Measurement. Joseph Spring. Based on Software Metrics by Fenton and Pfleeger

Transcription

1 Measurement Joseph Spring Based on Software Metrics by Fenton and Pfleeger

2 Discussion Measurement Direct and Indirect Measurement Measurements met so far Measurement Scales and Types of Scale

3 Measurement Everyday Examples Write down three general measurements that you have met in everyday life

4 Measurement Definition Measurement is 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 An entity is an object or an event where an object is for example a person or a room An event is for example the testing phase of a software project, or a journey, An attribute is a feature or property of an event. For example The area of a room, the colour of a room, the cost of a journey The elapsed time in a testing phase When describing entities using attributes we often use numbers or symbols, e.g. price in pounds sterling, height in cm or inches, clothing in small, medium or large abstractions for our perception of the real world Note we can make judgements about entities by knowing and analysing their attributes e.g. height of a person, James is over 7 ft tall

5 Direct and Indirect Measurement These were discussed last week Direct Measurement A Definition Examples Indirect Measurement A Definition Examples

6 Measurements met so far Experimental Models Measurements from Data Theoretical Models Measurements Probability Stochastic Lines of Code Function Points Reliability Complexity

7 Measurements met so far Prediction Systems A prediction system consists of A Mathematical Model A set of prediction procedures for determining unknown parameters Interpreting results Example Reliability (Uniform and Exponential) Complexity (McCabe s Cyclomatic Complexity for a program)

8 Classifying Software Measures An internal attribute of a product, process or resource are those that can be measured purely in terms of the product, process or resource itself. So an internal attribute is one that can be measured by examining the product, process or resource on its own separate from its behaviour Examples Consider a set of s/w modules without executing the code we can determine several internal attributes: Size in terms of LOC, complexity (eg in terms of number of decision points, McCabe), dependencies among modules, faults in the code, (misplaced commas, inappropriate use of a command, )

9 Classifying Software Measures An external attribute of a product, process or resource are those that can be measured only with respect to how the product, process or resource relates to its environment. Here the behaviour of the product, process or resource is important rather than the entity itself Examples Again for a set of s/w modules some errors we can only find when we run the code: for example number of failures experienced by the user, difficulties experienced in navigation, length of time to search a database,.

10 Classifying Software Measures What of: nominal data ordinal data interval data Ratio data absolute data Include examples for each of the above

11 Nominal Scale (Nominal Data) The most primitive form of Measurement Example Consider a study into the location of software faults, in which the possible locations are at the specification stage, the design stage, or the coding stage So the entity = faults and the attribute = location of fault Two possible mappings M 1 and M 2 could be: M 1 1 if x is a specification fault 2 if x is a design fault M2 3 if x is a coding fault 101 if x is a specification fault if x is a design fault if x is a coding fault

12 Nominal Scale (Nominal Data) There are two characteristics for the Nominal Scale: The empirical relation system consists only of different classes. There is no notion of ordering among the classes Any distinct numbering or symbolic representation of the classes is an acceptable measure, but there is no notion of magnitude associated with the numbers or symbols M 1 1 if x is a specification fault 2 if x is a design fault M2 3 if x is a coding fault 101 if x is a specification fault if x is a design fault if x is a coding fault

13 Ordinal Scale (Ordinal Data) Example Let the set of entities be software modules Let the attribute be complexity Let there be five classes of attribute: trivial, simple, moderate, complex and incomprehensible Note Here the attributes have an implicit order relation: that applies to the different classes R = is less complex than

14 Ordinal Scale (Ordinal Data) A mapping a if x is trivial b if x is simple M( x) c if x is moderate d if x is complex e if x is incomprehensible is valid providing a, b, c, d, e preserve the implicit order e.g. a < b < c < d < e e.g. a = 1, b = 2, c = 3, d = 4, e = 5 Qu. What of : a = 10, b = 11, c = 4, d = 5, e = 6 or a = 10, b = 11, c = 12, d = 13, e = 13

15 Ordinal Scale (Ordinal Data) Characteristics of the Ordinal Scale The empirical relation system consists of classes that are ordered with respect to the attribute Any mapping that preserves the ordering (a monotonic function) is acceptable The numbers are only used to rank the classes. +, -, x, and \ have no meaning here

16 Interval Scale (Interval Data) This scale captures more information than the previous two on the size of the intervals separating the classes; giving an understanding in some sense of the jump from one class to another Characteristics of the interval scale An interval scale preserves order, as with the ordinal scale An interval scale preserves differences, but not ratios So we know the difference between any two classes in ran(m) but the ratio of two classes in ran(m) doesn t make sense Addition and subtraction are acceptable for the interval scale but not multiplication or division

17 Interval Scale (Interval Data) Examples 1. Consider differences in air temperature measured in 0 C or 0 F. We may say that the difference between one degree and another is the same. However, suppose that in London the temperature is 20 0 C and in Madrid it was 30 0 C. We cannot say that it is 2/3 as hot in London as in Madrid or that it is 50% hotter in Madrid than London 2. For the M(x) example from the Ordinal scale slide if b-a = c-b = d-c = e-d then the attribute is measurable on an interval scale For example a = 1, b = 2, c = 3, d = 4, e = 5 a = 0, b = 2, c = 4, d = 6, e = 8 a = 3.1, b = 5.1, c = 7.1, d = 9.1, e = 11.1

18 Ratio Scale (Ratio Data) To preserve ratios we require the following characteristics: The measurement mapping preserves ordering, the size of intervals between entities and ratios between entities There is a zero element, representing a total lack of the attribute The measurement mapping must start at zero and increase at equal intervals, known as units All arithmetic can be meaningfully applied to the classes in the range of the mapping

19 Ratio Scale (Ratio Data) Examples 1. The length of a physical object, enabling us to make statements such as one entity is twice as long as another entity 2. The length of s/w code is also measurable on a ratio scale. E.g. lines of code, 1000;s of lines of code, number of characters in the code,

20 Absolute Scale (Absolute Data) For absolute measures M and M there exists only one transformation that maps between the two, the identity I. hence M and M are the same Characteristics of Absolute Data The measurement for an absolute scale counts the number of elements in the entity set The attribute always takes the form number of occurances of x in the entity There is only one possible measurement mapping the actual count All arithmetic analysis of the resulting count is meaningful

21 Absolute Scale (Absolute Data) Examples 1. In software engineering 1. The number of failures observed during integration testing 2. The number of people working on a software project can only be counted in one way the number of people Note 1. LOC is not an absolute measure for the attribute program length since there are different ways to measure the attribute: lines of code, 1000;s of lines of code, number of characters in the code, number of bytes, 2. However LOC is an absolute measure if the attribute is number of lines of code

22 Discussion Measurement Direct and Indirect Measurement Measurements met so far Measurement Scales and Types of Scale