1. 1 SIM5102 Software Evaluation Fundamental of Software Measurement

2. 2 The Basic Of Measurements (1) How much must we know about an attribute before it is reasonable to consider measuring it? For example; do we know enough about ‘size’ of web sites to be able to measure it? Or ‘complexity’ of programs? How do we know if we have really measured the attribute we wanted to measure? For example; does the count of the number of ‘broken links’ found on a web sites during integration testing measure the quality of the site? If not, what does the count tell us?

3. 3 The Basics Of Measurement (2) Using measurement, what meaningful statements can we make about an attribute and the entities that process it? For example; is it meaningful to talk about doubling a design’s quality? If not, how do we compare different designs? What meaningful operations can we perform on measures? For example; does it make sense to calculate the average productivity for a group of developers, or the average quality of a set of web sites?

4. 4 The Basics Of Measurement  To answer these questions, we must establish the basics of a theory of measurement?  Measurement Theory  Tells us the rules to be applied  Why Rules?  To be consistent in our measurement  To provide a basis for interpreting data  The measurement theory we’ll use is the Representational Theory of Measurement

5. 5 The Representational Theory Aims to formalize our intuition about how the world works  Obtained data must represent attributes of the entities we observe  Manipulation of the data must preserve observed relationships among entities  Intuition is the starting point for all measurement

6. 6 Real, Empirical, and Formal World Real worl d Emp irica l Worl d For mal Worl d Intuition and Observation Mapping Modeling & Verification

7. 7 Real, Empirical, and Formal World Entit y A Entit y B 42 33 M(A ) > M(B ) Intuition and Observation Mapping Modeling & Verification

8. 8 Number SystemReal World 50 Tree A M Tree B45 M Tree C 35 M M(Tree A) > M(Tree B) M(Tree A) > M(Tree C) M(Tree B) > M(Tree C) Tree A taller than Tree B Tree A taller than Tree C Tree B taller than Tree C Empirical relation preserved under M as Numerical relation

9. 9 Empirical and Numerical Relations Empirical relation Numerical Relation “ taller than” “ is tall” “ much taller than” x > y x > 70 x > y + 15 A is taller than B if and only if M(A) > M(B) A is tall if and only if M(A) > 70 A is much taller than B if and only if M(A) > M(B) + 15

10. 10 Representation Condition Required Rules for mapping  the data we obtain as MEASURES should represent attributes of the entities we observe  Manipulation of the data should preserve relationships that we observe among the entities

11. 11 Key Steps of Formal Measurement 1. Identify attribute for some real world entity 2. Identify empirical relations for attribute 3. Identify numerical relations corresponding to each empirical relation 4. Define the model for the mapping from real world entities to numbers 5. Check that numerical relations preserve and are preserved by empirical relation

12. 12 McCabe’s cyclomatic complexity If G is the control graph for a program P. G has e edges (arcs) and n nodes. V(G) = e –n + 2 e = 16, n = 13, V(G) = 5 V(G) is the number of linearly independent paths in G

13. 13 Cyclomatic Number  What is the entity?  What is the attribute?  What is the empirical relation?  What is the numerical relation?  What is the model for the mapping?

14. 14 Cyclomatic Number  Given two programs P1 and P2  Cyclomatic number for P1 = 4 and cyclomatic number for P2 = 9  Does that mean that P2 is more complex than P2

15. 15 Some measures used in SE Completed project Rate of occurrence of failure in CPU timeReliabilityProgram code Number of faults found per KLOCEfficiencyTester Number of faults found per KLOCRate at which faults are found Integration testing process Hours from start to finishDurationIntegration testing process Number of executable statementsLengthProgram code Number line of code (LOC)LengthProgram code Days from start to finishDurationCompleted project Months from start to finishDuration MeasuresAttributesEntity

16. 16 Direct & Indirect Measurement Direct measurement of an attribute of an entity involves no other attribute or entity  Length of source code (measured by LOC)  Duration of testing process (measured by elapsed time in hours)  Number of defects discovered during the testing process (measured by counting defects)  Time a programmer spends on a project (measured by weeks works)

17. 17 Programmer productivity Module defect density Indirect Measurement Defect detection efficiency LOC produced Person month of effort Number of defects module size Number of defect detected total number of defects Requirement stability Test effectiveness ratio System Spoilage number of initial requirement Total number of requirement Number of items covered Total number of items Effort spent fixing faults total project effort

18. 18 Measurement Scales  Purpose of performing mapping M is to be able to manipulate data in the numerical system and use the results to draw conclusions about the attribute in the empirical system.  Not all mappings are the same and the differences among the mappings can restrict the type of analysis one can do  The measurement mapping M, together with the empirical and numerical systems are a measurement scale.

19. 19 Scale Types  Five major types  Nominal  Ordinal  Interval  Ratio  Absolute  Knowing the characteristics of each type helps us to interpret the measures

20. 20 Nominal Scale  The most primitive form of measurement  Defines classes or categories, and places entities in a particular class or category, based on the value of the attribute  Characteristics The empirical relation system consists only of different class No notion of ordering Any numbering or symbolic representation of the classes is acceptable, but there is no notion of magnitude associated with the numbers or symbols

21. 21 Examples of nominal scale EntitiesAttributesCategories FruitsType Apple, orange, durian Software faults LocationSpecification, Design, code ? ? ?

