The Basic of Measurement 11/10/2018 SWEN 5430 Software Metrics

The representational theory of measurement Empirical relations The representational theory of measurement seeks to formalize our intuition about the way the world works. Data we obtain as measures should represent attributes of the entities we observe. Manipulation of this data should preserve relationships among the entities. 11/10/2018 SWEN 5430 Software Metrics

The representational theory of measurement Empirical relations Measurement is a mapping from the empirical world to the formal, relational word. A measure is the number or symbol assigned to an entity by this mapping in order to characterize an attribute. A Measure is used to characterize an attribute 11/10/2018 SWEN 5430 Software Metrics

The representational theory of measurement The rules of the mapping The real world is the domain of the mapping The mathematical world is the range Attributes mapped to a mathematical system give us the range of: Real numbers Integers Non-numeric symbols 11/10/2018 SWEN 5430 Software Metrics

The representational theory of measurement The representation condition of measurement The representation condition asserts that a measurement mapping must map entities into numbers and empirical relations into numerical relations in such a way that the empirical relations preserve and are preserved by the numerical relations. 11/10/2018 SWEN 5430 Software Metrics

Measurement and models A model is an abstraction of reality, allowing the us to strip away detail and view an entity or concept from a particular perspective. Models give understanding how measures are derived and how to interpret the behavior back in the real world. 11/10/2018 SWEN 5430 Software Metrics

Measurement and models Defining attributes Graph on page 39 11/10/2018 SWEN 5430 Software Metrics

Measurement and models Direct and indirect measurement Direct measurement of an attribute of an entity involves no other attribute or entity. Indirect measurement uses combinations of attributes of other entities to obtain a measurement. Page 40 examples. 11/10/2018 SWEN 5430 Software Metrics

Measurement and models Measurement for prediction Measurement for prediction always requires some kind of mathematical model that relate the attributes to be predicted ( the future) to some other attributes that we can measure now (the present). 11/10/2018 SWEN 5430 Software Metrics

Measurement and models Measurement for prediction (continued) A prediction system consists of a mathematical model together with a set of prediction procedures for determining unknown parameters and interpreting result (Littlewood, 1988). 11/10/2018 SWEN 5430 Software Metrics

Measurement scales and scale types Normal Ordinal Interval Ratio Absolute 11/10/2018 SWEN 5430 Software Metrics

Meaningfulness in measurement Understanding scale type enables us to determine when statements about measurement make sense. 11/10/2018 SWEN 5430 Software Metrics

Meaningfulness in measurement Statistical operations on measures 11/10/2018 SWEN 5430 Software Metrics

Meaningfulness in measurement Objective and subjective measures 11/10/2018 SWEN 5430 Software Metrics

Meaningfulness in measurement Measurement in extended number systems 11/10/2018 SWEN 5430 Software Metrics

Meaningfulness in measurement Indirect measurement and meaningfulness 11/10/2018 SWEN 5430 Software Metrics

Summary Measurement requires us to identify intuitively understood attributes possessed by clearly defined entities. Then we assign numbers or symbols to the entities in a way that captures our intuitive understanding about the attribute. The intuitive understanding leads to the identification of relations between entities. 11/10/2018 SWEN 5430 Software Metrics

Summary To measure the attribute , we define corresponding relations in some number system. Then measurement assigns numbers to the entities is such a way that these relations are preserved. 11/10/2018 SWEN 5430 Software Metrics

Summary This relationship between the domain and range relationship is called the representation condition. Five well known representation condition Normal Ratio Ordinal Absolute Interval 11/10/2018 SWEN 5430 Software Metrics

Summary The scale type for a measure determines what kind of statement we can meaningfully make using the measurement. Many SWEN attributes are not directly measurable and we have to determine when statements and operations are meaningful. 11/10/2018 SWEN 5430 Software Metrics