# scales

Document Sample

```					         Measurement Scales

The “richness” of the measure

scale2                                   1
Status Report on
Software Measurement
Shari Pfleeger, Ross Jeffrey, Bill
Curtis, Barbara Kitchenham
IEEE Software March/April 97

scale2                                        2
What is the status of Soft Measure?

scale2                               3
Scales
 nominal
 ordinal
 interval
 ratio
 absolute

scale2            4
Scales
 defined    in terms of allowed transformations
– this is not convenient
– research topic
» how to relate abstractions to scales

scale2                                               5
Nominal
 The weakest scale
 Classic example
– numbers on sports uniforms
 Transformation
– Any 1-1 mapping
 Stats
– mode, frequency, median, percentile

scale2                                           6
Nominal Scales
 Not  valid - “Our team is better because the
numbers on our uniforms total more than
 Not valid - “Ch 11, Ch 13, Ch27, and Ch49
equal 100% of your viewing needs”

scale2                                                7
Ordinal
 Gives an “ordering”
 Classic example
– class rank
 Transformation
– any monotonic transformation
 Statistics
– spearman correlation

scale2                                    8
Class Rank
 Not    valid - “I am ranked 4th and you are
ranked 8th, so I am twice as good as you
are.”

scale2                                               9
Interval
 The size of the intervals are constant
 Classic example
– temparature
 Transformation
– aX + b
 Statistics
– mean, stand dev., pearson correlation

scale2                                             10
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

scale2                                            11
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).

scale2                                                   12
Diurnal Variation
 68 F - 32 F is twice 50 F - 32 F
 20 C - 0 C is twice 10 C - 0 C

scale2                                    13
Ratio
 Classic   example
– length measurement
 Transformation
– aX
 Statistics
– geometric mean, coefficient of variation

scale2                                                14
Ratio Scales
 have a well-accepted zero
 convert from one to another by
multiplication

scale2                                  15
Absolute
 Counting
 Classic   example
– marbles
 Transformation
– no
 Some     practioners do not consider this a
scale separate from the ratio scale

scale2                                               16
Classifying Scales
 ShoeSize
 Money
 LOC
 McCabe’s Cyclomatic Number

scale2                              17
Measurement Theory
 circa1900 - applied to physics
 1940’s - applied to psychology, sociology
 1990’s - applied to software measurement

scale2                                             18
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”

scale2                                                   19
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

scale2                                            20
Terminology
 entity is an object or event
 attribute is a feature or property of the
entity

scale2                                             21
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)

scale2                               22
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

scale2                                                  23
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

scale2                                                    24
Examples
 less than - if a < b than b is not < a
 less than or equal - a is “less than or equal”
to a

scale2                                                  25
Numerical
   A set of entities
– also called the “answer set”
– usually numbers - natural numbers, integers or
reals
A    set of relations
– often “less than” or “less than or equal”

scale2                                                      26
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

scale2                                        27

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 7 posted: 9/2/2012 language: English pages: 27