1. The Basic of Measurement
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2. The representational theory of measurement
Empirical relations
The representational theory of measurement seeks to formalize our intuition about the way the world works.
Data we obtain as measures should represent attributes of the entities we observe.
Manipulation of this data should preserve relationships among the entities.
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3. The representational theory of measurement
Empirical relations
Measurement is a mapping from the empirical world to the formal, relational word.
A measure is the number or symbol assigned to an entity by this mapping in order to characterize an attribute.
A Measure is used to characterize an attribute
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4. The representational theory of measurement
The rules of the mapping
The real world is the domain of the mapping
The mathematical world is the range
Attributes mapped to a mathematical system give us the range of:
Real numbers
Integers
Non-numeric symbols
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5. The representational theory of measurement
The representation condition of measurement
The representation condition asserts that a measurement mapping must map entities into numbers and empirical relations into numerical relations in such a way that the empirical relations preserve and are preserved by the numerical relations.
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6. Measurement and models
A model is an abstraction of reality, allowing the us to strip away detail and view an entity or concept from a particular perspective.
Models give understanding how measures are derived and how to interpret the behavior back in the real world.
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7. Measurement and models
Defining attributes
Graph on page 39
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8. Measurement and models
Direct and indirect measurement
Direct measurement of an attribute of an entity involves no other attribute or entity.
Indirect measurement uses combinations of attributes of other entities to obtain a measurement.
Page 40 examples.
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9. Measurement and models
Measurement for prediction
Measurement for prediction always requires some kind of mathematical model that relate the attributes to be predicted ( the future) to some other attributes that we can measure now (the present).
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10. Measurement and models
Measurement for prediction (continued)
A prediction system consists of a mathematical model together with a set of prediction procedures for determining unknown parameters and interpreting result (Littlewood, 1988).
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11. Measurement scales and scale types
Normal
Ordinal
Interval
Ratio
Absolute
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12. Meaningfulness in measurement
Understanding scale type enables us to determine when statements about measurement make sense.
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13. Meaningfulness in measurement
Statistical operations on measures
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14. Meaningfulness in measurement
Objective and subjective measures
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15. Meaningfulness in measurement
Measurement in extended number systems
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16. Meaningfulness in measurement
Indirect measurement and meaningfulness
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17. Summary
Measurement requires us to identify intuitively understood attributes possessed by clearly defined entities.
Then we assign numbers or symbols to the entities in a way that captures our intuitive understanding about the attribute.
The intuitive understanding leads to the identification of relations between entities.
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18. Summary
To measure the attribute , we define corresponding relations in some number system.
Then measurement assigns numbers to the entities is such a way that these relations are preserved.
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19. Summary
This relationship between the domain and range relationship is called the representation condition.
Five well known representation condition
Normal Ratio
Ordinal Absolute
Interval
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20. Summary
The scale type for a measure determines what kind of statement we can meaningfully make using the measurement.
Many SWEN attributes are not directly measurable and we have to determine when statements and operations are meaningful.
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