Chapter 4
Test Dimensionality and Factor Analysis
Test dimensionality crucial in test development, evaluation, use
3 fundamental psychometric questions about test dimensionality:
3 main types of test:
1. Unidimensional tests
2. Multidimensional tests with correlated dimensions
3. Multidimensional tests with uncorrelated dimensions
- Must know what test type is used as have important psychometric differences
Test dimensionality
- When measuring a physical or psychological attribute, intention is to measure
a single attribute of the object/person
- Composite score should also ideally only reflect one dimension
Q1. Tests can measure on single or multiple dimensions
- Each test dimension likely to be scored separately
Q2. Some test dimensions are related to each other, whilst others are independent
- Nature of associations can be important for meaningfulness of total score of a
test
Q3. If we score and interpret dimension of a test, must understand the score’s
psychological meaning
1. Unidimensional tests- tests including items that only reflect a single
attribute, so responses to items are only driven by one attribute
, o Test questions usually have conceptual homogeneity (CH)-
responses to each item are a function of the same psychological
attribute
o Single score is computed reflecting single psych. attribute measured
All items combined to create composite (total) score
2. Multidimensional Tests with Correlated Dimensions- multiple
dimensions that are associated with each other
Eg. Stanford-Binet test
o Groups of questions assessing different psych. attributes
Groups= subtests- each reflect different facet
o Responses to question affected by specific or factor attribute
Higher-order factor- general psychological attribute
potentially affecting each specific attribute
o Can produce variety of scores
Typically, each subtest has own subtest score
Each subtest is unidimensional and questions in it have
CH
o Have score for each subtest, which is evaluated regarding its’
psychometric quality
Could have some subtests with good quality and others with bad
o Often scored to produce total score, combined across many subtests
3. Multidimensional Test with Uncorrelated Dimensions- multiple
dimensions that are not associated with each other
Eg. personality tests (Five Factor Inventory)
o No total test score computed (unlike w/ correlated dimensions)
o Score obtained for each dimension
o Each dimension score evaluate in terms of psychometric quality
Psychological Meaning of Test Dimensions
To interpret test dimensions accurately, must research the psychological attribute
represented by each test
Factor Analysis
Most common method of examination
Allows addressing of Q1-Q3, allowing insight to potential scores, evaluation, and use
of the tests
2 main types:
1. Exploratory factor analysis (EFA)
o More common type
o Easily to conduct with basic stat. software
o Used in early stages of psychometric analysis/development
2. Confirmatory factor analysis (CFA)
EFA Overview
- Better to base arguments on empirical data
o Subjects answer on Likert scale
o Enter data into statistical software compute program
o Compute correlation amongst the items
- Set=highly correlated items, shows psychological factor
Test Dimensionality and Factor Analysis
Test dimensionality crucial in test development, evaluation, use
3 fundamental psychometric questions about test dimensionality:
3 main types of test:
1. Unidimensional tests
2. Multidimensional tests with correlated dimensions
3. Multidimensional tests with uncorrelated dimensions
- Must know what test type is used as have important psychometric differences
Test dimensionality
- When measuring a physical or psychological attribute, intention is to measure
a single attribute of the object/person
- Composite score should also ideally only reflect one dimension
Q1. Tests can measure on single or multiple dimensions
- Each test dimension likely to be scored separately
Q2. Some test dimensions are related to each other, whilst others are independent
- Nature of associations can be important for meaningfulness of total score of a
test
Q3. If we score and interpret dimension of a test, must understand the score’s
psychological meaning
1. Unidimensional tests- tests including items that only reflect a single
attribute, so responses to items are only driven by one attribute
, o Test questions usually have conceptual homogeneity (CH)-
responses to each item are a function of the same psychological
attribute
o Single score is computed reflecting single psych. attribute measured
All items combined to create composite (total) score
2. Multidimensional Tests with Correlated Dimensions- multiple
dimensions that are associated with each other
Eg. Stanford-Binet test
o Groups of questions assessing different psych. attributes
Groups= subtests- each reflect different facet
o Responses to question affected by specific or factor attribute
Higher-order factor- general psychological attribute
potentially affecting each specific attribute
o Can produce variety of scores
Typically, each subtest has own subtest score
Each subtest is unidimensional and questions in it have
CH
o Have score for each subtest, which is evaluated regarding its’
psychometric quality
Could have some subtests with good quality and others with bad
o Often scored to produce total score, combined across many subtests
3. Multidimensional Test with Uncorrelated Dimensions- multiple
dimensions that are not associated with each other
Eg. personality tests (Five Factor Inventory)
o No total test score computed (unlike w/ correlated dimensions)
o Score obtained for each dimension
o Each dimension score evaluate in terms of psychometric quality
Psychological Meaning of Test Dimensions
To interpret test dimensions accurately, must research the psychological attribute
represented by each test
Factor Analysis
Most common method of examination
Allows addressing of Q1-Q3, allowing insight to potential scores, evaluation, and use
of the tests
2 main types:
1. Exploratory factor analysis (EFA)
o More common type
o Easily to conduct with basic stat. software
o Used in early stages of psychometric analysis/development
2. Confirmatory factor analysis (CFA)
EFA Overview
- Better to base arguments on empirical data
o Subjects answer on Likert scale
o Enter data into statistical software compute program
o Compute correlation amongst the items
- Set=highly correlated items, shows psychological factor
