Marketing Research PPT - III

Marketing Research
Unit - III
Dr. Ravindra
Associate Professor
Department of Commerce
Indira Gandhi University,
Meerpur, Rewari

Sampling: Process and Designs
Introduction
Once the researcher has formulated the problem and
developed a research design including the questionnaire, he
has to decide whether the information is to be collected from
all the people comprising the population. In case the data are
collected from each member of the population of interest, it is
known as the census survey. If, on the other hand, data are to
be collected only from some member of the population, it is
known as the sample survey. Thus, the researcher has to
decide whether he will conduct a census or a sample survey to
collect the data needed for his study.
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Dr. Ravindra, IGU, Meerpur

Some Basic Terms
1. Population: In statistical usage the term population is
applied to any finite or infinite collection of individuals. It
has displayed the older term universe, which is derived from
the universe of discourse of logic. It is practically
synonymous with aggregate and does not necessarily refer to
a collection of living organisms.
2. Census: The complete enumeration of a population or
groups at a point in time with respect to well-defined
characteristics such as population, production, traffic on
particular roads. In some connection the term is associated
with the data collected rather than the extent of the collection
so that the term Sample, Census has distinct meaning.
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The partial enumeration resulting from a failure to cover
the whole population, as distinct from a designed sample
enquiry, may be referred to as an ‘incomplete census’.
3. Sample: A part of a population or a subset from a set of
units, which is provided by some process or other, usually
by deliberate selection with the object of investigating the
properties of the parent population or set.
4. Sample Survey: A survey which is carried out using a
sampling method, i.e. in which a portion only, and not the
whole population, is surveyed.
5. Sampling Unit and Frame: A decision has to be taken

concerning a sampling unit before selecting sample. Sampling
unit may be geographical one such as state, district, village
etc., or a construction unit as house, flat, etc., or it may be a
social unit such as family, club, school, etc., or an individual.
The list of sampling units is called as ‘frame’ or ‘sampling
frame’. Sampling frame contain the names of all items of a
universe.
6. Sampling Error: That part of the difference between a
population value and an estimate thereof, derived from a
random sample, which is due to the fact that only a sample of
values is observed; as distinct from errors due to imperfect
selection, bias in response or estimation, errors of observation

and recording, etc. The totality of sampling errors in all
possible samples of the same size generates the sampling
distribution of the statistic which is being used to estimate the
parent value.
7. Bias: Generally, an effect which deprives a statistical result of
representativeness by systematically distorting it, as distinct
form a random error which may distort on any one occasion
but balances out on the average.
8. Biased Sample: A sample obtained by a biased sampling
process, that is to say, a process which incorporates a
systematic component of error, as distinct from random error
which balances out on the average. Non-random sampling is

often, though not inevitably, subject to bias, particularly when
entrusted to subjective judgment on the part of human beings.
Advantages of Sampling
The following are several advantages of sampling:
1. Sampling is cheaper than a census survey. It is obviously
more economical.
2. Since magnitude of operations involved in a sample survey
is small, both the execution of the field work and the
analysis of the results can be carried out speedily.
3. Sampling results in greater economy of effort as a relatively

small staff is required to carry out the survey and to tabulate
and process the survey data.
4. A sample survey enables the researcher to collect more
detailed information than would otherwise be possible in
census survey. Also, information of a more specialized type
can be collected, which would not be possible in a census
survey on account of the availability of a small number of
specialists.
5. Since the scale of operations involved in a sample survey is
small, the quality of the interviewing, supervision and other
related activities can be better than the quality in a census
survey.

Limitations of Sampling
1. When the information is needed on every unit in the
population such as individuals, dwelling units or business
establishments, a sample survey cannot be of much help for
it fails to provide information on individual count.
2. Sampling gives rise to certain errors. If these errors are too
large, the results of the sample survey will be of extremely
limited use.
3. While in a census survey it may be easy to check the
omissions of certain units in view of complete coverage, this
is not so in the case of a sample survey.

The Sampling Process
Having looked into the major advantages and limitations of
sampling, we now turn to the sampling process. It is the
procedure required right from defining a population to the
actual selection of sample elements. There are seven steps
involved in this process.
1. Define the Population: It is the aggregate of all the
elements defined prior to selection of the sample. It is
necessary to define population in terms of (i) elements, (ii)
sampling units, (iii) extent, and (iv) time.
2. Identify Sampling Frame: Identify the sampling frame,
which could be a telephone directory, a list of blocks and
localities of a city, a map or any other list consisting of all

the sampling units. It may be pointed out that if the frame
is incomplete or otherwise defective, sampling will not be
able to overcome these shortcomings.
3. Specify the Sampling Unit: The sampling unit is the
basic unit containing the elements of the target population.
The sampling unit may be different from the element. For
example, if one wanted a sample of housewives, it might
be possible to have access to such a sample directly.
However, it might be easier to select households as the
sampling unit and then interview housewives in each of
the selected households.

