Scaling and Measurement techniques

Measurement, Scaling, Instrument Designing and Sampling
3-1 Excel Books4-1
3UNIT
Measurement, Scaling,
Instrument Designing
and Sampling

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In our daily life we are said to measure when we use some
yardstick to determine weight, height, or some other feature
of a physical object.
We also measure when we judge how well we like a song, a
painting or the personalities of our friends.
We, thus, measure physical objects as well as abstract
concepts.
Measurement is a relatively complex and demanding task,
specially so when it concerns qualitative or abstract
phenomena.
By measurement we mean the process of assigning
numbers to objects or observations, the level of
measurement being a function of the rules under which the
numbers are assigned.
Defining Measurement

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Defining Measurement
Properties like weight, height, etc., can be measured
directly with some standard unit of measurement, but it is
not that easy to measure properties like motivation to
succeed, ability to stand stress and the like.
We can expect high accuracy in measuring the length of
pipe with a yard stick, but if the concept is abstract and the
measurement tools are not standardized, we are less
confident about the accuracy of the results of measurement.
When we measure, we attempt to identify the dimensions,
quantity, capacity, or degree of something.
Measurement is formally defined as the act of measuring by
symbols or numbers to something according to a specific
set of rules.

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Technically speaking, measurement is a process of mapping
aspects of a domain onto other aspects of a range
according to some rule of correspondence.
In measuring, we devise some form of scale in the range (in
terms of set theory, range may refer to some set) and then
transform or map the properties of objects from the domain
(in terms of set theory, domain may refer to some other set)
onto this scale.

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For example, in case we are to find the male to female
attendance ratio while conducting a study of persons who
attend some show, then we may tabulate those who come to
the show according to sex.
In terms of set theory, this process is one of mapping the
observed physical properties of those coming to the show
(the domain) on to a sex classification (the range).
The rule of correspondence is: If the object in the domain
appears to be male, assign to “0” and if female assign to “1”.
Similarly, we can record a person’s marital status as 1, 2, 3
or 4, depending on whether the person is single, married,
widowed or divorced.
We can as well record “Yes or No” answers to a question as
“0” and “1” (or as 1 and 2 or perhaps as 59 and 60).

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Measurement Scale
The most widely used classification of measurement scales
are:
(a) nominal scale;
(b) ordinal scale;
(c) interval scale; and
(d) ratio scale.

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(A) Nominal scale
Nominal scale is simply a system of assigning number
symbols to events in order to label them.
The usual example of this is the assignment of numbers of
basketball players in order to identify them.
Such numbers cannot be considered to be associated with
an ordered scale for their order is of no consequence; the
numbers are just convenient labels for the particular class
of events and as such have no quantitative value. Nominal
scales provide convenient ways of keeping track of people,
objects and events.

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One cannot do much with the numbers involved.
For example, one cannot usefully average the numbers on
the back of a group of football players and come up with a
meaningful value.
Neither can one usefully compare the numbers assigned to
one group with the numbers assigned to another.
The counting of members in each group is the only possible
arithmetic operation when a nominal scale is employed.
Accordingly, we are restricted to use mode as the measure
of central tendency.
There is no generally used measure of dispersion for
nominal scales. Chi-square test is the most common test of
statistical significance that can be utilized, and for the
measures of correlation, the contingency coefficient can be
worked out.

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Nominal scale is the least powerful level of measurement.
It indicates no order or distance relationship and has no
arithmetic origin.
A nominal scale simply describes differences between
things by assigning them to categories. Nominal data are,
thus, counted data.
The scale wastes any information that we may have about
varying degrees of attitude, skills, understandings, etc.
In spite of all this, nominal scales are still very useful and are
widely used in surveys and other ex-post-facto research
when data are being classified by major sub-groups of the
population.

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The lowest level of the ordered scale that is commonly used
is the ordinal scale.
The ordinal scale places events in order, but there is no
attempt to make the intervals of the scale equal in terms of
some rule.
Rank orders represent ordinal scales and are frequently
used in research relating to qualitative phenomena.
A student’s rank in his graduation class involves the use of
an ordinal scale.
One has to be very careful in making statement about scores
based on ordinal scales.
(B) Ordinal scale

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For instance, if Ram’s position in his class is 10 and Mohan’s
position is 40, it cannot be said that Ram’s position is four
times as good as that of Mohan.
The statement would make no sense at all.
Ordinal scales only permit the ranking of items from highest
to lowest.
Ordinal measures have no absolute values, and the real
differences between adjacent ranks may not be equal.
All that can be said is that one person is higher or lower on
the scale than another, but more precise comparisons
cannot be made.

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Thus, the use of an ordinal scale implies a statement of
‘greater than’ or ‘less than’ (an equality statement is also
acceptable) without our being able to state how much
greater or less.
The real difference between ranks 1 and 2 may be more or
less than the difference between ranks 5 and 6.
Since the numbers of this scale have only a rank meaning,
the appropriate measure of central tendency is the median.
A percentile or quartile measure is used for measuring
dispersion.
Correlations are restricted to various rank order methods.
Measures of statistical significance are restricted to the
non-parametric methods.

