Measurement,Reliability &Validity

8/10/2019 Measurement,Reliability &Validity

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An Introduction to the Scale of

Measurement

Measurement is assigning numbers toobservations in such a way that the numbers areamenable for analysis .

The number represents the property beingstudied.

All the variables can not be measured in onescale.There are four scale of measurement viz;Nominal, Ordinal, Interval and Ratio scale ofmeasurement.


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1.Nominal Scale

The operation is partitioning the objects, personsor characteristics in to mutually exclusive subclasses and the relation between the members

of the class is equivalence (=).Classifying a group of persons into male andfemale and assigning numbers as 0 and 1.

Automobile license plate numbers are otherexamples.Numbers only denote do not connote.


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2.Ordinal Scale

Objects of one category are not different( asmeasured in nominal scale) but they stand insome kind of relation amongst them. < or > ,=

We rank objects/ statements by giving countingnumbers.These numbers are not isomorphic to thesystem of arithmetic. The successive differenceare not same.Expl 1 : Ranking of individuals with respect tolevels of income, Exam results: passed in

1st,2nd or 3rd class.etc


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Likert Scale numbers are often considered asmeasured in ordinal scale

Listed below are some of the services thatmay influence the choice of a bank.Please rate the following in a 5 point scale1- Least Important5- Most important

We normally rank the attributes/variablesin a Likert Scale.Ranks are not isomorphic to the system of

arithmetic .


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Example 2 (Contd)

Services 1 2 3 4 5

1.Courteousservice

2.Competence of staff

3.Fastaction oncomplaints

5.No ofbranches

6.Availability of ATMservices

7.Financialstrength ofthe bank


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3.Interval Scale

An interval scale is characterized by acommon and constant unit ofmeasurement, but with an arbitrary zero.Consider the measurement of temperaturein two scales e.g. F & CThe two scale conform to the lineartransformation such as

F = 9/5 C + 32


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Two points to observe

1. Zero points in the two scale are arbitrary.2.The ratio of difference between reading on one

scale is equal to that of the other scale. But theratio of scale value is not equal due to thearbitrary zero.E.g. Cen 0 10 30 100

Fer 32 50 86 21230-10/10-0 = 86-50/50-32 = 2

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


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4.Ratio Scale

A Ratio Scale of Measurement has all thecharacteristics of interval scale with truezero point at its origin.This scale is isomorphic to the system ofarithmetic (with a true zero).It has known ratio of any two interval andknown ratio of any scale value


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Consider the following.

Measurement of area is done with acre orhectare which are in ratio scale.

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

Known ratio of difference

6-4/ 4-2 = 15 - 10/ 10 - 5 = 1Known ratio of scale value

2:5 = 4:10 = 6:15


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Scale of Measurement and Statisticalanalysis

The numbers assigned by nominal and ordinalscales known as non-metric & are not amenablefor some statistical analysis.

Interval and ratio scales are known as metricscale of measurement and the variablesmeasured in this scale are amenable forstatistical tools.However, variables measured in all the scale ofmeasurement are used in social sciencedepending on the objectives & mode of use.


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Reliability and Validity

After assigning numbers to theobjects/events, properties according torules the researcher asks two questions.

1. What is the reliability of the measuringinstrument?

2.What is its validity?

These two are important since thenumbers represent the phenomena understudy.


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Reliability

Reliability in the context of measurement isbased on the probability of errors.It implies: If the same object or property is

measured again and again with the samemeasuring instrument we get similar result.To the extent that the errors are present in ameasuring instrument, to that extent theinstrument is unreliable.Thus, reliability is the relative absence of error ofmeasurement in a measuring instrument.


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Reliability Measures

A Measure of reliability is the proportion of the"true" variance to the total obtained variance ofthe data yielded by a measuring instrument.

Alternatively it is the proportion of the errorvariance to the total obtained variance yieldedby a measuring instrument subtracted from theindex of "One".E.g. 1. R 2 = ESS/TSS or 1- RSS/TSSCronbach's Alpha - Measures dimension.


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Validity

Validity concerns an enquiry in to the reality of avariable and theoretical consistency.Consider the following two sets of varables

1. Gender, Domicile, Length, Weight, income etc.2.Personality,Brand preference, loyalty, awarenessFor the former there are specific measures, but for

the later there are indirect ways to measure. A measurement may be reliable but may nothave validity.


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Types of Vilidity

Researchers refer to three types of validityViz Content, Criterion & Construct validity

a ) Content validityIt is the extent to which a measuringinstrument provides adequate coverage ofthe concept/topic/ entities.

E.g . A proxy variable representing a qualitativevariable

A representative sample in a sample study,


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Criterion validity

It relates to efficiency of a model inestimation and prediction.These could be achieved with the

use of different specification withrespect to variables or the use ofdifferent statistical models or

relationships.The model having least error issupposed to have criterion validity.


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Construct Validity

It is more complex, subjective & abstract andunites psychometric notions with theoreticalnotions.It is not only validating the relationship, butone must try to validate the theory behind ite.g. in a dependency relationship Y and a fewXi s are related and the researcher asks whysuch a relationship may exit?A Pr ior i Reason ing has to be given whichconcerns theory, logical judgment &researchers articulation.


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A priori reasoningTwo variable cases

(i) Demand of X = f (Price of X )

(ii) Income Tax Rev. of

GoI

= (Industrialization)

(iii) AgriculturalProduction

= f (Area under cultivation)

(iv) Production of agroup of small scaleindustries

= f (Working Capital)

(v) Industrial Production = f (Employment in Organised Sector)


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A priori reasoning.

# More than two variables

(i) Demand of X = f (Price of X, Price of Substitute, Adv.Expenditure)

(ii) Income Tax Rev. of

GoI

= (PCI, Literacy Rate, Industrialization)

(iii) AgriculturalProduction

= f (Area under cultivation, % of areairrigated, fertilizer use)

(iv) Production of agroup of small scaleindustries

= f (Working Capital, Proximity tomarket, Ratio of Number of TechnicalPersons/Total Employees)

(v) Index of IndustrialProduction

= f (Expenditure in R & D, Employmentin Organised Sector)


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Construct validity is addressed withrespect to the following

Specification of proxy variables or quantification ofqualitative variables.Whether the researcher is near the property being

measured while specifying proxy variables. Specification of relationship between dependent andindependent variables (proper articulation with validlogic)

Redundant relationship with no a priori reasoning shouldbe avoided Specification of functional forms e.g. Linear,Quadratic, multiplicative, logarithmic etc.

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Measurement,Reliability &Validity