As mentioned in the preceding step, the sampling frame
should be complete and accurate otherwise the selection of the
sampling unit might be defective.
4. Specify the Sampling Methods: It indicate how the sample
units are selected. One of the most important decisions in this
regard is to determine which of the two – probability and non
– probability sample – is to be chosen. Probability samples are
also known as random samples and non – probability samples
as non – random samples.
5. Determine the Sample Size: In other words, one has to
decide how many elements of the target population are to be
chosen. The problem of sample size is discussed in the next
section of the unit.

6. Specify the Sampling Plane: This means that one should
indicate how decisions made so far are to be implemented. For
example, if a survey of households is to be conducted, a
sampling plane should define a household, contain instructions
to the interviewer as to how he should take a systematic
sample of households, advise him on what he should do when
no one is available on his visit to the household, and so on.
These are some pertinent issues in a sampling plan should
provide answers.
7. Select the Sample: This is the final step in the sampling
process. A good deal of office and fieldwork is involved in the
actual selection of the sampling element. Most of the problems

Types of Sampling Design
in this stage are faced by the interviewer while contacting the
sample-respondents.
Types of Sampling Designs
The method of selecting a sample is of fundamental
importance and depends upon the nature of data and
investigation. The techniques of selecting a sample are
classified as – ‘probability sampling’ and ‘non-probability
sampling’ . We take up these two designs separately.
Probability Sampling
Probability sampling is also known as ‘random sampling’ or
‘chance sampling’. Under this sampling design, every item of
the universe has an equal chance of inclusion in the sample.

It is, so to say, a lottery method in which individual units
are picked up from the whole group not deliberately but
by some mechanical process. Here it is blind chance alone
that determine whether one item or the other is selected.
The results obtained from probability or random sampling
can be assured in terms of probability i.e., we can measure
the errors of estimation or the significance of results
obtained from a random sample, and this fact bring out the
superiority of random sampling design over the deliberate
sampling design. Random sampling ensures the law of

Statistical Regularity which states that if on an average the
sample chosen is a random one, the sample will have the
same composition and characteristics as the universe. This
is the reason why random sampling is considered as the
best technique of selecting a representative sample.
1. Simple Random Sampling: Simple random sampling
from a finite population refers to that method of sample
selection which gives each possible sample combination
an equal probability of being picked up and each item in
the entire population to have an equal chance of being

included in the sample. This applies to sampling without
replacement i.e., once an item is selected for the sample,
it cannot appear in the sample again, sampling with
replacement is used frequently less in which procedure,
the element selected for the sample is returned to the
population before the next element is selected. In such a
situation the same element could appear twice in the
sample before the second element is chosen. In brief, the
implications of random sampling are;
(a) It gives each element in the population an equal
probability of getting into the sample, and all choices are
independent of one another.

(b) It gives each possible sample combination an equal
probability of being chosen.
Keeping this in view we can define a simple random
sample from a finite population as a sample which is
chosen in such a way that each of the N Cn possible
samples has the same probability, 1/ N Cn of being
selected. There are number of way through which the
unit can be selected like; lottery method, random number
table developed by various statistician i.e. Tippett, Yates,
Fisher etc.

Simple random sample, we have discussed above is
‘simple random sample without replacement ‘, here, a unit
which is selected once is not replaced back to the
population, i.e., one sampling unit can be selected only
once. Other alternative to this design is ‘simple random
sample with replacement’. Because of the probability of
over-representation of some sampling units, this design is
not of much practical usage.
So far we have talked about random sampling, keeping in
view only the finite populations. But what about random
sampling in context of infinite population? It is relatively

difficult to explain the concept of random sampling from
an infinite population. However, a few examples will
show the basic characteristics of such a sample. Suppose
we consider the 20 throws of a fair dice as a sample from
the hypothetically infinite population which consists of the
results of all possible throws of the dice. If the probability
of getting a particular number, say 1, is the same for each
throw and the 20 throws are all independent, then we say
that the sample is random. Similarly, it would be said to
be sampling from an infinite population if we sample with
replacement from a finite population and our sample
would be considered as a random sample if in each draw

all elements of the population have the same probability of
being selected and successive draws happen to be
independent. In brief, one can say that the selection of
each item in a random sample from an infinite population
is controlled by the same probabilities and that successive
selections are independent of one another.
2. 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 percent 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. 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. For instance, every 25th
item produced by a certain production process is
defective. If we are to select a 4% sample of the items in
this process in a systematic manner, we would either get
all defective items or all good items in our sample
depending upon the random starting position. If all