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Any questions that ask respondent to rate something are
using ordinal scales. E.g.
1. How would you rate the service of our wait-staff?
•Excellent
•Very good
•Good
•Fair
•Poor
2. If there are 4 different brands of talcum powder and if
a respondent ranks them based on say, “Freshness” in to
Rank 1 having maximum Freshness Rank 2 the second
maximum Freshness, and so on, and ordinal sacles results.

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(C) Interval scale
In the case of interval scale, the intervals are adjusted in
terms of some rule that has been established as a basis for
making the units equal. The units are equal only in so far as
one accepts the assumptions on which the rule is based.
Interval scales can have an arbitrary zero, but it
is not possible to determine for them what may be called
an absolute zero or the unique origin. The primary
limitation of the interval scale is the lack of a true zero; it
does not have the capacity to measure the complete
absence of a trait or characteristic.

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An interval scale tell us whether P is as much higher than Q
as Y is than Z on a particular attribute.
In other words, in an interval scale, the difference between
may two adjacent positions is the same as the one between
any other two adjacent positions.

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The Fahrenheit scale is an example of an interval scale
and shows similarities in what one can and cannot do with
it.
One can say that an increase in temperature from 30° to
40° involves the same increase in temperature as an
increase from 60° to 70°, but one cannot say that the
temperature of 60° is twice as warm as the temperature of
30° because both numbers are dependent on the fact that
the zero on the scale is set arbitrarily at the temperature
of the freezing point of water.
The ratio of the two temperatures, 30° and 60°, means
nothing because zero is an arbitrary point.

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Interval scales provide more powerful measurement than ordinal scales
for interval scale also incorporates the concept of equality of interval. As
such more powerful statistical measures can be used with interval
scales.
Mean is the appropriate measure of central tendency, while standard
deviation is the most widely used measure of dispersion. Product
moment correlation techniques are
appropriate and the generally used tests for statistical significance are
the ‘t’ test and ‘F’ test.

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(C) Ratio scale
Ratio scales are the most sophisticated of scales, since it
incorporates all the characteristics of nominal, ordinal and
interval scales.
As a result, a large number of descriptive calculations are
applicable.
This is a scale with a true zero point.
It also has all of the lower level characteristics of equal
intervals, rank order, and ability to mark a value with a
name.
Some examples are height, weight, response time, annual
income etc..
Here is an example of the presence of a true zero point; If
your annual income exactly zero dollars then you earned no
annual income at all. You can buy absolutely nothing with
zero dollars. Zero means Zero.

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When a scale consists not only of equidistant points but also
has a meaningful zero point, then we refer to it as a ratio
scale.
If we ask respondents their ages, the difference between
any two years would always be the same, and “zero”
signifies the absence of age or birth.
Hence a 100-year old person is indeed twice as old as a 50-
year old one .
Sales figures, quantities purchased and market share are all
expressed on a ratio scale.
Ratio scales should be used to gather quantitative
information, and we see them perhaps most commonly when
respondents are asked for their age, income, years of
participation, etc..

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Ratio scales are not widely used in marketing research
unless a base item is made available for comparison.
A ratio scale has a natural zero point and further numbers
are placed at equally appearing intervals. For example
scales for measuring physical quantities like – length, weight
etc..
The ratio scale, is commonly used in the physical sciences.
To have a ratio scale the absolute zero point needs to be
determined.
A ten-inch rod can be said to be exactly twice as long as five
inch one, because both the rods share a common starting
point, namely the real zero point.

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Criteria for good measurement
Irrespective of the data collection technique used, it is
critical that the researcher analyze it for Reliability, validity
and practicality.
1. Reliability:
The extent to which results are consistent over time
and accurate representation of the total population
under study is referred to as reliability.
In other words, if the results of a study can be
reproduced under a similar methodology, then the
research instrument is considered to be reliable.

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Should you have a question that can be misunderstood, and
therefore is answered differently by respondents, you are
dealing with low reliability.
The consistence with which questionnaire items are
answered can be determined through the test-retest
method, whereby a respondent would be asked to answer(s)
the same question at two different times.
This attribute of the instrument is actually referred to as
reliability.
If we are dealing with a stable measure, then the result
should be similar.
A high degree of stability indicates a high degree of
reliability, since the results are repeatable.

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It is the degree to which measures are free from error and
therefore yield consistent results.
Two dimensions underlie the concept of reliability:
Repeatability
internal consistency
Test retest method of determining reliability involves
administering the same scale or measure to the same
respondents at two separate times to test for stability.

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2. Validity:
it is the ability of scale or measuring instrument to
measure what is intend to measure.
validity is the extent to which differences found
with a measuring instrument reflect true
differences among those being tested. But the
question arises: how can one determine validity without
direct confirming knowledge? The answer may be that we
seek other relevant evidence that confirms the answers we
have found with our measuring tool.
What is relevant, evidence often depends upon the nature of
the research problem and the judgement of the researcher.
But one can certainly consider three types of validity in this
connection:

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(i) Content validity;
(ii) Criterion-related validity and
(iii) Construct validity
(i) Content validity is the extent to which a measuring
instrument provides adequate coverage of the topic under
study. If the instrument contains a representative sample of
the universe, the content validity is good.
Its determination is primarily judgemental and intuitive. It
can also be determined by using a panel of persons who
shall judge how well the measuring instrument meets the
standards, but there is no numerical way to express it.

