3359_Scale of Measurement,Reliabilty&Validity

8/8/2019 3359_Scale of Measurement,Reliabilty&Validity

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An Introduction to Scale ofAn Introduction to Scale of

MeasurementMeasurement

Measurement is assigning numbers toMeasurement is assigning numbers to

observations in such a way that theobservations in such a way that the

numbers are amenable for analysis.numbers are amenable for analysis.The number represents the property beingThe number represents the property being

studied.studied.

Theoreticians distinguish between fourTheoreticians distinguish between four

types of measurement scale viz; Nominal,types of measurement scale viz; Nominal,

Ordinal, Interval and Ratio scale ofOrdinal, Interval and Ratio scale of

measurement.measurement.


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1.Nominal Scale1.Nominal Scale

The operation is partitioning the objects, personsThe operation is partitioning the objects, persons

or characteristics in to mutually exclusive subor characteristics in to mutually exclusive sub

classes and the relation between the membersclasses and the relation between the members

of the class is equivalence (=).of the class is equivalence (=).

Classifying a group of persons into male andClassifying a group of persons into male and

female and assigning numbers as 0 and 1.female and assigning numbers as 0 and 1.

Automobile license plate numbers are otherAutomobile license plate numbers are other

examples.examples.

Numbers only denote do not connote.Numbers only denote do not connote.


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2.Ordinal Scale2.Ordinal Scale

Objects of one category are not different( asObjects of one category are not different( as

measured in nominal scale) but they stand inmeasured in nominal scale) but they stand in

some kind of relation amongst them. < or > ,=some kind of relation amongst them. < or > ,=

We rank objects/ statements by giving countingWe rank objects/ statements by giving counting

numbers.numbers.

These numbers are not isomorphic to theThese numbers are not isomorphic to the

system of arithmetic. The successive differencesystem of arithmetic. The successive differenceare not same.are not same.

Likert scale or Exam results in 1st,2nd or 3rdLikert scale or Exam results in 1st,2nd or 3rd

class.class.


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3.Interval Scale3.Interval Scale

An interval scale is characterized by aAn interval scale is characterized by a

common and constant unit ofcommon and constant unit of

measurement, but with an arbitrary zero.measurement, but with an arbitrary zero.Consider the measurement of temperatureConsider the measurement of temperature

in two scales e.g. F & Cin two scales e.g. F & C

The two scale conform to the linearThe two scale conform to the linear

transformation such astransformation such as

F = 9/5 C + 32F = 9/5 C + 32


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Two points to observeTwo points to observe

1.1. Zero points in the two scale are arbitrary.Zero points in the two scale are arbitrary.

2.The ratio of difference between reading on one2.The ratio of difference between reading on one

scale is equal to that of the other scale. But thescale is equal to that of the other scale. But the

ratio of scale value is not equal due to theratio of scale value is not equal due to the

arbitrary zero.arbitrary zero.

E.g. Cen 0 10 30 100E.g. Cen 0 10 30 100

Fer 32 50 86 212Fer 32 50 86 2123030--10/1010/10--0 = 860 = 86--50/5050/50--32 = 232 = 2

But 0 : 32 # 10:50 # 30: 86 # 100 : 212But 0 : 32 # 10:50 # 30: 86 # 100 : 212


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Ratio ScaleRatio Scale

A Ratio Scale of Measurement has all theA Ratio Scale of Measurement has all the

characteristics of interval scale with truecharacteristics of interval scale with true

zero point at its origin.zero point at its origin.This scale is isomorphic to the system ofThis scale is isomorphic to the system of

arithmetic (with a true zero).arithmetic (with a true zero).

It has (amongst other characteristics of theIt has (amongst other characteristics of the

three scales) known ratio of any twothree scales) known ratio of any two

interval and known ratio of any scale valueinterval and known ratio of any scale value


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Consider the following.Consider the following.

Measurement of area is done with acre orMeasurement of area is done with acre or

hectare which are in ratio scale.hectare which are in ratio scale.

Area in Ha 2 4 6 8 10Area in Ha 2 4 6 8 10 Area in acre 5 10 15 20 25 Area in acre 5 10 15 20 25

Known ratio of differenceKnown ratio of difference

66--4/ 44/ 4--2 = 152 = 15 -- 10/ 1010/ 10 -- 5 = 15 = 1Known ratio of scale valueKnown ratio of scale value

2:5 = 4:10 = 6:152:5 = 4:10 = 6:15


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Scale of Measurement and StatisticalScale of Measurement and Statistical

analysisanalysis

The numbers assigned by nominal and ordinalThe numbers assigned by nominal and ordinal

scale are not amenable for some statistical tools.scale are not amenable for some statistical tools.

These two are know as nonThese two are know as non--metric scale ofmetric scale of

measurement where as interval and ratio scalesmeasurement where as interval and ratio scales

are known as metric scale of measurement.are known as metric scale of measurement.

Numbers measured in metric scale areNumbers measured in metric scale are

amenable for statistical tools and are used inamenable for statistical tools and are used inmathematical models.mathematical models.

However, all the scale of measurementHowever, all the scale of measurement

are used in social scienceare used in social science


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Sources of error in measurement.Sources of error in measurement.(With special reference to social research)(With special reference to social research)

1. Respondent: His psychological state, physical1. Respondent: His psychological state, physical

condition, awareness, time etc.condition, awareness, time etc.

Situation: Presence of people, unsureSituation: Presence of people, unsure

anonymity, and other situational factors.anonymity, and other situational factors.