elements of the universe are observed in a manner
representative of the total population, i.e. the population
list is in random order, systematic sampling is considered
equivalent to random sampling. But if this is not so, then
the results of such sampling may, at times, not be very
reliable. In practice, systematic sampling is used when
lists of population are available and they are of
considerable length.
3. Stratified Sampling: If a population from which a sample
is to be drawn does not constitute a homogeneous group,
stratified sampling technique is generally applied in order

to obtain a representative sample. Under stratified
sampling the population is divided into several sub-
populations that are individually more homogeneous than
the total population (the different sub-populations are
called ‘strata’) and then we select items from each stratum
to constitute a sample. Since each stratum is more
homogeneous than the total population, we are able to get
more precise estimates for each stratum and by estimating
more accurately each of the component parts, we get a
better estimate of the whole. In brief, stratified sampling
results is more reliable and detailed information can be
obtained from this sampling method.

The following three questions are highly relevant in the
context of stratified sampling:
(a) How to form strata?
(b) How should items be selected from each stratum?
(c) How many items be selected from each stratum or how
to allocate the sample size of each stratum?
Regarding the first question, we can say that the strata
be formed on the basis of common characteristics of the
items to be put in each stratum. This means that various
strata be formed in such a way as to ensure elements
being most homogeneous within each stratum and most

heterogeneous between the different strata. Thus, strata
are purposively formed and are usually based on past
experience and personal judgment of the researcher.
In respect of the second question, we can say that the
usual method, for selection of items for the sample from
each stratum, resorted to is that of simple random
sampling. Systematic sampling can be used if it is
considered more appropriate in certain situations.
regarding the third question, we usually follow the method
of proportional allocation under which the size of the
samples from the different strata are kept proportional to
the sizes of the strata. It is not necessary that satisfaction

be done keeping in view a single characteristics.
Population are often stratified according to several
characteristics. Stratification of this type is know as
cross-stratification, and up to a point such stratification
increases the reliability of estimates and is much used in
opinion survey.
From what has been stated above in respect of stratified
sampling, we can say that the sample so constituted is the
result of successive application of purposive and random
sampling methods. As such it is an example of mixed
sampling. The procedure wherein we first have
stratification and then simple random sampling is know

as stratified random sampling.
4. 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 unit in these small areas
or clusters.
Thus, in cluster sampling the total population is divided
into a number of relatively small sub-divisions which are
themselves clusters of still smaller units and then some of

these clusters are randomly selected for inclusion in the
overall sample.
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. If cluster happen to be some geographic sub-divisions,
in that case cluster sampling is better known as area sampling.

In other words, cluster designs, where the primary
sampling unit represents a cluster of units based on
geographic area, are distinguished as area sampling. The
plus and minus points of cluster sampling are also
applicable to area sampling.
5. Multi-stage Sampling: Multi-stage sampling is a further
development of the principle of cluster sampling.
Suppose, we want to investigate the working efficiency of
nationalized 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.
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 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’.
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 multi-stage sampling because of
sequential clustering, whereas this is not possible in most
of the simple designs.

6. Sampling with Probability Proportional to Size: In case
the cluster sampling units do not have the same number or
approximately the same number of elements, it is
considered appropriate to use a random selection process
where the probability of each cluster being included in
the sample is proportional to the size of the cluster. For
this purpose, we have to list the number of elements in
each cluster irrespective of the method of ordering the
cluster. Then we must sample systematically the
appropriate number of elements from the cumulative total.
The actual number selected in this way do not refer to
individual elements, but indicate which clusters and how

from the cluster are to be selected by simple random
sampling or by systematic sampling. The results of this
type of sampling are equivalent to those of a simple
random sample and the method is less cumbersome and is
also relatively less expensive.
7. Sequential Sampling: This sampling design is some what
complex sample design. The ultimate size of the sample
under this technique is not fixed in advance, but is
determined according to mathematical decision rules on
the basis of information yielded as survey progresses.

This is usually adopted in case of acceptance sampling plan in
context of statistical quality control. When a particular lot is
to be accepted or rejected on the basis of two samples, it is
known as double sampling and in case the decision rests on
the basis of more than two samples but the number of samples
is more than two but it is neither certain nor decided in
advance, this type of system is often referred to as sequential
sampling. Thus, in brief, we can say that in sequential
sampling, one can go on taking samples one after another as
long as one desires to do so.
Non Probability Sampling