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(ii) Criterion-related validity relates to our ability to
predict some outcome or estimate the existence of some
current condition. This form of validity reflects the success
of measures used for some empirical estimating purpose.
The concerned criterion must possess the following
qualities:
Relevance: (A criterion is relevant if it is defined in terms
we judge to be the proper measure.)
Freedom from bias: (Freedom from bias is attained when
the criterion gives each subject an equal opportunity to
score well.)
Reliability: (A reliable criterion is stable or reproducible.)
Availability: (The information specified by the criterion
must be available.)

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In fact, a Criterion-related validity is a broad term that
actually refers to
(i)Predictive validity and
(ii)Concurrent validity.
The former refers to the usefulness of a test in
predicting some future performance whereas the latter
refers to the usefulness of a test in closely relating to other
measures of known validity. Criterion-related validity is
expressed as the coefficient of correlation between test
scores and some measure of future performance or
between test scores and scores on another measure of
known validity.

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(iii) Construct validity is the most complex and abstract.
A measure is said to possess construct validity to the degree
that it confirms to predicted correlations with other
theoretical propositions.
Construct validity is the degree to which scores on a test
can be accounted for by the explanatory constructs of a
sound theory. For determining construct validity, we
associate a set of other propositions with the results
received from using our measurement instrument. If
measurements on our devised scale correlate in a predicted
way with these other propositions, we can conclude that
there is some construct validity.

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3. Test of Practicality
The practicality characteristic of a measuring instrument can be
judged in terms of economy, convenience and interpretability.
From the operational point of view, the measuring instrument
ought to be practical i.e., it should be economical, convenient and
interpretable.
Economy consideration suggests that some trade-off is
needed between the ideal research project and that which the
budget can afford.
The length of measuring instrument is an important area where
economic pressures are quickly felt.
Although more items give greater reliability as stated earlier, but
in the interest of limiting the interview or observation time, we
have to take only few items for our study purpose. Similarly, data-
collection methods to be used are also dependent at times upon
economic factors.

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Convenience test suggests that the measuring instrument
should be easy to administer.
Although more items give greater reliability as stated
earlier, but in the interest of limiting the interview or
observation time, we have to take only few items for our
study purpose.
Similarly, data-collection methods to be used are also
dependent at times upon economic factors.

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For this purpose one should give due attention to the proper
layout of the measuring instrument.
For instance, a questionnaire, with clear instructions
(illustrated by examples), is certainly more effective and
easier to complete than one which lacks these features.
Interpretability consideration is specially important
when persons other than the designers of the test are to
interpret the results.
The measuring instrument, in order to be interpretable, must
be supplemented by
(a) detailed instructions for administering the test;
(b) scoring keys;
(c) evidence about the reliability and
(d) guides for using the test and for interpreting results.

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SCALING TECHNIQUES

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1. Comparative Scale

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 A comparative Scale asks respondents to rate a concept
by comparing it with a benchmark.
 Comparative scales involve the direct comparison of
stimulus objects.
 Comparative scale data must be interpreted in relative
terms and have only ordinal or rank order properties.

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Advantages:
 Small differences between stimulus objects can be
detected.
 Same known reference points for all respondents.
 Easily understood and can be applied.
 Involve fewer theoretical assumptions.
Disadvantages
 Ordinal nature of data

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Comparative Rating Scale is of 4 types
 Paired comparisons
 Rank order scale
 Constant Sum Scale
 The Q Sort technique

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Paired comparisons:
Here the respondents are presented with two objects at a
time and asked to pick the one they prefer according to
some criterion.
The data obtained are ordinal in nature. It is most widely
used scale.

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Rank order scaling:
Respondents are presented with several objects
simultaneously and asked to order or rank them according
to some criterion.
It is possible that the respondent may dislike the brand
ranked 1 in an absolute sense.
Rank order scaling also results in ordinal data. Only (n-1)
scaling decisions need be made in rank order scaling.
Rank the various brands of smart phones in order of
preference.
Rank the various brands of smart phones in order of
preference. Begin by picking out the one brand that you like
the most and assign it a number 1. Then find the second
most preferred brand and assign it a number 2.

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Continue this process until you have ranked all the brands of
smart phones in order of preference.
The least preferred brand should be assigned a rank of 10.
No two brands should receive the same rank number.
The criterion of preference is entirely up to you.
There is no wrong or right answer.

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Constant sum scaling
Respondents allocate a constant sum of units, such as 100
points to attributes of a product to reflect their importance.
If an attribute is unimportant, the respondent assigns it zero
points.
If an attribute is twice as important as some other attribute,
it receives twice as many points.
The sum of all the points is 100.
Hence name of scale is constant sum scale. The limitations
of scale is that

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The Q Sort technique
 It is used to discriminate among large number of objects
quickly. It uses a rank order procedure and the objects are
sorted into piles (place (things) one on top of another.) based
on similarity with respect to some criteria.
 The number of objects to be sorted should be between 60-
140 approximately
For example here we are talking nine brands. On the basis of
taste we classify the brands into tasty, moderate and non
tasty.
 We can classify on the basis of price also Low, medium,
high. Then we can attain the perception of people that
whether they prefer low priced brand, high or moderate.

