This document discusses measurement, validity, reliability, and levels of measurement. It provides definitions and methods for testing validity and reliability. There are four levels of measurement - nominal, ordinal, interval, and ratio - which determine the appropriate statistical analyses. Validity is tested through content, predictive, concurrent, and construct validity. Reliability refers to consistency and is estimated through test-retest and internal consistency methods. Measurement is important for research as it allows for goal setting and evaluating outcomes.

1. An assignment on
Measurement:-Meaning, postulates and levels of measurement, use of
appropriate statistics at different levels of measurement,
criteria for judging the measuring instrument and
importance of measurement in research.
Validity :-Meaning and methods of testing.
Reliability :-Meaning and methods of testing.
SUBMITTED BY:
Patel Vishvajeet J.

2. 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.

3. 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.

4. 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.

5. (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.

6. (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.

7. 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.

8. 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.

9. 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.

10. (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.

11. (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.

12. 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 .

13. 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.

14. (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 .