An assignment on

Measurement:-Meaning, postulates and levels of measurement, use ofappropriate statistics at different levels of measurement,criteria for judging the measuring instrument andimportance of measurement in research.

Validity :-Meaning and methods of testing.

Reliability :-Meaning and methods of testing.

SUBMITTED BY:

Patel Vishvajeet J.

Measurement

Meaning

• The action of measuring something

• The size, length, or amount of something, as established by measuring

Postulates and levels of measurement

Postulate 1: The Wave Function

The state of a QM system is completely described by a wave function.

We will place a few requirements on the wave function:

• 1. Normalizable

• 2. Single Valued

• 3. Continuous

Single valued requires that there be a single value of the function for a given

interval.

Continuous requires that the function and the first-derivative of the function be

smoothly varying w/ no discontinuities.

Postulate 2: Operators

• For every measurable property of the system there exists a corresponding

operator

Postulate 3: Measurements

• For any measurement involving an observable corresponding to an

operator, the only values that will be measured will be eigenvalues of the

operator.

Postulate 4: Expectation Values

• If the system is in a state described by a wave function and the value of the

observable a is measured once each on many identically prepared systems.

Levels of Measurement

• Introduction

We classify data obtained from measurements using numbers and we can

do this with different levels of precision or levels of measurement. There

are 4 levels of measurement and it is important to know what level of

measurement you are working with as this partly determines the arithmetic

and statistical operations you can carry out on them. The four levels of

measurement in ascending order of precision are, nominal, ordinal,

interval and ratio.

(1) Nominal

• At the first level of measurement, numbers are used to classify data. In fact

words or letters would be equally appropriate. Example is blood groups where

the letter A, B, O and AB represent the different classes.

(2) Ordinal

• In ordinal scales, values given to measurements can be ordered. So numbers

on an ordinal scale represent a rough and ready ordering of measurements but

the difference or ratios between any two measurements represented along the

scale will not be the same. As for the nominal scale, with ordinal scales you

can use textual labels instead of numbers to represent the categories. There are

many everyday examples of measurements assigned to ordinal scales: social

class gradings I, II, III, IV,.

(3) Interval

• On an interval scale, measurements are not only classified and ordered

therefore having the properties of the two previous scales, but the distances

between each interval on the scale are equal right along the scale from the low

end to the high end. Two points next to each other on the scale, no matter

whether they are high or low, are separated by the same distance. So when you

measure temperature in centigrade the distance between 96 and 98O, for

example, is the same as between 100 and 102 C.

(4) Ratio

Measurements expressed on a ratio scale can have an actual zero. Apart from

this difference, ratio scales have the same properties as interval scales. The

divisions between the points on the scale have the same distance between

them and numbers on the scale are ranked according to size. There are many

examples of ratio scale measurements, length, weight, temperature on the

kelvin scale, speed and counted values like numbers of people, exam marks

etc.

MEASUREMENT AND STATISTICS

Most good statistics texts present ‘decision trees’ which help you select the

correct statistical test to use providing you know the answers to a number of

simple questions about your data and research design. These are very useful,

and simple versions are provided on bivariate analyses. These decision trees

ask about the level of measurement for your data as well as the nature of the

distribution of scores on the measure that you expect in the population from

which your sample scores were drawn. The topic of distributions of scores is

dealt with in level of measurement issue is pertinent here, particularly at the

boundary between ordinal and interval level measures.

The attraction of parametric tests, ones that assume something about

the distribution of scores in the population (e.g.t-test, ANOVA), is that

there are many more of them than non-parametric tests. They often

allow you to ask interesting questions about your data that are not

easily answered without using such parametric procedures. To say that

your measure is only ordinal, rather than interval level, usually rules

out these useful procedures. Two views have developed over the

appropriateness of treating ordinal measures as interval ones. One

view states that, most of the time, providing you have a good-quality

ordinal measure, you will arrive at the same conclusions as you would

have using more appropriate tests. It is sometimes argued (see

Minium, King & Bear 1993) that while most psychological measures

are technically ordinal measures, some of the better measures lie in a

region somewhere between ordinal and interval level measurement.

Criteria for judging the measurement

Typically success should be judged by the ability to meet objectives. Using this

definition, success criteria would include.

• high levels of sales

• high levels of profits

• high levels of consumer satisfaction

• the production of high quality products

• strong reputation

• Sustained growth

Importance of measurement in research

• Set goals before you measure.