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We can classify sixty brands or pile it into three piles.
So the number of objects is to be placed in three piles low ,
medium or high.
Thus this technique is an attempt to classify subjects in
terms of their similarity to attribute under study.

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2. NON COMPARATIVE RATING SCALES

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 Here each object is scaled independently of the others in
the stimulus set.
 The resulting data are generally assumed to be interval
or ration scaled.
 Respondents evaluate only one object at a time, and for
this reason non-comparative scales are often referred to as
monadic scales.
 Types of non comparative scales are
 Continuous rating scale
 Itemized rating scale
 Likert scale
 Semantic Differential Scale
 Stapel’s Scale
Multi Dimensional Scaling
 Thurston Scales etc..

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1. Continuous Rating Scale2.1

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2.2 Itemized Rating Scale
It is different from continuous rating scales. They have a
number of brief descriptions associated with each
category. They are widely used in marketing research.
They essentially take the form of multiple category
questions.
The respondents are provided with a scale that has a
number or brief description associated with each category.
The categories are ordered in terms of scale position, and
the respondents are required to select the specified
category that best describes the object being rated.

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2.2.1 Likert Scale
It was developed by Rensis Likert.
Here the respondents are asked to indicate a degree of
agreement and disagreement with each of a series of
statement.
Each scale item has 5 response categories ranging from
strongly agree and strongly disagree.
5
Strongly agree
4
Agree
3
Indifferent
2
Disagree
1
Strongly
disagree

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For the likert scale, various opinion statement are collected,
edited and then given to a group of subjects to rate the
statement on a five point continuum:
1 = Strongly agree; 2 = agree; 3 = undecided; 4 = disagree;
5 = strongly disagree.
The subjects express the degree the (one to five) of their
personal agreement or disagreement with each of the
statements. Only those items which in the analysis best
differentiate the high scores and the low scorers of the
sample subjects are retained and the scale is ready for use.

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To measure the attitude of a given group of respondents,
this scale is given to them and every respondent indicates
whether s/he strongly agrees, agrees, is undecided, or
strongly disagrees with each statement.
The respondent’s attitude score is the sum of her/his ratings
of all the statements. For this reason, the Likert scale is
known as the scale of Summated Ratings.

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Likert scales are of ordinal type, they enable one to rank
attitudes, but not to measure the difference between
attitudes.
By and large, a greater majority of researcher prefer the
Likert technique.
In many research studies we come across seven-point
scales being used, which bear the appearance of the Likert
Scale.
It must be noted that the typical Likert technique requires an
item analysis to establish that all the items in the scale
measure the same attitude – no matter whether the scale
has five or more points.

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A typical Likert scale has 20 – 30 statements. While
designing a good Likert scale, first a large pool of
statements relevant to the measurement of attitude has to
be generated and then from the pool statements, the
statements which are vague(unclear) and non-
discriminating have to be eliminated.

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2.2 Stapel's Scale
It was developed by Jan stapel.
Modern versions of the Stapel scale place a single adjective
as a substitute for the semantic differential when it is
difficult to create pairs of bipolar adjectives.
This scale has some features:
1. Each item has only one word/phrase indicating the
dimension it represents
2. Each item has ten response categories.

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For example, in the following items, suppose for quality of
ice-cream, we ask respondents to rank from +5 to -5.
Select a plus number for words which best describe the ice
cream accurately.
Select a minus number for words you think do not describe
the ice-cream quality accurately. Thus, we can select any
number from +5 to -5.
+5 for more accurate and -5 for very inaccurate.

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This scale is presented vertically
+5
+4
+3
+2
+1
High Quality
-1
-2
-3
-4
-5
This is unipolar rating scale.

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2.3 Semantic Differential Scale
It is developed by Osgood, Suci and Tannenbaum, can be
used to measure attitudes from the meaning
(semantic = meaning or psychological significance) which
people give to a word or concept that is related to an
attitude object.
This instrument consists of a series of bipolar adjectives
such as fair – unfair, pleasant – unpleasant, good – bad,
clean-dirty, valuable-worthless etc.
Each pair constitutes a continnum of seven points, the end
point begin the opposites of the adjetive pairs and the mid
point being neutral position.

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In this scale, the thing being evaluated is presented once at the
top of the page. The scale consist of pairs of adjectives
located at the two endpoints of a standard response format.
I think Al Gore is
Smart
Bad
Beautiful
Stupid
Good
Ugly

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When Semantic Differential Scale is used to develop an
image profile, it provides a good basis for comparing images
of two or more items.
The big advantage of this scale is its simplicity, while
producing results compared with those of the more complex
scaling methods.
The method is easy and fast to administer, but it is also
sensitive to small differences in attitude, highly versatile,
reliable and generally valid.

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2.4 Multi dimensional scaling
It consists of a group of analytical techniques which are
used to study consumer attitudes related to perceptions
and preferences. It is used to study the major attributes of
a given class of products perceived by the consumers in
considering the product and by which they compare the
different ranks.
 To study which brand competes most directly with each
other.
 To find out whether the consumers would like a new
brand with a combination of characteristics not found in
market.
 What would be the consumers ideal combination of
product attributes.
 What sales and advertising messages are compatible
with consumers brand perceptions.