Non-probability sampling methods includes; Judgment
sampling /Purposive sampling, Convenience sampling,
Quota sampling and Snowball sampling. Let see all these
sampling methods in detail.
1. Judgment/Purposive Sampling: The main characteristic
of judgment sampling is that units or elements in the
population are purposively selected. It is because of this
that judgment samples are also called purposive samples.
Since the process of selection is not based on the random
method, a judgment sample is considered to be non-
probability sampling. Occasionally it may be desirable to
use judgment sampling. Thus, an expert may be asked to

select a sample of ‘representative’ business firms. The
reliability of such a sample would depend upon the
judgment of the expert. The quota sample, is in a way a
judgment sample where the actual selection of units
within the earlier fixed quota depends on the interviewer.
It may be noted that when a small sample of a few units is
to be selected, a judgment sample may be more suitable as
the errors of judgment are likely to be less than the
random errors of a probability sample. However, when a
large sample is to be selected, the element of bias in the

selection could be quite large in the case of a judgment
sample. Further, it may be costlier than the random
sampling.
2. Convenience Sampling: Convenience sampling, as the
name implies, is based on the convenience of the
researcher who is to select a sample. This type of
sampling is also called accidental sampling as the
respondents in the sample are included in it merely on
account of their being available on the spot where the
survey is in progress. Thus, a researcher may stand at a

certain prominent point and interview all those or selected
people who pass through that place. A survey based on
such a sample or respondents may not be useful if the
respondents are not representative of the population. It is
not possible in convenience sampling to know
‘representativeness’ of the selected sample. As such, it
introduces an unknown degree of bias in the estimate. In
view of this major limitation, convenience sampling
should be avoided as far as possible. It may however be
more suitable in exploratory research, where the focus is
on getting new ideas and insights into a given problem.

3. Quota Sampling: Quota sampling is quite frequently used
in marketing research. It involves the fixation of certain
quota, which are to be fulfilled by the interviewers. In
this sampling design we my fix certain controls which can
be either independent or inter-related. A survey of 2000
households has been chosen, subject to the condition that
1200 of these should be from rural areas and 800 from the
urban areas of the territory. Likewise, of the 2000
households, the rich households should number 150, the
middle class ones 650 and the remaining 1200 should be
from the poor class. In first case there are independent
quota control, where as, in second case it is inter-related

quota controls. Inter-related quota controls allow less
freedom of selection of the units than that available in the
case of independent controls.
There are certain advantages in both the schemes.
Independent controls are much simpler, especially from
the viewpoint of interviewers. They are also likely to be
cheaper as interviewers may cover their quotas within a
small geographical area. In view of this, independent
controls may affect the representativeness of the quota
sampling. Inter-related quota controls are more
representative through such controls may involve more
time and effort on the part of interviewers. Also, they may

be costlier than independent quota controls.
In view of the non-random element of quota sampling, it
has been severely criticized especially by statisticians,
who consider it theoretically weak and unsound. There are
points both in favor of and against quota sampling.
Advantages
• It is economical, as travelling costs can be reduced.
• It is administratively convenient.
• When the field work is to be done quickly, perhaps quota
sampling is most appropriate and feasible.
• It is independent of the existence of sampling frames.

4. Snowball Sampling: In the initial stage of snowball
sampling, sample units may or may not be selected by
using probability methods. Subsequently, additional units
are obtained on the basis of information given by initial
sample units. Against, these units may provide other
names to the researcher. In this way, the sample build up
as more and more names are covered by it. The need for
snowball sampling arises because of the difficulty in
identifying the respondents right in the beginning of the
proposed research study.

Characteristics of Good Sample Design
A good sample design requires the judicious balancing of four
broad criteria – goal orientation, measurability, practicality
and economy.
1. Goal Oriented: This suggest that a sample design should be
oriented to the research objectives, tailored to the survey
design, and fitted to the survey conditions. If this done, it
should influence the choice of the population, the
measurement as also the procedure of choosing a sample.
2. Measurability: A sample design should enable the
computation of valid estimates of its sampling variability.

Normally, this variability is expressed in the form of
standard errors in surveys. However, this is possible only
in the case of probability sampling. In non-probability
samples, such as a quota sample, it is not possible to know
the degree of precision of the survey results.
3. Practicality: This implies that the sample design can be
followed properly in the survey, as envisaged earlier. It is
necessary that complete, correct, practical and clear
instructions should be given to the interviewer so that no
mistakes are made in the selection of sampling units and
the final selection in the field is not different from the
original sample design.

Practicality also refers to simplicity of the design, i.e. it
should be capable of being understood and followed in
actual operation of the field work.
4. Economy: Finally, economy implies that the objectives of
the survey should be achieved with minimum cost and
effort. Survey objectives are generally spelt out in terms
of precision, i.e. the inverse of the variance of survey
estimates. For a given degree of precision, the sample
design should give the minimum cost. Alternatively, for a
given per unit cost, the sample design should achieve
maximum precision.

