direction and strength of the relationshipAs “r” approaches +1, strength increases
in a direct relationship (positive)As “r” approaches -1, strength increases
in an inverse relationship (negative)As “r” approaches 0, the relationship is
weak or non existent (at zero)
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Correlation (cont)
Correlation coefficient “r”
0 to +.3 = weak+.4 to +.6 = medium +.7 to +1.0 = strong
0 to -.3 = weak -.4 to -.6 = medium -.7 to -1.0 = strong
-1 0 +1
DirectInverseWeak
Strong
Strong
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Correlation ExamplesSAT score Coll. GPA
930 3.0
750 2.9
1110 3.8
625 2.1
885 3.3
950 2.6
605 2.8
810 3.2
1045 3.0
910 3.5
r = .35
Missed Classes Coll. GPA
3 3.0
5 2.9
2 3.8
8 2.1
1 3.3
6 2.6
3 2.8
1 3.2
3 3.0
0 3.5
r = -.67
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Correlation Scatterplots
Plotting two sets of scores from the previous examples on a graph? Place person A’s SAT score on the x-
axis, and his/her GPA on the y-axis Continue this for person B,C, D etc.
This process forms a “Scatterplot.”
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Examples of Scatterplots
SAT & GPA Correlation
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 200 400 600 800 1000 1200
SAT
GP
A
Missed Classes & GPA
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 1 2 3 4 5 6 7 8 9
Missed classes
GP
A
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Scatterplots (cont)
What correlation (r ) do you think this graph has?
How about this correlation?
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More Scatterplots
What might this correlation be?
This correlation?
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More Scatterplots
This correlation? Last one
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Coefficient of Determination (Shared Variance)
The square of the correlation (r = .80, r2 = .64)
A statement about factors that underlie the variables that account for their relationship.Correlation between depression and anxiety = .85. Shared variance = .72. What factors might underlie both depression and
anxiety?
Depression Anxiety
Shared Trait Variance
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Validity
What is validity? The degree to which all accumulated
evidence supports the intended interpretation of test scores for the intended purpose
Lay Def’n: Does a test measure what it is supposed to measure?
It is a unitary concept; however, there are 3 general types of validity evidence
1.Content Validity2.Criterion-Related Validity3.Construct Validity
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Content Validity
Is the content of the test valid for the kind of test it is? Developers must show evidence that the
domain was systematically analyzed and concepts are covered in correct proportion
Four-step process:Step 1 - Survey the domain Step 2 - Content of the test matches the
above domainStep 3 - Specific test items match the contentStep 4 - Analyze relative importance of each
objective (weight)
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Content Validity (cont)Survey of Domain
Step 1: Survey the Domain
Step 2: Content MatchesDomain
Step 3: Test items reflect content
Step 4: Adjusted for relative importance
Content Matches Domain
Item 1x 3
Item 2x2
Item 3x1
Item 4x2
Item 5x
2.5
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Content Validity (cont)
Face Validity Not a real type of content validity A quick look at “face” value of questions Sometimes, questions may not “seem” to
measure the content, but do (e.g., panic disorder example in book (p. 48)
How might you show content validity for an instrument that measures depression?
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Criterion-Related Validity: Concurrent and Predictive
Validity
Criterion-Related Validity The relationship between the test and a
criterion the test should be related to
Two types: Concurrent Validity – Does the
instrument relate to another criterion “now” (in the present)?
Predictive Validity – Does the instrument relate to another criterion in the future?
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Criterion-Related Validity: Concurrent Validity
Example 1 100 clients take the BDI Correlate their scores with clinicians’
ratings of depression of the same group of clients.
Example 2 500 people take test of alcoholism
tendency Correlate their scores with how significant
others rate the amount of alcohol they drink.
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Criterion-Related Validity: Predictive Validity
Examples: SAT scores correlated with how well
students do in college. ASVAB scores correlated with success
at jobs. GREs correlated with success in
graduate school. (See Table 3.1, p. 50) Do Exercise 3.2, p. 49
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Construct Validity
Construct Validity Extent to which the instrument measures a
theoretical or hypothetical trait Many counseling and psychological
constructs are complex, ambiguous and not easily agreed upon: Intelligence Self-esteem Empathy Other personality characteristics
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Construct Validity (cont)Four methods of gathering evidence for construct validity:
1. experimental design2. factor analysis3. convergence with other instruments4. discrimination with other measures.
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Construct Validity: Experimental Design
Creating hypothesis and research studies that show the instrument captures the correct concept Example:
Hypothesis: The “Blank” depression test will discriminate between clinically depressed clients and “normals.”
Method: Identify 100 clinically depressed clients Identify 100 “normals” Show statistical analysis
Second Example: Clinicians measure their depressed clients before, then after, 6 months of treatment
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Construct Validity: Factor Analysis
Factor analysis: Statistical relationship between subscales of test How similar or different are the sub-scales? Example:
Develop a depression test that has three subscales: self-esteem, suicidal ideation, hopelessness.
Correlate subscales correlate: Self-esteem and suicidal ideation: .35 Self-esteem and hopelessness: .25 Hopelessness and suicidal ideation: .82
What implications might the above scores have for this test?
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Construct Validity: Convergent Validity
Convergent Evidence – Comparing test scores to other, well-
established tests Example:
Correlate new depression test against the BDI Is there a good correlation between the two? Implications if correlation is extremely high?
