Defining Scaling and Establishing its Need
- Score scale
- Scaling defined
o Numerically ordering objects of an assessment, or more precisely, attributes of the object.
o Orders the variable
o Eg
§ Male / female – unusual in that it is not hierarchical
o Ordinal
o Most scales are interval
o Employing the proper scale
§ Eg
· Likert – 7 points
· IQ - 40 – 160
§ Audience
o Indifference in the scale
§ Scale must be indifferent to object being measured.
§ Eg – gender of examinee
o Need for scaling
§ Interpretable / useful
Reliably Making Judgments
- The Just Noticeable Difference
o We can tell differences
o Threshold – point along continuum where we can agree a change has occurred
- Fechner's Law
Early to Current Scaling Models
- Deterministic and Probability Scaling Models
o Probabilistic models estimate likelihood of an event, such as chance of observing a certain test score given a particular set of conditions (ie item difficulty, trait level of examinee)
Dimensional Scaling
- Dimensionality Explained
o Unidimensional scaling
§ Test is appraising one only construct / trait
o Multidimensional scaling
§ Eg
· Extraversion and self-efficiacy are distinct phenomena, and each can be hypothesized as a latent construct. When considered concurrently, however, their individual variances overlap, meaning that their latencies have an oblique relationship.
· Multidimensional models appraise distances between traits and the specified dimensions
· …. When traits have a lot in common ….
Types of Scales
- General conditions for ordered scales
- Levels of measurement
o Nominal
o Ordinal
o Interval
o Ratio
Intervals For Scales
- Equal and nonequal interval scales
- Non-equal interval scale conveys more info re distribution than equal interval scales
Types of Measurement
- Ipsative vs normative measurement
- Ipsative – raw score that sums to constant for a given examinee
o Forced choice formats
- Isomorphic measurement
o Direct one-to-one relationship exists between entities used for measurement and the object that each represents.
o Most nominal level measurement
o Isomorphic transformation à recoding
Derived Scales
Eg
- Standard score
- Percentiles
- Scaled scores
- Normal curve equivalents
- Grade level scores
- Stanines
Basic Transformations in Score Scales
Non-linear transformations
Transformations for Development Scales
Characteristics of score scales
GW Questions / Comments
- Multidimensional tests : is it the case of main effects and interaction effect.
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