Sample Size Decisions
Introduction
After having looked into sample designs in the preceding
section of the PPT, we now turn to another important
aspect of sampling, namely, the sample size. When a
survey is undertaken and when it is not possible to cover
the entire population, the marketing researcher has to
answer a basic question. How larger should the sample
be? We will focus our attention on this basic problem and
discuss how decisions on sample size are taken.
Determining the Sample Size
There are two basic approaches to the problems of sample

size, the adhoc or practical approach and the statistical
approach. The former is widely used in marketing
research.
1. Practical Method:
According to this approach, a sample size of less than a
few hundred units is not chosen. This is because when a
field survey is undertaken, interviewer are appointed,
trained and asked to conduct field investigations. Since
all this would cost substantially, it would not be worth it
for the marketing research if only a small sample is
chosen. A survey confined to a relatively high cost per

interview. Another consideration in favor of selecting a
reasonable size of sample is that it enables the researcher
to test several hypothesis. This is especially true for
samples in the sub –groups. Such hypotheses can be tested
with a high degree of statistical significance when the
sample size is reasonably large. Another practical
consideration in case of a stratified sample is that the
overall sample size is so fixed that the sample size within
each stratum is not less than 30. A common practice in
this regard is to determine the sample size of each stratum
first and then add up the samples of all the strata to obtain
the overall sample size.

2. Statistical Principles
The second approach based on statistical principles is
obviously scientific. A good researcher is expected to
follow it rather than the rule-of-thumb approach.
According to the statistical approach, the problem of
sample size involves several aspect such as the type of
sample design, the homogeneity in the population from
which a sample is to be chosen and the availability of
finance, personnel and time for the conduct of the field
survey. In view of all these considerations, the question of
sample size becomes difficult. Since a comprehensive
discussion of all these aspects would need a good deal of

space, only some basic principles for determining sample
size are discussed.
However, before this is done, it is necessary to have some
idea of sampling distribution, which forms the basis for
any problem on sample size.
Sampling Distribution of the Mean
According to the central limit theorem, the various
arithmetic means of a large number of random samples of
the same size will form a normal distribution. If an
arithmetic mean of all possible sample means is
calculated, it will coincide with the population mean.

Main Considerations for Sample Size Decisions
There are three considerations required to be checked when
determining the sample size necessary to estimate the
population mean. These are;
1.The extent of error or imprecision allowed.
2. The degree of confidence desired in the estimate.
3. Estimate of the standard deviation of the population.
The first two consideration involve the judgment of the
researcher. The third consideration is the responsibility of the
researcher. Sometime, estimates of standard deviation are
available, from earlier studies. Even when standard deviation

is not available, it can calculated from the summary tables
contain the data. However, if this too is not possible, the
researcher may choose a small sample from which the
standard deviation is calculated. He then uses the sample
standard deviation as an estimate of the population
standard deviation and then determines the final sample
size.
We may consider the problem of determining sample size
in two different situations, namely when the standard
deviation of the population is known and when it is
unknown.

Determination of sample Size When Standard Deviation is
Known
1. Extent of Error: The first consideration relates to the extent
of error allowed. This is indicated by the standard error (the
standard deviation of the sample means). The researcher
himself has to decide the magnitude of the standard error that
he can tolerate. Although this is a difficult question, it is
necessary to fix the limit of the standard error beyond which it
should not exceed. The fixation of standard error should not
be confined to overall results but should also be applied to
various sub-groups. One way is to first determine the size of
each sub-group on the basis of a given degree of precision.
The total of the size of each sub-group could then be taken as

the overall size of the sample, though it may turn out to be too
large and on considerations of time and money, it may not be
acceptable to the researcher.
2. The Degree of Confidence: A second consideration is the
degree of confidence that the researcher wants to have in the
results of the study. In case he wants to be 100 percent
confident of the results, he is left with no option but to cover
the entire population. However, as this is often not possible on
account of cost, time and other constraints, the researcher
should be satisfied with less then 100 percent confidence.
Normally, three confidence level, namely, 99 percent, 95
percent and 90 percent are used. When a 99 percent
confidence level is used, it implies that there is a risk of only

1 percent of the true population statistics falling outside the
range indicated by the confidence interval. In the case of a
95 % confidence level, such a risk is of 5 percent and in
the case of 90 percent confidence level, it is of 10 percent.
In marketing research studies, the most frequently used
norm is the 5 % confidence level.
It should be noted that there is a trade off between the
degree of precision and the degree of confidence. For
given size of a sample, one can specify one of these two
but not both of them at the same time. The formula to
determine the size of n is:

Z2 ό 2
n =
E2
Where, E = the maximum error allowed.
Z = the confidence level.
ό = the standard deviation of the population.
When Standard Deviation of the Population is Unknown
So far the discussion was confined to such cases where
standard deviation of the population was known. Many a time,
the standard deviation is not known. In such cases too, the

method followed is the same except that an estimate of
the population standard deviation in place of its previously
known value is taken. Sometimes, the researcher may
undertake a pilot survey to ascertain the standard
deviation. If this is not possible, the researcher may have
to use some alterative approach. As we know, the entire
area under the normal curve falls within µ ± 3ó. This
mean that we should have some idea of the range of
variation, i.e., the difference between the highest item and
the lowest item. This range need to be divided by six in
order to get an estimate of the standard deviation.