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SAMPLING

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“The selection of some part of an aggregate or
totality on the basis of which a judgement or
inference about the aggregate or totality is made.”
it is the process of obtaining information about an entire
population by examining only a part of it.

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In most of the research work and surveys, the usual
approach happens to be to make generalisations or to draw
inferences based on samples about the parameters of
population from which the samples are taken.
The researcher quite often selects only a few items from the
universe for his study purposes.
All this is done on the assumption that the sample data will
enable him to estimate the population parameters.

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The items so selected constitute what is technically called a
sample, their selection process or technique is called
sample design and the survey conducted on the basis of
sample is described as sample survey.
Sample should be truly representative of population
characteristics without any bias so that it may result in valid
and reliable conclusions.

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NEED FOR SAMPLING
Sampling is used in practice for a variety of reasons such as:
1.Sampling can save time and money. A sample study is
usually less expensive than a census study and produces
results at a relatively faster speed.
2. Sampling may enable more accurate measurements for a
sample study is generally conducted by trained and
experienced investigators.
3. Sampling remains the only way when population contains
infinitely many members.

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4. Sampling remains the only choice when a test involves the
destruction of the item under study.
5. Sampling usually enables to estimate the sampling errors
and, thus, assists in obtaining information concerning some
characteristic of the population.

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STEPS
IN
SAMPLE
DESIGN

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POPULATION

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Population is any complete group.
For example. People
Sales territories
Stores
Census is investigation of all individual elements that make
up a population.
For example, in the study of agriculture yields, all the
cultivated farms will be population.
In the study of socio-economic conditions of a particular
village, all families or house in the village will be the
population.

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According to the size of population there are two types of
population:
Finite population:
When number of units in the population is finite, it is
called finite population. For example, the population of
student enrolled in a year in a college is a finite population
as the number of student is finite number.
Infinite population:
When the number of units in a population is very large,
that is practically infinite population. For example, the
number of units produced of a product in a continuous
process is an infinite population

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The target population is the collection of elements or objects
that posses the information sought by the researcher and
about which inferences are to be made.
It is a relevant population and operationally defined.
The target population should be defined in terms of
elements, sampling units, extent and time

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Sampling Frame

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Sampling Frame known as ‘Source list’ from which sample is
to be drawn.
It contains the names of all items of a universe (in case of
finite universe only).
If source list is not available, researcher has to prepare it.
Such a list should be comprehensive, correct, reliable and
appropriate.
It is extremely important for the source list to be as
representative of the population as possible.

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Sample is subset of a larger population.
Sample unit is an element, or a unit containing the element,
that is available for selection at some stage of the sampling
process. There are three types of sampling units:
Primary Sampling Units (PSU)
Secondary Sampling Units
Tertiary Sampling Units

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Sampling element is the object about which or from which
the information is desired, e.g. the respondent.
Extent refers to the geographical boundaries.
Time is the time period under consideration.
Sampling is always subject to error.
Sampling error is the difference between the sample results
and the result of a census conducted using identical
procedures.
It is the statistical fluctuations due to chance variations.

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Errors associated with sampling are as follows.
Sampling frame errors
Random sampling error
Non response error

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SAMPLING METHODS
TECHNIQUES

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PROBABILITY TECHNIQUES

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Probability sampling technique
Here, the sample is selected in such a way that each unit
within the population has chance of being selected.
Most estimates tend to cluster around the true population or
universe mean.
When plotted on a graph, these means form what is called
the normal or bell curve.
There are four main types of probability or random
sampling .
Random sampling
Stratified sampling
Systematic sampling
Cluster sampling

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Simple random sampling
Here, each element in the population has a known and equal
probability of selection.
Each possible sample of a given size (n) has a known and
equal probability of being the sample actually selected.
This implies that every element is selected independently of
every other element.
A sampling procedure that assures that each element in the
population has an chance of being selected is referred to as
simple random sampling.

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Let us assume that you had a school with a 1000 students,
divided equally into boys and girls, and you wanted to select
100 of them for further study.
You might pull up all their names in a drum and pull 100
names out.
Here each person have equal chance of being selected, we
can also easily calculate the probability of a given person
being chosen, since we know sample size(n) and the
population (N) and it becomes a simple matter of division:
n/N*100
OR
(100/1000)*100 = 10%
This means that every student in the school as a 10% chance
of being selected using this method.

3-94
Many statistics books include a table of random numbers,
which are predetermined set of random numbers.
It is possible to start at any point on the table and move in
any direction to choose the numbers required for sample
size.
However, technology has given us a number of other
alternatives.

3-95
Procedure for simple random sampling
1.Select a suitable sampling frame.
2.Each element is assigned a number from 1 to N
(population size)
3.Generate n (sample size)
4.The numbers generated denote the elements that should
be include in the sample.