(e.g., .96) Implications if correlation is extremely low?
(e.g., .21)
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Construct Validity: Discriminant Validity
Discriminant Evidence – Correlate test scores with other tests that
are different Hope to find a meager correlation Example:
Compare new depression test with an anxiety test.
Implications if correlation is extremely high? (e.g., .96)
Implications if correlation is extremely low? (e.g., .21)
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Validity Recap
Three types of validity Content Criterion
Concurrent Predictive
Construct validity Experimental Factor Analysis Convergent Discriminant
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Reliability
Accuracy or consistency of test scores.Would you score the same if you took the test over, and over, and over again?Reported as a reliability(correlation) coeffiecient. The closer to r = 1.0, the less error in the test.
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Three Ways of Determining Reliability
1.Test-Retest2.Alternate, Parallel, or Equivalent
Forms3.Internal Consistency
a. Coefficient Alphab. Kuder-Richardsonc. Split-half or Odd Even
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Test-Retest ReliabilityGive the test twice to same group of people.
E.g. Take the first test in this class, and very soon after, take it again. Are the scores about the same?
person 1 person 2 person 3 person 4 person 5 others….
1st test: 35 42 43 34 38 2nd test: 36 44 41 34 37
Graphic:
Problem: Person can look up answers between 1st and second testing
TimeA A
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Alternate, Parallel, or Equivalent Forms
Reliability
Have two forms of same test Give students two forms the same timeCorrelate scores on first form with scores on second form. Graphic:
Problem: Are two “equivalent” forms ever really equivalent?
A B
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Internal Consistency Reliability
How do individual items relate to each other and the test as a whole?Internal Consistency reliability is going “within” the test rather than using multiple administrationsHigh speed computers and only one test administration has made internal consistency popularThree types:
Split-Half or Odd-Even Cronbach’s Coefficient Alpha Kuder-Richardson
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Split-half or Odd-even Reliability
Correlate one half of test with other half for all who took the testExample:
Person 1 scores 16 on first half of test and 16 on second half
Person 2 scores 14 on first half and 18 on second half Also get scores for persons 3, 4, 5, etc. Correlate all persons scores on first half with their
scores on second half The correlation = the reliability estimate
Use “Spearman Brown formula to control for shortness of test
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Split-half or Odd-even Reliability Internal
Consistency
Example Continued: Person Score on 1st Half Score on 2nd half 1 16 16 2 14 18 3 12 20 4 15 17 And so forth….. Problem: Are any two halves really
equivalent? Graphic: A
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Cronbach’s Alpha and Kuder-Richardson Internal
Consistency
Other types of Internal Consistency: Average correlation of all of the
possible split-half reliabilities Two popular types:
Cronbach’s Alpha Kuder-Richardson (KR-20, KR-21)
Graphic: A
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Cross-Cultural Fairness
Issues of bias in testing did not get much attention until civil rights movement of 1960’s.Series of court decisions established is was unfair to use tests to track students in schools. Black and Hispanic students were being
unfairly compared to whites-not their norm group.
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Cross-Cultural Fairness
Americans with Disabilities Act: Accommodations for individuals taking tests for
employment must be made Tests must be shown to be relevant to the job in
question.
Buckley Amendment (FERPA): Right to access school records, including test
records. Parents have the rights to their child’s
records
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Cross-Cultural Fairness
Carl Perkins Act: Individuals with a disability have the right to
vocational assessment, counseling and placement.
Civil Rights Acts: Series of laws concerned with tests used in
employment and promotion.
Freedom of Information Act: Assures access to federal records, including test
records. Most states have expanded this law so that it also
applies to state records.
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Cross-Cultural Fairness
Griggs v. Duke Power Company Tests for hiring and advancement much show ability to
predict job performance. Example: Can’t give a test to measure
intelligence for those who want to get a job as a road worker.
IDEIA and PL 94-142: Assures rights of students (age 2 – 21) suspected of
having a learning disability to be tested at the school’s expense.
Child Study Teams and IEP set up when necessary
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Cross-Cultural Fairness
Section 504 of the Rehabilitation Act: Relative to assessment, any instrument
used to measure appropriateness for a program or service must measure the individual’s ability, not be a reflection of his or he disability.
The Use of Intelligence Tests with Minorities: Confusion and Bedlam (See Insert 3.1, p. 58)
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Disparities in Ability
Cognitive differences between people exist, however, they are clouded over by issues of SES, prejudice, stereotyping, etc: are there real differences?Why do differences exist and what can be done to eliminate these differences?Often seen as environmental-No Child Left BehindExercise 3.4, p. 58: Why might their be differences among cultural groups on their ability scores?
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Practicality
Several practical concerns: Time Cost Format(clarity of print, print size,
sequencing of questions and types of questions)
Readability Ease of Administration, Scoring, and
Interpretation
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Selecting & Administering Tests
Five Steps:1. Determine your client’s goals2. Choose instruments to reach client goals.3. Access information about possible instruments:
Source books: E.g.,: Buros Mental Measurement Yearbook and Tests in Print
Publisher resource catalogs Journals in the field Books on testing Experts The internet
4. Examine validity, reliability, cross-cultural fairness, and practicality.
5. Make a wise choice.
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