Relative Precision
So far the discussion was concerned with the basis of
absolute precision measured in terms of specific units. We
now introduce another dimension, namely, the relative
precision. It can be defined as the extent of precision
relative to level. Suppose the mean is 200 and a relative
precision of 10 percent is aimed at. This would mean a
confidence interval from 180 to 220. In case the mean is
100, the confidence interval will be from 90 to 110.
When applying relative precision instead of absolute
precision, the usual formula;

Z2 ό 2 Z2 ό 2
n = , is transformed to n = , where r
E2 r2 µ
is the relative precision.
This can be written as (Z2 / r2) C2, where C is the
coefficient of variation.
In the above form of the formula, it is necessary to have
values of three variables namely, Z, r and C. since Z
relates to the desired level of significance, it will be
known. So also r will be known as it indicates the level of

precision which has to be decided in advance. It is only C
that is not known and which needs to be estimated. The
researcher has to very carefully use his judgment
regarding the magnitude of the population mean and the
population standard deviation. If there are some earlier
studies available for his guidance, he should draw upon
them in order to make his judgment as realistic as
possible. It may be noted that if the coefficient of
variation C turns out to be higher than that actually given
by the ratio of the sample standard deviation to the sample
mean, then this would show that the sample size should
have been larger and vice versa.

Sample Size and Other Factors
It should be noted that a marketing research study is usually a
compromise between technical compliance and practical
limitations faced by researcher. Some of these constraints
which influence sample size are discussed here.
1. Several Objectives: A marketing research study is seldom
conducted to estimate a single parameter. Generally several
objectives are involved in a single study. Now, a sample size
may vary from one objective to another on account of the
expected variance. It is not necessary to go through the
process of determining the sample for all objectives. The

general approach is to choose a few crucial question on
the basis of which the sample size is determined. The
researcher should especially include objectives that are
likely to have greater variability as their inclusion will be
more crucial for sample size.
2. Cost Constraints: Another major factor that influences
sample size is the cost involved in drawing the sample and
undertaking the survey on the basis of the sample chosen.
This does not mean that a company having plenty of
finance should go in for a large sample. Availability of
large funds should not be a criterion for increasing the
sample size. These funds can be better utilized elsewhere.

When a firm find that the study will cost too much, an
alternative before it is to increase the size of the allowable
error. A lower degree of precision would need a lower
sample size than envisaged earlier. There could be several
combinations of the extent of confidence and precision
which can be though of by the firm. It has to chose one of
these feasible combinations keeping in mind the financial
resources at its disposal. It is possible that reducing the
degree of confidence or precision or both may undermine
the utility of the study so much so that it may even drop
the idea of conducting the field survey.

3. Time Constraints: At times, management wants prompt
results on the basis of a proposed marketing research study. It
fears that delay in getting the findings of the study will be
hardly useful in decision-making. In such a situation, the
researcher has to keep in mind the time factor. Accordingly,
the sample size should be so limited that the marketing
research report can be completed within the stipulated time.
4. Nature of Data Analysis: Another factor that may affect the
sample size is the nature of data analysis planned for the
proposed study. If the researcher need only univariate
analysis, the sample size is determined on the basis of criteria

explained earlier. This means that the relationship between the
sample size and desired precision on one variable is to be
determined. In case the research study involves two or more
variables, i.e. bivariate and multivariate study, the study
requires different sample sizes so that valid estimates of
population parameters can be made. In general, as the number
of parameters increases, the requirement of sample size also
increases. However, there may be some multivariate studies,
which may not require a large sample size.
Sample Size Decisions When Estimating Proportions
The foregoing discussion was carried out in relation to sample

size for estimating mean values. At times, it is the proportion
of population with a particular attribute that becomes more
relevant to the marketing researcher than the mean value. The
formula is as under;
Z2 [Ԉ (1 - Ԉ) ]
n =
E2
Relative Precision
As was discussed earlier, while determining sample size when
estimate means, here too the same approach is applicable in

respect of relative precision. The term ‘relative precision’
signifies that the size of the interval will be within a certain
percent of the value, regardless of its level. For example, if the
sample proportion is 0.4 and if the relative precision is to be
within ± 10 percent then the interval would be 0.36 to 0.44.
Statistical Efficiency
The term ‘efficiency’ or ‘statistical efficiency’ is frequently
used in discussions of sampling. A sample design is
considered statistically more efficient than another if its
standard error of the mean is smaller, given the same sample
size. Conversely, a more efficient sample design will yield as

precise a result as an alternative sample design but with a
smaller sample. Thus, efficient implies a comparison of
two or more sample designs, Symbolically;
óu
EA = × 100
óA
Where, EA = the statistical efficiency of sampling design
A, expressed as a percentage.
óu = the standard error of the appropriate statistics, e.g.,
mean, produced by an unrestricted single-stage sample of
size n.