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Advantages:
1.No partiality is done.
2.Units have the characteristics of universe, hence units are
representative.
3.Simplicity of methods makes no possibility of error.
4.It saves money, time and labor.
Disadvantages:
1.The selector has no control over the selection of units.
2.Researcher may not prepare the whole field when the
universal is vast.
3.No homogeneous not possible
4.No question of alternatives, no replacement of selected
units

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Stratified Sampling
It is a two step process in which the population is partitioned
into subpopulation, or strata.
The strata should be mutually exclusive and collectively
exhaustive in that every population element should be
assigned to one and only one stratum and no population
elements should be omitted.
Next, elements are selected from each stratum by a random
procedure.
A major objective of stratified sampling is to increase
precision without increasing cost.

3-98

3-99
Strata 1 Strata 2 Strata 3

3-100
The elements within a stratum should be as homogeneous
as possible, but the elements in the different strata should
be as heterogeneous as possible.
The stratification variables should also be closely related to
the characteristic of interest.
Finally, the variables should decrease the cost of the
stratification process by being easy to measure and apply.
There are two types of stratified sampling methods.
1. proportioned stratified sampling
2. disproportioned stratified sampling

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In proportionate stratified sampling, the size of the sample
drawn from each stratum is proportionate to the relative size
of that stratum in the total population.
In disproportionate stratified sampling, the size of the
sample fro each stratum is proportionate to the relative size
of that stratum and to the standard deviation of the
distribution of the characteristic of interest among all the
elements in that stratum.
In this random sampling technique, the whole population is
first into mutually exclusive subgroups or strata and then
units are selected randomly for each stratum.

3-102
The segments are based on some predetermined criteria
such as geographic location, size or demographic
characteristic.
It is important that the seg/ments be as heterogeneous as
possible.

3-103
Procedure for stratified sampling
1. Select a suitable frame.
2. Select the stratification variable(s) and the number of
strata, H.
3. Divide the entire population in to H strata. Based on the
classification variable, each element of the population is
assigned to one of the H strata.
4. In each stratum, number the elements form 1 to Nh.(the
population size of h)
5. Determine the sample size of each stratum, nh based on
proportionate or disproportionate stratified sampling.
6. In each stratum, select a simple random simple size nh.

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Advantages
•Neither group or class of importance is totally neglected as
units of each are represented in the sample.
•If different classes are divided properly, selection of few
units represents the whole group.
•On the classification of regional basis, units are not in
contact easily. This leads to economy of time and money.
•There is a facility in substitution of units. If someone is not
contacted easily, the other person of the same class can be
substituted for him. Such inclusion result will not show any
contradicting.

3-105
Disadvantages
•The sample does not become representative if selected
sample has more or less units of a class.
•If the size of different group are different, no equal
proportional quality can be viewed.
•Non-proportional selection leads to more emphasis in the
end. During such time researcher can be biased, hence
samples will not representative.
•If group is not expressed properly, the difficulty is seen
about the unit to be kept under which group or class.

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Systematic Sampling
If a systematic pattern is introduced into random sampling, it
is referred to as “systematic sampling”.
In some instances, the most practical way of sampling is to
select every ith
item on a list. Sampling of this type is known
as systematic sampling.
An element of randomness is introduced into this kind of
sampling by using random numbers to pick up the unit with
which to start.
For instance, if a 4 per cent sample is desired, the first item
would be selected randomly from the first twenty-five and
thereafter every 25th item would automatically be included
in the sample.

3-107
System
Every 3rd
house

3-108
Thus, in systematic sampling only the first unit is selected
randomly and the remaining units of the sample are selected
at fixed intervals. Although a systematic sample is not a
random sample in the strict sense of the term, but it is often
considered reasonable to treat systematic sample as if it
were a random sample.
Systematic sampling has certain plus points. It can be taken
as an improvement over a simple random sample in as much
as the systematic sample is spread more evenly over the
entire population.
It is an easier and less costlier method of sampling and can
be conveniently used even in case of large populations. But
there are certain dangers too in using this type of sampling.
If there is a hidden periodicity in the population, systematic
sampling will prove to be an inefficient method of sampling.

3-109
•Procedure for systematic sampling:
1.Select suitable sampling frame.
2.Each element is assigned a number 1 to N(population size)
3.Determine the sampling interval i.
i = N/n. If I is a fraction, round to the nearest integer.
4.Select a random number, r, between 1 to i , as explained in
simple random sampling.
For example, there are 10000 elements in the population and
a sample of 100 is desired. In this case the sampling interval,
I, is 10. A random number between 1 and 10 is selected. If,
for example, this number is 9, the sample consists of
elements 9,19,29,39,49 and so on..

3-110
Advantages
 It is more straight-forward than random sampling
A grid doesn’t necessarily have to be used, sampling just
has to be at uniform intervals
A good coverage of the study area can be more easily
achieved than using random sampling
Disadvantages
 It is more biased, as all members or points have equal
chance of being selected.
It may therefore lead to over or under representation of a
particular pattern.

3-111
Cluster Sampling
If the total area of interest happens to be a big one, a
convenient way in which a sample can be taken is to divide
the area into a number of smaller non-overlapping areas and
then to randomly select a number of these smaller areas
(usually called clusters), with the ultimate sample consisting
of all (or samples of) units in these small areas or clusters.
Thus in cluster sampling the total population is divided into a
number of relatively small subdivisions which are
themselves clusters of still smaller units and then some of
these clusters are randomly selected for inclusion in the
overall sample.

