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SOEN 384 Management, Measurement and Quality Control http://users.encs.concordia.ca/~s384_2/ Lecture 15: Software Engineering Management (SEM) : Representational Theory of Measurement • •Fenton’s book SOEN384-F10-L15: representational theory of 1 measurement Agenda Review Representational theory of measurement Scale types and meaningful statistics Nominal ordinal Next? SOEN384-F10-L15: representational theory of measurement 2 Evolution of an information need into a measurement plan SOEN384-F10-L15: representational theory of measurement 3 Plan Measurement activity SOEN384-F10-L15: representational theory of measurement 4 GQM Review: measurement information model (ISO/IEC 15939:2007 standard) Select & SOEN384-F10-L15: Specify representational theory of measurement Measures 6 Measurable Concepts and Related Questions SOEN384-F10-L15: representational theory of measurement 7 Select and Specify Measures Are we measuring correctly the specified measurable concepts? SOEN384-F10-L15: representational theory of measurement 8 Agenda Review Representational theory of measurement Scale types and meaningful statistics Nominal ordinal Next? SOEN384-F10-L15: representational theory of measurement 9 Representational theory of measurement Empirical Numerical Relational Measurement Procedure Relational Structure E Structure N Measurement is a mapping of empirical (observed) objects to numerical (mathematical) objects using a valid and reliable mechanism, called a homomorphism soen337-W09-L11: review 10 Representational Theory of Measurement in Examples Tom is tall. 185cm John is taller than Tom. 195cm >185cm Software A is reliable. 300 bugs/10 KLOC Software B is more reliable. 150 bugs /1 KLOC •to measure is to assign numbers to the entities Tom, Software A, etc. according to clearly defined rules; •“cm”, “bug”, “KLOC” are measurement units •Here, “tall”, “taller than”, “reliable”, “more reliable” are relations. SOEN384-F10-L15: representational theory of measurement 11 Representational Problem Measurement is a mapping of empirical (observed) objects Have to be to numerical meaningful! (mathematical) http://www.micha objects using a elbach.de/ot/ang_ hering/index.html valid and reliable mechanism, called a homomorphism SOEN384-F10-L15: representational theory of measurement 13 Meaningfulness of Mathematical Manipulations Example: Assume there are four football players with the numbers 2, 4 , 6, 8 on their shirts. We now calculate the arithmetic mean AR=(2+4+6+8)/4 = 5 Can we say that the player with number 5 represents the average performance of the four players? Answer: no because the numbers are only identification of the players … SOEN384-F10-L15: representational theory of measurement 15 Meaningfulness of the analysis of measurement data Example 2: Given two distances D1=10km and D2=5km: Can we say that the distance D1 is twice as long as the distance D2? (D1=D2*2) Will this statement be meaningful if the length is measured in meters or yards? SOEN384-F10-L15: representational theory of measurement 16 Meaningfulness and Scale Types of measurement data Five Major Types: Nominal, Ordinal, Interval, Ratio, Absolute Shown in increasing level of richness (the relations of each are contained in the next, when applicable) SOEN384-F10-L15: representational theory of measurement 17 Nominal Scale Type Defines categories of attributes of objects (entities) places each entity in a particular category, based on the value of its attribute. We do not know which categories are better (no preference) SOEN384-F10-L15: representational theory of measurement 18 Nominal Scale Type: Example 2.6, Fenton Entity: software failure Attribute: criticality Categories of software failures according to their criticality: R1: delayed response R2: incorrect output R3: data loss SOEN384-F10-L15: representational theory of measurement 19 Example 2.6: Measurement Method SOEN384-F10-L15: representational theory of measurement 20 Nominal Scale Type Properties Structure-Preserving Mapping Given two empirical entities a, b: Examples of Permissible Statistics & Statistical Tests: Frequency Mode Nonparametric tests which do not depend on preference or ranking SOEN384-F10-L15: representational theory of measurement 21 Nominal Scale Type: Key Points Classification Partitions the set of empirical entities into categories (also called equivalence classes) with respect to a certain attribute Equivalence operation: No knowledge about relationships among categories Empirical Requirements for the partitioning: Empirical Classes are jointly exhaustive ALL