óA = the standard error of the appropriate statistics,
produced by sampling design A of size n.
If the degree of precision required is specified in advance,
regardless of the sample design, then the relative size of
the sample required would indicate efficiency.
Symbolically;
nu
EA = × 100
nA
Where, EA = the efficiency of sampling design A, based
on relative sample size and expressed as a percentage.

nA = the size of the sample, using the unrestricted single-
stage sampling design,
nu = the size of the sample, using the unrestricted single-
stage sampling design.
It may be noted that when a comparison is made of
standard errors of the mean of different sample designs
regarding the same rupee expenditure, it will indicate
relative economic efficiency. In other words, economic
efficiency is measured in terms of the precision of results
per rupee of cost. Marketing researchers are generally
concerned with economic efficiency of sample designs
and aim at obtaining maximum efficiency of this type.

Population Size and Sample Size
We have discussed earlier in detail how to determine
sample size. An important point worth noting is that in all
our calculations, the size of the population has not entered
into the calculation of the size of sample. This is indeed
very surprising but it is really so. We may slightly modify
this statement and say that the population size has no direct
effect on the sample size. The point to note is that
variability of the population characteristics is important and
not the size of the population. The greater the variability of
a given characteristics in the population, greater would be
the sample size with some specified level of precision.

In other words, it can be said that population size does not
directly affect the sample size but only indirectly through its
impact on variability. When the population size is large, it is
quite possible that its variability too is high. Likewise, smaller
the population size, the variability is likely to be lower. The
sample size can be calculated with the help of the following
formula;
n = nN / (N + n – 1)
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The data, after collection, has to be prepared for analysis. The
collected data is raw and it must be converted to the form that

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is suitable for the required analysis. The results of the
analysis are affected a lot by the form of the data. So,
proper data presentation is a must to get reliable results.
Data Preparation Process
The plan of data analysis is decided in advance before
collecting the data. Data preparation process is guided by
that plan of data analysis. Important steps of data
preparation process are as follows:
(i) Questionnaire checking.
(ii) Editing
(iii) Coding

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(iv) Classification
(v) Tabulation
(vi) Graphical representation
(vii) Data cleaning
(viii) Data adjusting
Lets describe each of the above processes.
1. Questionnaire Checking: When the data is collected
through questionnaires, the first step of data preparation
process is to check the questionnaires if they are
acceptable or not. This involves the examination of all
questionnaires for their completeness and interviewing

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quality. Usually this step is undertaken at the time of data
collection. If questionnaires checking was not done at the
time of collection, it should be done latter. A
questionnaire may not be acceptable if:
(i) It is incomplete partially or fully.
(ii) It is answered by a person who has inadequate
knowledge or does not qualify for the participation.
(iii) It is answered in such a way which gives the impression
that the respondent could not understand the questions.
If sufficient number of questionnaires are not accepted
the researcher may like to collect more data.

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2. Editing: Editing of the data is a process of examining the
collected raw data to detect errors and omissions and to
correct these when possible. As a matter of fact, editing
involves a careful scrutiny of the completed questionnaires
and/or schedules. Editing is done to assure that the data are
accurate, consistent with other facts gathered, uniformly
entered, as completed as possible and have been well arranged
to facilitate coding and tabulation.
With regard to points or stages at which editing should be
done, one can talk of field editing and central editing. Field
editing consists in the review of the reporting forms by the

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investigator for completing what the latter has written in
abbreviated and/or in illegible form at the time of
recording the respondents’ responses. This type of editing
is necessary in view of the fact that individual writing
styles often can be difficult for others to decipher. This
sort of editing should be done as soon as possible after the
interview, preferably on the very day or on the next day.
While doing field editing, the investigator must restrain
himself and must not correct errors of omission by simply
guessing what the informant would have said if the
question had been asked.

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Central editing should take place when all forms or
schedules have been completed and returned to the office.
This type of editing implies that all forms should get a
through editing by a single editor in a small study and by a
team of editors in case of a large inquiry. Editor(s) may
correct the obvious errors such as an entry in the wrong
place, entry recorded in months when it should have been
recorded in weeks, and the like. In case of inappropriate
on missing replies, the editor can sometimes determine the
proper answer by reviewing the other information in the
schedule. At times, the respondent can be contacted for
clarification. The editor must strike out the answer if the

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same is inappropriate and he has ‘no answer’ is called for.
All the wrong replies, which are quite obvious, must be
dropped from the final results, especially in the context of
mail surveys.
Editors must keep in view several points while performing
their work;
(a) They should be familiar with instructions given to the
interviewers and coders as well as with the editing
instructions supplied to them for the purpose.
(b) While crossing out an original entry for one reason or
another, they should just draw a single line on it so that
the same may remain legible.

