scale2 1 measurement scales the “richness” of the measure
TRANSCRIPT
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Measurement Scales
The “richness” of the measure
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Status Report on Software Measurement
Shari Pfleeger, Ross Jeffrey, Bill Curtis, Barbara Kitchenham
IEEE Software March/April 97
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What is the status of Soft Measure?
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Scales
nominal ordinal interval ratio absolute
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Scales
defined in terms of allowed transformations– this is not convenient– research topic
» how to relate abstractions to scales
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Nominal
The weakest scale Classic example
– numbers on sports uniforms Transformation
– Any 1-1 mapping Stats
– mode, frequency, median, percentile
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Nominal Scales
Not valid - “Our team is better because the numbers on our uniforms total more than the numbers on your uniforms”
Not valid - “Ch 11, Ch 13, Ch27, and Ch49 equal 100% of your viewing needs”
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Ordinal
Gives an “ordering” Classic example
– class rank Transformation
– any monotonic transformation Statistics
– spearman correlation
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Class Rank
Not valid - “I am ranked 4th and you are ranked 8th, so I am twice as good as you are.”
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Interval
The size of the intervals are constant Classic example
– temparature Transformation
– aX + b Statistics
– mean, stand dev., pearson correlation
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Converting Temps
How do we convert from fahrenheit to celsius?– (F-32)*5/9 = C– 68 F = 36*(5/9) = 20 C– 50 F = 18* (5/9) = 10 C– 32 F = 0*(5/9) = 0 C
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Temperature
not valid - “it is twice as hot today as yesterday” - this is scale dependent - if it is true for fahrenheit, it is not true for celsius
valid - “the diurnal variation today is twice what it was yesterday” (the difference between max and min).
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Diurnal Variation
68 F - 32 F is twice 50 F - 32 F 20 C - 0 C is twice 10 C - 0 C
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Ratio
Classic example – length measurement
Transformation– aX
Statistics– geometric mean, coefficient of variation
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Ratio Scales
have a well-accepted zero convert from one to another by
multiplication
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Absolute
Counting Classic example
– marbles Transformation
– no Some practioners do not consider this a
scale separate from the ratio scale
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Classifying Scales
Grades Shoe Size Money LOC McCabe’s Cyclomatic Number
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Measurement Theory
circa 1900 - applied to physics 1940’s - applied to psychology, sociology 1990’s - applied to software measurement
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Measurement
“the process by which numbers or symbols are assigned to attributes of entities in the real world in such a way as to describe them according to clearly defined rules”
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Measure (Fenton)
a mapping from the document to the answer set that satisfies measurement theory
the value in the answer set that corresponds to a document
compare to “metric” which is just a mapping
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Terminology
entity is an object or event attribute is a feature or property of the
entity
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Representational TOM
empirical relation system– (C,R)
numerical relation system– (N,P)– M maps (C,R) to (N,P)
representation condition– x<y iff M(x)<M(y)
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Empirical
A set of entities, E A set of relationships, R
– often “less than” or “less than or equal”– note that not everything has to be related
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Relationships - R
The set of relationships R is mathematically defined as a subset of the crossproduct of the elements, ExE
Note that not every pair of elements has to be related and an element may or may not be related to itself
Since we are interested in comparing entities, “less than” or “less than or equal”, are good relationships
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Examples
less than - if a < b than b is not < a less than or equal - a is “less than or equal”
to a
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Numerical
A set of entities– also called the “answer set”– usually numbers - natural numbers, integers or
reals A set of relations
– usually already exists– often “less than” or “less than or equal”
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The Mapping
The representation condition– M(x) rel M(y) if x rel y– x rel y iff M(x) rel M(y)
Both have been used by classical measurement theory authors
Fenton prefers the second definition
Questions
Questions