4185 4185 scale of measurement,reliability&validity

7/27/2019 4185 4185 Scale of Measurement,Reliability&Validity

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Observation, Theorizing and Mathematical

Model building necessitates knowledge on

a) Concept, construct and variables

b) Measurement or quantification ofvariables

c) Reliability and validity relating to the

measurement of variables and

specification of relationships between

them.


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An Introduction to the Scale of

Measurement

Measurement is assigning numbers to

observations in such a way that the

numbers are amenable for analysis.

The number represents the property being

studied.

There are four scale of measurement viz;

Nominal, Ordinal, Interval and Ratio scale

of measurement.


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1.Nominal Scale

The operation is partitioning the objects, persons

or characteristics in to mutually exclusive sub

classes and the relation between the members

of the class is equivalence (=).Classifying a group of persons into male and

female and assigning numbers as 0 and 1.

Automobile license plate numbers are other

examples.

Numbers only denote do not connote.


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2.Ordinal Scale

Objects of one category are not different( as

measured in nominal scale) but they stand in

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

We rank objects/ statements by giving countingnumbers.

These numbers are not isomorphic to the

system of arithmetic. The successive difference

are not same.

Expl : Ranking of individuals,Exam results:

passed in 1st,2nd or 3rd class.etc


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Likert Scale numbers are often considered as

measured in ordinal scale

Listed below are some of the services that

may influence the choice of a bank.

Please rate the following in a 5 point scale

1- Least Important

5- Most important

(A 7 point scale could be used)


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Example 2 (Contd)

Services 1 2 3 4 5

1.

Courteous

service

2.Compete

nce of staff

3.Fast

action on

complaints

5.No of

branches

6.Availabilit

y of ATM

services

7.Financial

strength ofthe bank


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3.Interval Scale

An interval scale is characterized by a

common and constant unit of

measurement, but with an arbitrary zero.

Consider the measurement of temperature

in two scales e.g. F & C

The two scale conform to the linear

transformation 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 the

ratio 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 the

characteristics of interval scale with true

zero point at its origin.

This scale is isomorphic to the system of

arithmetic (with a true zero).

It has known ratio of any two interval and

known ratio of any scale value


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Consider the following.

Measurement of area is done with acre or

hectare 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 Statistical

analysis

The numbers assigned by nominal and ordinal

scale are not amenable for some statistical tools.

These two are know as non-metric scale of

measurement where as interval and ratio scalesare known as metric scale of measurement.

Numbers measured in metric scale are

amenable for statistical tools and are used in

mathematical models.

However, all the scale of measurement

are used in social science


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

Instrument: The Techniques especially for the

qualitative variables (Proxy variables) along with

inadequate sampling, inadequate response

choice, ambiguous questions etc in surveys.Respondent: His psychological state, physical

condition, awareness, time etc.

Situation: Presence of people, unsureanonymity, and other situational factors.

Measurer: His behavior, style, noting down

observation, incorrect coding, faulty calculation.


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Reliability and Validity

After assigning numbers to the

objects/events, properties according to

rules the researcher asks to questions.

1. What is the reliability of the measuring

instrument?

2.What is its validity?

These two are important since thenumbers represent the phenomena under

study.


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Reliability

Reliability in the context of measurement is

based on the probability of errors.

Reliability 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 a

measuring instrument, to that extent the

instrument is unreliable.

Thus, reliability is the relative absence of error of

measurement in a measuring instrument.


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Reliability and Errors

Two types of errors: Systematic & Random

Systematic error results in biased measurement

but random errors are self compensating.

Measuring qualitative and quantitative variables.

Consider the following variables:

- Brand loyalty, industrialization, economic status

-Mass, weight, income, profit, revenueThe probability of error is likely to be more in

qualitative variables used in social research.


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Reliability Measures

A Measure of reliability is the proportion of the

"true" variance to the total obtained variance of

the data yielded by a measuring instrument.

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

by a measuring instrument subtracted from the

index of "One".

E.g. 1. R 2 = ESS/TSS or 1- RSS/TSS

Cronbach's Alpha - Measures dimension.


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Validity

Validity concerns an enquiry in to the reality of a

variable and theoretical consistency.

Consider the following two sets of varables

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

2.Personality,Brand preference, loyalty, awareness

For the former there are specific measures, but for

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

have validity.


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Types of Vilidity

Researchers refer to three types of validity

Viz Content, Criterion & Construct validity

a ) Content validity

It is the extent to which a measuring

instrument provides adequate coverage of

the concept/topic/ entities.

E.g a representative sample in a sample study,a proxy variable representing a qualitative

variable


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Criterion related Validity

Mostly used in empirical research.

It relates to the predictive efficiency of an

instrument.

Consider the following examples.

1. Specification of variables: Investment potential

could be estimated/predicted by composition of

income group or MPS of groups of people ?

2. Types of specification of a model: linear, non-

linear, etc using a time series )


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Criterion validity.

It relates to efficiency in estimationand prediction.

Estimation and prediction could be

with the use of differentspecification or the use of different

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 & abstractand unites psychometric notions with

theoretical notions.

It is not only validating the relationship,

but one must try to validate the theorybehind it e.g. in a dependency relationship

Y and a few X s are related and the

researcher asks why such a relationshipmay exit?

A Prior i Reasoninghas to be given which

concerns theory, judgment & articulation.


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A priori reasoning.

Consider the following

# Two Variables Case:

i) Demand = f (Price)

ii) Demand of X = f (Adv. Expenditure)iii) Rate of Capital Formation = f (Savings)

iv) Stock Prices = f (EPS)

v) Productivity = f (Mandays lost due to strike)

vi) Agricultural Production = f (Area under cultivation)

vii) Production of Paddy = f (% of area irrigated)

viii) Price of crop = f (Production)

Contd..


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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) Agricultural

Production

= f (Area under cultivation, % of area

irrigated, fertilizer use)

(iv) Production of a

group of small scale

industries

= f (Working Capital, Proximity to

market, Ratio of Number of Technical

Persons/Total Employees)

(v) Index of Industrial

Production

= f (Expenditure in R & D, Employment

in Organised Sector)


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Construct validity is addressed with

respect to the following

Specification of proxy variables or

quantification of qualitative variables.

Specification of relationship betweendependent and independent variables

(proper articulation with valid logic)

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

logarithmic etc.


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The following may be considered to

achieve construct validity

Whether the researcher is near the

property being measured while specifying

proxy variables.

Redundant relationship may not be

worked out ( with no a priori reasoning)

Far off relationship may be avoided.

4185 4185 scale of measurement,reliability&validity

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