3359_Scale of Measurement,Reliabilty&Validity
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Transcript of 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)