3-112
Suppose we want to estimate the proportion of machine
parts in an inventory which are defective.
Also assume that there are 20000 machine parts in the
inventory at a given point of time, stored in 400 cases of 50
each. Now using a cluster sampling, we would consider the
400 cases as clusters and randomly select ‘n’ cases and
examine all the machine parts in each randomly selected
case.

3-113

3-114
Cluster sampling, no doubt, reduces cost by concentrating
surveys in selected clusters. But certainly it is less precise
than random sampling.
There is also not as much information in ‘n’ observations
within a cluster as there happens to be in ‘n’ randomly
drawn observations.
Cluster sampling is used only because of the economic
advantage it possesses; estimates based on cluster samples
are usually more reliable per unit cost.

3-115
Multi-stage sampling is a further development of the
principle of cluster sampling.
Suppose we want to investigate the working efficiency of
nationalised banks in India and we want to take a sample of
few banks for this purpose.
The first stage is to select large primary sampling unit such
as states in a country.
Then we may select certain districts and interview all banks
in the chosen districts.
This would represent a two-stage sampling design with the
ultimate sampling units being clusters of districts.

3-116
If instead of taking a census of all banks within the selected
districts, we select certain towns and interview all banks in
the chosen towns.
This would represent a three-stage sampling design.
If instead of taking a census of all banks within the selected
towns, we randomly sample banks from each selected town,
then it is a case of using a four-stage sampling plan.
If we select randomly at all stages, we will have what is
known as ‘multi-stage random sampling design’.

3-117
Ordinarily multi-stage sampling is applied in big inquires
extending to a considerable large geographical area, say,
the entire country. There are two advantages of this
sampling design viz.,
(a)It is easier to administer than most single stage designs
mainly because of the fact that sampling frame under multi-
stage sampling is developed in partial units.
(b)A large number of units can be sampled for a given cost
under multistage sampling because of sequential clustering,
whereas this is not possible in most of the simple designs.

3-118
Advantages
 It is a cheap, quick and easy. Instead of sampling an entire
country when using simple random sampling, the
researcher can allocate his limited resources to the few
randomly selected cluster or area when using cluster
samples.
Related to the first advantage, the researcher can also
increase his sample size with this technique. Considering
that the researcher will only have to take the sample from a
number of areas or clusters, he can then select more
subjects since they are more accessible.

3-119
Disadvantages
 It is the least representative of the population.
Here, the degree of error is high.

3-120

3-121
NON PROBABILITY
TECHNIQUES

3-122
Here, the sampling is selected in such a way that the chance
of being selected of each unit within the population of
universe is unknown.
Indeed, the selection of the subjects is arbitrary, the
researcher relies on hisher experience and judgment.
As a result there are no statistical techniques that allow for
the measurement of sampling error, and therefore it is not
appropriate to project the sample characteristics to the
population.
In spite of this significant shortcoming, its is very popular in
hospitality and tourism research.
Almost all qualitative research methods rely on non
probability sampling techniques.

3-123
There are four main types.
 Convenience Sampling
 Quota Sampling
 Judgment Sampling
 Snowball sampling

3-124

3-125
Convenience Sampling
 It attempts to obtain a sample of convenient elements.
Often, respondents are selects because they happen to
be in the right place at the tight time.
Examples are..
 Use of students, and members of social organizations
 Mall intercept interviews without qualifying the
respondents
 People on the street interviews

3-126
 Here, the selection of units from the population is based
in easy availability andor accessibility.
 The major disadvantage of this technique is that we have
no idea how representative the information collected
about the sample is to the population as a whole.
 But the information could still provide some fairly
significant insights, and be a good source of data in
exploratory research.

3-127

3-128
Judgement sampling
 It is a form of convenience sampling in which the
population elements are selected based on judgement of
the researcher.
Examples..
 Test marks
 Expert witness used in court
 Here, the researcher or some other expert uses hisher
judgement in selecting the units from the population for
study based on the population’s parameters.
 It might be the most appropriate if the population to be
studied is difficult to locate or if some members are
thought to be better then others to interview. This
determination is often made on the advice and with the
assistance of the client.

3-129
Snowball Sampling
 Here, an initial group of respondent is selected, usually
at random.
 After being interviewed, these respondents are asked to
identify others who belong to the target population of
interest.
 Subsequent respondents are selected based on the
referrals.
 A variety of procedures are there for snowball sampling.
Initial respondents are selected by probability methods.
Additional respondents are obtained from information
provided by the initial respondents.
 It is used when the members of the population are those
who are less known

3-130

3-131
Quota sampling
 It may be viewed as two stage judgmental sampling.
 The first stage consists of developing control categories,
or quotas, of population elements.
 In the second stage, sample elements are selected based
on convenience or judgement.
 In quota sampling, the population is first segmented into
mutually exclusive sub-groups, just as in stratified
sampling.
 Then judgement is used to select the subjects or units
from each segment based on a specified proportion.
 In this second step which makes the technique one of
non-probability sampling.

3-132
Advantages of quota sampling are the speed with which
information can be collected, the lower cost of doing so and
the convenience it represents.

