f02measure13 1 Software Measurement Measurement is essential for a science

f02measure13 2 Measurement u “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”

f02measure13 3 Uses of Measurements u assessment u prediction –mathematical model –inherently stochastic

f02measure13 4 Types of Measurements u Process measures –Identify essential characteristics of process –e.g. GQM - Goal - Question - Measure - if we want to improve customer satisfaction, measure number of defect reports u Product measures –identify essential characteristics of document –e.g. LOC, McCabe’s Cyclomatic Number

f02measure13 5 Properties of Measures u Monotonicity u Scale Types –nominal –ordinal –interval –ratio –absolute

f02measure13 6 LOC u Why isn’t the Lines of Code measure very useful? u It is not an essential characteristic of software u It is not very useful as a predictor

f02measure13 7 Height and weight u Why are height and weight useful in measuring people?

f02measure13 8 Using Measures u Can we take the average of heights, temps, grades, shoe sizes, jersey numbers? u Can we add two heights, temps, grades, jersey numbers, shoe sizes? u Can we compare ratios of heights, temps, grades, jersey numbers, shoe sizes?

f02measure13 9 Software Measurement Measurement Theory

f02measure13 10 Measurement Theory u circa applied to physics u 1940’s - applied to psychology, sociology u 1990’s - applied to software measurement

f02measure13 11 Representational TOM u empirical relation system –(C,R) u numerical relation system –(N,P) u M maps (C,R) to (N,P) u representation condition –x M(x)<M(y)

f02measure13 12 Empirical u A set of entities, E u A set of relationships, R –often “less than” or “less than or equal” –note that not everything has to be related

f02measure13 13 Numerical u A set of entities –also called the “answer set” –usually numbers - natural numbers, integers or reals u A set of relations –usually already exists –often “less than” or “less than or equal”

f02measure13 14 The Mapping u The representation condition –M(x) rel M(y) if x rel y –x rel y iff M(x) rel M(y) u Both have been used by classical measurement theory authors u I prefer the first definition

f02measure13 15 Height

f02measure13 16 Representation Condition u If Fred is shorter than or equal to Bill, then Fred’s height is less than or equal to Bill’s height u if x <= y, then m(x) <= m(y)

f02measure13 17 Classic Example u McCabe’s Cyclomatic Number u Empirical - Control Flow Graph u Numerical (Answer Set) - integers u mapping - E-N+2

f02measure13 18 “BIG” example u We want to measure people as BIG –i.e. height and weight u Empirically, if two people are the same height, the heavier is bigger –if two people are the same weight, the taller is bigger u Answer set is real or tuple?

f02measure13 19 Statistics u The scale type implies usable statistics –Mean of values – at least interval –Ratios between values – at least ratio

f02measure13 20 Piles of blocks

f02measure13 21 Average of measures