22. 22 Ordinal Scale Often useful to augment the nominal scale with information about an ordering of classes or categories Characteristics  The empirical relation system consists of classes that are ordered with respect to the attribute  Any mapping that preserve the ordering is acceptable  The numbers represent ranking only, so addition, subtraction, and any other arithmetic operations have no meaning

23. 23 Examples of ordinal scale EntitiesAttributesCategories Softwarecomplexitytrivial, simple, moderate, Modulecomplex, incomprehensible Academics titletutor, lecturer, senior lecturer, Associate Prof., Prof ? ? ?

24. 24 Interval Scale Useful to augment the ordinal scale with information about the size of the intervals that separates the classes Characteristics  Preserve order  Preserve differences but not ratios. That is we know the difference between any two of the ordered classes in the range of the mapping, but computing the ratio of the two classes in the range does not make sense  Addition and subtraction are acceptable operations, but not multiplication and division

25. 25 Examples of interval scale EntitiesAttributesCategories ProjectTime relative tonumber of days start of project Methodcomplexityvery low, low, average, high, very high ? ? ?

26. 26 Ratio Scale The most useful scale of measurement, common in the physical science Characteristics  Preserving ordering, the size of interval between entities, and ratios between entities  There is a zero element, representing total lack of the attribute  Mapping must start at zero and increase at equal interval, known as units  All arithmetic can be meaningfully applied to the classes in the range of mapping

27. 27 Examples of ratio scale EntitiesAttributesCategories Source codeLengthLOC Web Sitesizenumber of web pages ? ? ?

28. 28 Absolute Scale This is the most restrictive scale Characteristics  The measurement for an absolute scale is made simply by counting the number of elements in the entity set  The attribute always takes the form “number of occurrences of x in the entity”  There is only one possible measurement mapping, namely the actual count  All arithmetic analysis of the resulting counting is meaningful

29. 29 Examples of absolute scale EntitiesAttributesCategories Source code number of LOC number of LOC Web Site number of HTML files number of HTML files ? ? ?

30. 30 Meaningfulness in Measurement “ We say that a statement involving measurement is meaningful if its truth value is invariant of transformations of allowable scales”

31. 31 Meaningfulness in Measurement Ali is twice as tall as Mat The temperature in Tokyo today is twice that in London The difference in temperature between Tokyo and London today is twice that it was yesterday

32. 32 Meaningfulness in Measurement Ali is twice as tall as Mat  Ali is 180 cm tall  Mat is 90 cm tall same as  Ali is 5.9 feet tall  Mat is 2.95 feet tall Feet= centimeters/30.48 M(Ali) = 2 * M(Mat)

33. 33 Meaningfulness in Measurement The temperature in Tokyo today is twice that in London  Tokyo temperature = 40 C  London temperature = 20 C same as  Tokyo temperature = 104 F  London temperature = 68 F F = 9/5 * C + 32 M(Tokyo) = 2 * M(London)

34. 34 Meaningfulness in Measurement Yesterday  Tokyo = 35 C  London = 25 C Same as  Tokyo = 95 F  London = 77 F Today  Tokyo = 40 C  London = 20 C Same as  Tokyo = 104 F  London = 68 F 10 18 20 36 |M(TokyoT) – M(LondonT)| = 2 * |M(TokyoY) – M(LondonY)|

35. 35 Statistical operations on measures (1)  A measure’s scale type affects the set of operations and statistics that can be applied to the data.  Measures of central tendency (where the “middle” of the set is likely to be).  Measures of dispersion (how far data points wander off from the middle).

36. 36 Measures of central tendency # Web pages 20 25 26 27 35 45 46 67 89 90 100 123 Mean 59.9 Median 45.5 Mode 100.0 Sum 958.0 Mean = sum divided by number of items Median = value of the middle-ranked item Mode = value of the most commonly occurring item Sum = sum of values for all items

37. 37 Measures of dispersion Minimum = smallest value Maximum = largest value Standard deviation = indication of the spread of observations about the mean. Minimum 20.0 Maximum 123.0 Std deviation 35.1

38. 38 Important!  Mean and standard deviation cannot be computed on nominal and ordinal measures!!!!  Nominal and ordinal measures do not allow arithmetic operations such as addition, subtraction, multiplication and division.

39. 39 Summary of measurement scales and statistics relevant to each 1 Non-parametric Parametric Mean Pearson correlation Equivalence Greater than Known ratio of any Intervals Known ratio of any two Scale values Ratio Non-parametric Parametric Mean Standard deviation Pearson correlation Equivalence Greater than Known ratio of any Intervals Interval Non-parametricMedian Spearman r Kendal t Kendall W Equivalence Greater than Ordinal Non-parametricMode Frequency EquivalenceNominal Appropriate Statistical tests Examples of appropriate statistics Defining RelationsScale Type 1 Fenton and Pfleeger

40. 40 Objective vs. Subjective measures (1)  Objective measurement – consistency of measurement where different people produce the same measures. E.g., measuring size of a Web site as the number of local html files (those not pointed by external links).

41. 41 Objective vs. Subjective measures (2)  Subjective measurement – measures that depend on the environment in which they are made.  Can vary with the person measuring, and they can reflect the judgement of the measurer. E.g. measuring interface design, understandability of requirements etc.

42. 42 Reading  Chapter 2 Fenton and Pfleeger book.