3-133

3-134
SAMPLE DESIGN

3-135
It is a definite plane for obtaining a sample from a given
population is called ‘ sample design’.
It is a technique of selecting items for the sample.
It lay down the number of items to be included in the sample.
It should be reliable and appropriate for the research study
of the researcher.
It is determined before data are collected.
While developing a sample design, the following points must
be taken into consideration.

3-136
 Type of universe: In developing any sample design, the
first step is to define the universe i.e the set of objects to
be studied. The universe may be finite or infinite.
 Sample Frame: It contains the names of all items of a
universe. It should be representative of all population and
should be appropriate, reliable, correct and
comprehensive.
 Sample Unit: It is to be decided before selecting the
sample. Sampling units may be geographical,
constructional, social and individual.
 Sample Size: It refers to he number of items to be
selected from a universe to form a sample. Sample size
should not be very large or too small.

3-137
 Parameters of interest: While determining a sample
design, the specific population parameters, which of
interest, must be taken into account by the research.
 Budgetary constraints: The size as well as the type of
sample depends upon the cost consideration.
 Sampling procedure: Finally the researcher must decide
about techniques to be used in selecting the items for the
sample i.e. he must decide the type of sample. This
technique stands for the sample design itself. He should
select the sample design in such a way that for a given
sample size and for a given cost, the sample design has a
smaller sampling error.

3-138
 Sample size characteristics:
 It should be such, so that systematic bias can be controlled
in better way.
 It should result in a truly representative sample.
 It should ne viable in the context of funds available for the
research study.
 It should be such that the result of sample study can be
applied, in general, for the universe with a reasonable level
of confidence.
 It should result small sampling error.

3-139
 Important factors in determining appropriate sample
design are
 Degree of accuracy
 Resources
 Time
 Advanced knowledge of the population
 National versus local
 Need for statistical analysis

3-140
SAMPLE SIZE

3-141
 The sample size if dependent on the appropriate sample
design.
 It is frequently a matter as to the size of a sample drawn,
and the notation is that if the sample size is “not large”,
the sampling results are likely to be inaccurate.
 The sample size decision must be made on a case by
case basis, considering the variety of goals to be
achieved by a particular study and taking into account
numerous other aspects of the research design.
 The size of a sample depends upon the basic
characteristics of the population.
 If there is complete homogeneity, a sample size of 1
would be sufficient, while a larger sample is obviously
required where there is a heterogeneity.

3-142
 One way of dealing with heterogeneity is to break the
population into sub groups or strata, which displays
homogeneity among the sample units. This is know as
stratified (random) sampling, Which is statistically more
efficient than simple random sampling.
 Here we need sample frame such as a list of all students
in a college from which to drawn a sample.
 Where we are sampling from a very much larger
population, as in say, a city, we require a complete list of
all the households in the city from which to randomly
select a given sample, subject to certain characteristics
such as age, income etc.., which might be set as
“quotas”.

3-143
It is also necessary to ensure that the smallest sub-group
or stratum should contain “sufficient” sampling units so that
accurate and reliable estimates can be found of the
population stratum.
 Sample size is a balance act between precision and cost
survey.
 Daniel and Terrel have suggested a formula for
calculation of ample size when we have a fixed budget for a
sample study.
 The budget represents the total cost C for a sampling
study, which can be broken into two parts
 the fixed cost Cf
The variable cost per sampling unit Cu

3-144
 The sample size n is given by the formula:
n = C – Cf / Cu
 Let us assume that the budget available for a sample
survey is Rs 8,00,000; the cost per questionnaire
charged by the Market Research is Rs. 150, and the fixed
cost associate with the study are Rs. 1,50,000. Then we
have
n = 8,00,000 – 1,50,000 / 150
From which we find that the required sample size
n = 4,333

3-145
 Important qualitative factors in determining the sample
size are:
 The important of the decision
 The nature of the research
 The number of variables
 Confidence level
 Administrative concerns
 Sample sizes used in similar studies
 Cost constraints
 Resource constraints

3-146
SAMPLING PLAN
AND
SAMPLE SELECTION

3-147
 Sampling plan is a detailed outline of which
measurements will be taken at what times, on which
element, in what manner, and by whom.
 Sampling plans should be designed in such a way that the
resulting data will contain a representative sample of the
parameters of interest and allow for all questions, as
stated in the goals, to be answered.

3-148
 The step involved in developing a sampling plan are:
 Identify the parameters to be measured, the range of
possible values, and the required resolution
 Design a sampling scheme that details how and when
samples will be taken
 Select sample sizes
 Design data storage formats
 Assign roles and responsibilities

3-149
 Sampling plan must include target population, sampling
frame, sampling element, sampling unit, sampling
methodology to be adopted, method adopted for
determining sample size and procedure for actual
sample is selection in order to minimize sample error.
 Once the sampling plan has been developed it can be
verified and then passed on to the responsible parties for
execution.

3-150
Sample Selection
 It is very important to actually select the sample as per
sampling plan.
 Otherwise it results in sample selection error.
 Sample selection error is an administrative error caused
by improper selection of a sample during a survey,
resulting in accidental bias in the results.
 Sample Selection Error occurs in experiments when a
bias is introduced into the way in which experimental
units are assigned to groups.

Scaling and Measurement techniques

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