Measurer: His behavior, style, noting downMeasurer: His behavior, style, noting down

observation, incorrect coding, faulty calculation.observation, incorrect coding, faulty calculation.

Instrument: Inadequate sampling, defects inInstrument: Inadequate sampling, defects inmeasuring instrument, inadequate responsemeasuring instrument, inadequate response

choice, ambiguous questions etc.choice, ambiguous questions etc.


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Reliability and ValidityReliability and Validity

After assigning numbers to theAfter assigning numbers to the

objects/events, properties according toobjects/events, properties according to

rules the researcher asks to questions.rules the researcher asks to questions.

1. What is the reliability of the measurung1. What is the reliability of the measurung

instrument?instrument?

2.What is its validity?2.What is its validity?

These two are important since theThese two are important since thenumbers represent the phenomena undernumbers represent the phenomena under

study.study.


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ReliabilityReliability

Reliability in the context of measurement isReliability in the context of measurement is

based on the probability of errors.based on the probability of errors.

Reliability implies: If the same object or propertyReliability implies: If the same object or property

is measured again and again with the sameis measured again and again with the samemeasuring instrument we get the similar result.measuring instrument we get the similar result.

To the extent that the errors are present in aTo the extent that the errors are present in a

measuring instrument, to that extent themeasuring instrument, to that extent theinstrument is unreliable.instrument is unreliable.

Thus, reliability is the relative absence of error ofThus, reliability is the relative absence of error of

measurement in a measuring instrument.measurement in a measuring instrument.


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Reliability and ErrorsReliability and Errors

Two types of errors: Systematic & RandomTwo types of errors: Systematic & Random

Systematic error results in biased measurementSystematic error results in biased measurement

but random errors are self compensating.but random errors are self compensating.

Measuring qualitative and quantitative variables.Measuring qualitative and quantitative variables.

Consider the following variables:Consider the following variables:

-- Brand loyalty, industrialization, economic statusBrand loyalty, industrialization, economic status

--Mass, weight, income, profit, revenueMass, weight, income, profit, revenue

The probability of error is likely to be more inThe probability of error is likely to be more in

qualitative variables used in social research.qualitative variables used in social research.


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Reliability MeasuresReliability Measures

A Measure of reliability is the proportion of theA Measure of reliability is the proportion of the

"true" variance to the total obtained variance of"true" variance to the total obtained variance of

the data yielded by a measuring instrument.the data yielded by a measuring instrument.

Alternatively it is the proportion of the errorAlternatively it is the proportion of the errorvariance to the total obtained variance yieldedvariance to the total obtained variance yielded

by a measuring instrument subtracted from theby a measuring instrument subtracted from the

index of "One".index of "One".

E.g. 1. RE.g. 1. R 22 = ESS/TSS or1= ESS/TSS or1-- RSS/TSSRSS/TSS

Cronbach's AlphaCronbach's Alpha -- Measures dimension.Measures dimension.


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ValidityValidity

Validity concerns an enquiry in to the reality of aValidity concerns an enquiry in to the reality of a

variable and theoretical consistency.variable and theoretical consistency.

Consider the following two sets of varablesConsider the following two sets of varables

1. Gender, Domicile, Length, Weight, income etc.1. Gender, Domicile, Length, Weight, income etc.

2.Personality,Brand preference, loyalty, awareness2.Personality,Brand preference, loyalty, awareness

For the former there are specific measures, but forFor the former there are specific measures, but for

the later there are indirect ways to measure.the later there are indirect ways to measure.A measurement may be reliable but may notA measurement may be reliable but may not

have validity.have validity.


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Types of VilidityTypes of Vilidity

Researchers of ten refer to three types ofResearchers of ten refer to three types of

validity Viz;a ) Content b ) Criterion andvalidity Viz;a ) Content b ) Criterion and

c ) Construct validity.c ) Construct validity.a ) Content validity : It is the extent to whicha ) Content validity : It is the extent to which

a measuring instrument provides adequatea measuring instrument provides adequate

coverage of the concept/topic/ entities.coverage of the concept/topic/ entities.

E.g a representative sample of theE.g a representative sample of the

population.population.


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Criterion related ValidityCriterion related Validity

Mostly used in empirical research.Mostly used in empirical research.

It relates to the predictive efficiency of anIt relates to the predictive efficiency of an

instrument.instrument.Consider the following examples.Consider the following examples.

1. Investment potential could be predicted by1. Investment potential could be predicted by

composition of income group or MPS of groupscomposition of income group or MPS of groups

of people ?of people ?

2. Types of specification of a model (linear, non2. Types of specification of a model (linear, non--

linear,etc)linear,etc)


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Construct validity is addressed withConstruct validity is addressed with

respect to the followingrespect to the following

Specification of proxy variables or quantificationSpecification of proxy variables or quantification

of qualitative variables.of qualitative variables.

Specification of relationship between dependentSpecification of relationship between dependent

and independent variables (proper articulationand independent variables (proper articulationwith valid logic)with valid logic)

Specification of functional forms e.g. Linear,Specification of functional forms e.g. Linear,

Quadratic, multiplicative, logarithmic etc.Quadratic, multiplicative, logarithmic etc.


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The following may be considered toThe following may be considered to

achieve construct validityachieve construct validity

Whether the researcher is near theWhether the researcher is near the

property being measured while specifyingproperty being measured while specifying

proxy variables.proxy variables.

Far off relationship may be avoided.Far off relationship may be avoided.

Redundant relationship may not beRedundant relationship may not be

worked out ( with no a priori reasoning)worked out ( with no a priori reasoning)

3359_Scale of Measurement,Reliabilty&Validity

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