CATEGORIES TOGETHER SHOULD COVER ALL POSSIBLE CATEGORIES FOR THE ATTRIBUTE Empirical Classes are mutually exclusive A SIBJECT CAN BE CLASSIGIED INTO ONE AND ONLY ONE CATEGORY Numerical Requirements: Math. Operation: = soen337-W09-L10: a different number Each category is represented by theory (2) 22 Back to the 1st example: … Assume there are four football players with the numbers 2, 4 , 6, 8 on their shirts. Scale type? We now calculate the arithmetic mean AR=(2+4+6+8)/4 = 5 Is AR a meaningful statistical data? Answer: no because the arithmetic mean is not a meaningful mathematical operation on the nominal scale. SOEN384-F10-L15: representational theory of measurement 23 Example 2.6: from Nominal to Ordinal Next: add a new binary relation x more critical than y : Each data loss failure (R3) is more critical than incorrect output (R2) and delayed response failure (R1) Each incorrect failure (R2) is more critical than delayed response failure (R1) The measurement method shall be revised to account for this new binary relations SOEN384-F10-L15: representational theory of measurement 24 Example 2.6: Revised Measurement Method SOEN384-F10-L15: representational theory of measurement 25 Ordinal Scale Type Useful to augment the nominal scale with information about an ordering of the categories (such as preferences). The numbers represent ranking only, so addition, subtraction, and other arithmetic operations have no meaning. Why? No knowledge about the magnitude of the differences between categories of entities SOEN384-F10-L15: representational theory of measurement 26 Ordinal Scale Type Properties Structure-Preserving Mapping: preserves equivalence Given two empirical entities a, b: Math. Operations: =, <, > The numbers represent ranking only, so addition, subtraction, and other arithmetic operations have no meaning. SOEN384-F10-L15: representational theory of measurement 27 Ordinal Scale Type: Meaningful mathematical operations Examples of Permissible Statistics & Statistical tests: All nominal scale statistics Median Rank order statistics (f.e, Spearman’s correlation coefficient) Non-parametric SOEN384-F10-L15: representational theory of measurement 28 Exercises on Nominal and Ordinal Scale Types Determine the scale type of: Gender Marital status Distance Intelligence Score “Yes-No” voting system Blood types (A,B,AB,O) Letter grade system SOEN384-F10-L15: representational theory of measurement 29 Ordinal Scale Type Useful to augment the nominal scale with information about an ordering of the categories. The numbers represent ranking only, so addition, subtraction, and other arithmetic operations have no meaning. Why? No knowledge about the magnitude of the differences between categories of entities soen337-W09-L10: theory (2) 30 Ordinal Scale Type Properties Structure-Preserving Mapping: preserves equivalence Given two empirical entities a, b: Math. Operations: =, <, > The numbers represent ranking only, so addition, subtraction, and other arithmetic operations have no meaning. SOEN337-W08-L7-L8: Theory 31 Ordinal Scale Type (4) Examples of Permissible Statistics & Statistical tests: All nominal scale statistics Median Rank order statistics (f.e, Spearman’s correlation coefficient) Non-parametric soen337-W09-L10: theory (2) 32 Exercises on Nominal and Ordinal Scale Types Determine the scale type of: Gender Marital status Distance Intelligence Score “Yes-No” voting system Blood types (A,B,AB,O) Letter grade system soen337-W09-L9: theory (1) 33 Qualitative & Quantitative Aspects of Software Measurement Data Qualitative + Body of Knowledge = Quantitative soen337-W09-L11: review 34 Select and Specify Measures: Key Points Are we measuring correctly the specified measurable concepts? Yes, if we apply the representational theory of measurement SOEN384-F10-L15: representational theory of measurement 35 Representational theory of measurement Meaningful statistical analysis SOEN384-F10-L15: representational theory of measurement 36 Software Measurement Theory: Key Points Representational theory of measurement [Fenton 1998 ] rigorous framework for determining when a proposed measure really does characterize the attribute it is supposed to. rules for determining the scale types of measures, and hence to determine what statistical analysis is meaningful. SOEN384-F10-L15: representational theory of measurement 37 Questions? … soen337-W09-L9: theory (1) 38 Next? More scale types: Interval, Ratio, Absolute soen337-W09-L9: theory (1) 39

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posted: | 4/17/2011 |

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