Software Engineering Body of Knowledge (v3) (2014) (811503), страница 80
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In thisapproach, a measurement method is defined to bea precisely specified operation that yields a number (called the measurement result) when measuring an attribute. It follows that, to be useful,the measurement method has to be well defined.Arbitrariness in the method will reflect itself inambiguity in the measurement results.In some cases—particularly in the physicalworld—the attributes that we wish to measure areeasy to grasp; however, in an artificial world likesoftware engineering, defining the attributes maynot be that simple. For example, the attributes ofheight, weight, distance, etc. are easily and uniformly understood (though they may not be veryeasy to measure in all circumstances), whereasattributes such as software size or complexityrequire clear definitions.Operational definitions.
The definition of attributes, to start with, is often rather abstract. Suchdefinitions do not facilitate measurements. Forexample, we may define a circle as a line forminga closed loop such that the distance between anypoint on this line and a fixed interior point calledthe center is constant. We may further say that thefixed distance from the center to any point on theclosed loop gives the radius of the circle.
It may benoted that though the concept has been defined, nomeans of measuring the radius has been proposed.The operational definition specifies the exact stepsor method used to carry out a specific measurement. This can also be called the measurementmethod; sometimes a measurement procedure maybe required to be even more precise.The importance of operational definitionscan hardly be overstated. Take the case of theapparently simple measurement of height ofindividuals. Unless we specify various factorslike the time when the height will be measured(it is known that the height of individuals varyacross various time points of the day), how thevariability due to hair would be taken care of,whether the measurement will be with or withoutshoes, what kind of accuracy is expected (correctup to an inch, 1/2 inch, centimeter, etc.)—eventhis simple measurement will lead to substantialvariation.
Engineers must appreciate the need todefine measures from an operational perspective.3.1. Levels (Scales) of Measurement[4*, c3s2] [6*, c7s5]Once the operational definitions are determined,the actual measurements need to be undertaken.It is to be noted that measurement may be carried out in four different scales: namely, nominal,ordinal, interval, and ratio. Brief descriptions ofeach are given below.Nominal scale: This is the lowest level of measurement and represents the most unrestrictedassignment of numerals.
The numerals serve onlyas labels, and words or letters would serve as well.The nominal scale of measurement involves onlyclassification and the observed sampling unitsare put into any one of the mutually exclusiveand collectively exhaustive categories (classes).Some examples of nominal scales are:• Job titles in a company• The software development life cycle (SDLC)model (like waterfall, iterative, agile, etc.)followed by different software projectsIn nominal scale, the names of the different categories are just labels and no relationship betweenthem is assumed.
The only operations that can becarried out on nominal scale is that of countingthe number of occurrences in the different classesand determining if two occurrences have the samenominal value. However, statistical analyses maybe carried out to understand how entities belonging to different classes perform with respect tosome other response variable.Ordinal scale: Refers to the measurement scalewhere the different values obtained through theprocess of measurement have an implicit ordering. The intervals between values are not specified and there is no objectively defined zeroelement. Typical examples of measurements inordinal scales are:• Skill levels (low, medium, high)• Capability Maturity Model Integration(CMMI) maturity levels of software development organizationsEngineering Foundations 15-7• Level of adherence to process as measured ina 5-point scale of excellent, above average,average, below average, and poor, indicatingthe range from total adherence to no adherence at allMeasurement in ordinal scale satisfies the transitivity property in the sense that if A > B and B> C, then A > C.
However, arithmetic operationscannot be carried out on variables measured inordinal scales. Thus, if we measure customer satisfaction on a 5-point ordinal scale of 5 implyinga very high level of satisfaction and 1 implying avery high level of dissatisfaction, we cannot saythat a score of four is twice as good as a scoreof two. So, it is better to use terminology suchas excellent, above average, average, below average, and poor than ordinal numbers in order toavoid the error of treating an ordinal scale as aratio scale. It is important to note that ordinalscale measures are commonly misused and suchmisuse can lead to erroneous conclusions [6*,p274].
A common misuse of ordinal scale measures is to present a mean and standard deviationfor the data set, both of which are meaningless.However, we can find the median, as computationof the median involves counting only.Interval scales: With the interval scale, wecome to a form that is quantitative in the ordinary sense of the word. Almost all the usual statistical measures are applicable here, unless theyrequire knowledge of a true zero point. The zeropoint on an interval scale is a matter of convention. Ratios do not make sense, but the differencebetween levels of attributes can be computed andis meaningful.
Some examples of interval scale ofmeasurement follow:• Measurement of temperature in differentscales, such as Celsius and Fahrenheit. Suppose T1 and T2 are temperatures measuredin some scale. We note that the fact that T1is twice T2 does not mean that one object istwice as hot as another. We also note that thezero points are arbitrary.• Calendar dates. While the difference betweendates to measure the time elapsed is a meaningful concept, the ratio does not make sense.• Many psychological measurements aspire tocreate interval scales. Intelligence is oftenmeasured in interval scale, as it is not necessary to define what zero intelligence wouldmean.If a variable is measured in interval scale, mostof the usual statistical analyses like mean, standard deviation, correlation, and regression maybe carried out on the measured values.Ratio scale: These are quite commonly encountered in physical science.
These scales of measures are characterized by the fact that operationsexist for determining all 4 relations: equality, rankorder, equality of intervals, and equality of ratios.Once such a scale is available, its numerical values can be transformed from one unit to anotherby just multiplying by a constant, e.g., conversionof inches to feet or centimeters. When measurements are being made in ratio scale, existence ofa nonarbitrary zero is mandatory.
All statisticalmeasures are applicable to ratio scale; logarithmusage is valid only when these scales are used, asin the case of decibels. Some examples of ratiomeasures are• the number of statements in a softwareprogram• temperature measured in the Kelvin (K) scaleor in Fahrenheit (F).An additional measurement scale, the absolutescale, is a ratio scale with uniqueness of the measure; i.e., a measure for which no transformationis possible (for example, the number of programmers working on a project).3.2. Direct and Derived Measures[6*, c7s5]Measures may be either direct or derived (sometimes called indirect measures).
An example ofa direct measure would be a count of how manytimes an event occurred, such as the number ofdefects found in a software product. A derivedmeasure is one that combines direct measures insome way that is consistent with the measurementmethod. An example of a derived measure wouldbe calculating the productivity of a team as thenumber of lines of code developed per developermonth. In both cases, the measurement methoddetermines how to make the measurement.15-8 SWEBOK® Guide V3.03.3. Reliability and Validity[4*, c3s4, c3s5]A basic question to be asked for any measurement method is whether the proposed measurement method is truly measuring the concept withgood quality.
Reliability and validity are the twomost important criteria to address this question.The reliability of a measurement method isthe extent to which the application of the measurement method yields consistent measurementresults. Essentially, reliability refers to the consistency of the values obtained when the same itemis measured a number of times. When the resultsagree with each other, the measurement methodis said to be reliable.
Reliability usually dependson the operational definition. It can be quantifiedby using the index of variation, which is computed as the ratio between the standard deviationand the mean. The smaller the index, the morereliable the measurement results.Validity refers to whether the measurementmethod really measures what we intend to measure. Validity of a measurement method maybe looked at from three different perspectives:namely, construct validity, criteria validity, andcontent validity.3.4. Assessing Reliability[4*, c3s5]There are several methods for assessing reliability; these include the test-retest method, thealternative form method, the split-halves method,and the internal consistency method. The easiest of these is the test-retest method.
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