• Measure media with quantity and quality metrics, not advertising equivalents.

• Understand how people and business results change because of PR efforts.

• Utilize social media measurement – the same measurement ideas apply.

• Make sure all measurement is transparent.

VALIDITY

Means

A scale is said to be valid when it correctly measures what it is excepted to

Measure.

There are four types of validity measurement :

(1) Content validity

(2) Predictive validity

(3) Concurrent validity

(4) Construct validity

(1) Content validity : it is the representativeness or sampling adequacy of the

content the substance , the Matter the topics of a measuring instrument .

content validation is basically judgement. the items of a test must be Studied

each items being weighed for its presumed representativeness of the

universe.the universe of content must be Defined. it is also known as face

validity is exclusively a logical type of validity. E.g Package of practice of a

crop is said to have content validity when it has all the agronomic practices

involving from Seed to seed.

(2)Predictive validity : it is based on the measured association

between what a test predicts behaviour will be And the subsequent

behaviour exhibited by an individual group . this is achieved by

comparing test or scale score with One or more external variable or

criteria known or believed to measure the attribute under study . in any

case this is Characterized by prediction to an outside criterian and by

checking a measuring instrument either now or in the future Against

some outcome. e.g based on previous experience or performance

success in sericulture, forecasting the success apiculture may be

adopted.

(3)Concurrent validity : this is also same as predictive validity but

differs in time dimension . this predicts the Outcomes at present . in

this the sources of predictive behaviour are obtained simultaneously

with the exhibited Behaviour. e.g. Fore – casting yields of a crop on the

basis of prevailing weather condition. Prediction of rank is EAMCET

on the basis of intermediate marks.

(4)Construct validity : this is one of the most significant

advances of modern measurement theory and practice It unties

psychometric notions with theoretical notions. The significant points with

this is preoccupation with theory Theoretical construct and scientific

empirical enquiry involving the testing of hypothesized relations. It also

explain The theory under the validating instrument . construct validity is

generally determined through the application of Factors analysis to a

measuring instrument factors analysis is a techniques designed to determine

the basic Components of a measure.

e.g. social status depends on education economic status, income and

sociability.

Reliability

Means

Reliability is the ability of the measuring instrument to yield consistent results

when applicable to the same sample.

Reliability of measurement

In its simplest sense, reliability refers to the precision or accuracy of the

measurement or score. A well – made scientific Instrument should yield

accurate results both at present as well as over time . Reliability refers this

consistency of score Or measurement which is reflected in the reproducibility

of the score. The consistency of scores obtained upon testing

And retesting after a lapse of time is referred to as the temporal stability of a

test whereas , consistency of score Obtained from two equivalent sets of

items of a single test after a single administration is referred to as the internal

Consistency of the test score .

According to Anastasi (1968) , RELIABILITY refers to the consistency

of score obtained by The same individuals when re-examined with test

on different occasions or with different sets of equivalent items or Under

variable examining condition . for examples , if an individual receives a

score of 60 on an achievement test and Is assigned a rank , the person

should receive approximately the same rank when the test is

administered on the Second occasion .

The most common methods of estimating the reliability coefficient of

test score are :

(1) test- retest reliability

(2)Internal consistency reliability.

(1) Test- retest reliability : in this methods , a single form of the test is administered

twice on the same sample with a Reasonable time gap, say a fortnight . this yields

two independent sets of scores . the correlation between the two sets Of scores gives

the value of the reliability coefficient , which is also known as temporal stability

coefficient .A positive And significant correlation coefficient between the two sets of

scores indicate that the test is reliable.The time gap between two tests should not be

too short or too long . the time interval of a fortnight yields a Comparatively higher

reliability coefficient .

(2) Interval consistency reliability

this method indicates homogeneity of the test .the most common is the split –half

Methods , in which a test is divided in two halves . one half (one set) contains the

odd numbered items (1,3,5,7,etc) andThe other half (other set ) the even numbered

items (2,4,6,8,etc) A test should however , not be divided into first-halfAnd second-

half of the items . A single administrations of the two sets of items to a sample of

respondents, yields twoSets of score . A positive and significant correlation between

the two sets of scores indicates that the test is reliable.The advantage of the split –

half method is that all data necessary for the computation of the reliability

coefficient Are obtained in a single administration of the test . thus , the variability

which may be produced by the difference in two Administration of the same test (as

in test – retest method) is automatically eliminated .