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(c) They must make entries on the form in some distinctive
colour and that too in a standardized form.
(d) Editor’s initials and the date of editing should be placed
on each completed form or schedule.
3. Coding: Coding refers to the process of assigning
numeral or other symbols to answer so that responses can
be put into a limited number of categories or classes. Such
classes should be appropriate to the research problem
under consideration. They must also posses the
characteristics of exhaustiveness and also that of mutual
exclusively which means that a specific answer can be
placed in one and only one cell in a given category set.

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Another rule to be observed is that of unidimensionality by
which is meant that every class is defined in terms of only
one concept.
Coding is necessary for efficient analysis and through it
the several replies may be reduced to a small number of
classes which contain the critical information required for
analysis. Coding decisions should usually be taken at the
designing stage of the questionnaire. This makes it
possible to precode the questionnaire choices and which in
turn is helpful for computer tabulation as one can straight
forward key punch from the original questionnaires. But in
case of hand coding some standard method may be used.

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One such standard method is to code in the margin with a
coloured pencil. The other method can be to transcribe the
data from the questionnaire to a coding sheet. Whatever
method is adopted, one should see that coding errors are
also eliminated or reduced to the minimum level.
4. Classification: Most research studies result in a large
volume of raw data which must be reduced into
homogeneous groups if we are to get meaningful
relationships. This fact necessitates classification of data
which happens to be the process of arranging data in
groups or classes on the basis of common characteristics.

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Data having a common characteristics are placed in one class
and in this way the entire data get divided into a number of
groups or classes. Classification can be one of the following
two types, depending upon the nature of the phenomenon
involved;
(a) Classification According to Attributes: As stated above,
data are classified on the basis of common characteristics
which can be either be descriptive such as; literacy, gender,
honesty, etc. or numerical such as weight, height, income, etc.
Descriptive characteristics refer to qualitative phenomenon
which cannot be measured quantitatively; only their presence
or absence in an individual item can be noticed. Data obtained
this way on the basis of certain attributes are known as

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statistics of attributes and their classification is said to be
classification according to attributes.
Such classification can be simple classification or manifold
classification. In simple classification we consider only one
attribute and divide the universe into two classes – one class
consisting of items possessing the given attribute and the
other class consisting of which do not possess the given
attribute. But in manifold classification we consider two or
more attributes simultaneously, and divide that data into a
number classes ( Total No. of classes of final order is given by
2n , where n = number of attribute considered). Whenever data
are classified according to attributes, the researcher must see

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that the attributes are defined in such a manner that there
is least possibility of any doubt/ambiguity concerning the
said attributes.
(b) Classification According to Class-intervals: Unlike
descriptive characteristics, the numerical characteristics
refer to quantitative phenomenon which can be measured
through some statistical units. Data relating to income,
production, age, weight, etc. come under this category.
Such data are known as statistics of variables and are
classified on the basis of class intervals. For instance,
person whose incomes, say, are within Rs. 201 to Rs. 400
can form one group, those whose incomes are within Rs.

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401 to Rs. 600 can form another group and so on. In this way
the entire data may be divided into a number of groups or
classes or what are usually called, ‘class intervals.’ Each
group of class-interval, thus, has an upper limit as well as a
lower limit which are known as class limits. The difference
between the two class limits is known as class magnitude.
Classification according to class intervals usually involves the
following three main problems;
(i) How many classes should be there? What should be their
magnitudes?
There can be no specific answer with regard to the number of

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classes. The decision about this call for skill and experience of
the researcher. However, the objective should be to display
the data in such a way as to make it meaningful for the
analyst. Typically, we may 5 to 15 classes. With regard to
second part of the question, we can say that, to the extent
possible, class-interval should be of equal magnitudes, but in
some cases unequal magnitudes may result in better
classification. Hence the researcher’s objective judgment play
an important part in this connection. Multiples of 2, 5 and 10
are generally preferred while determining class magnitudes.
Some statisticians adopt the following formula, suggested by
H.A. Sturges, determining the size of class interval:

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i = R/(1 + 3.3. Log N)
Where,
i = size of class interval;
R = Range i.e. difference between the values of the largest
item and smallest item among the given item.
N = Number of items to be grouped.
It should also be kept in mind that in case one or two or very
few items have very high or very low values, one may use
what are known as open-ended intervals in the overall
frequency distribution. Such intervals may be expressed like
under Rs. 500 or Rs. 10001 and over. Such intervals are
generally not desirable, but often cannot be avoided. The

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researcher must always remain conscious of this fact
while deciding the issue of the total number of class
intervals in which the data are to be classified.
(ii) How to choose class limits?
While choosing class limits, the researcher must take into
consideration the criterion that the mid-point of a class-
interval and the actual average of items of that class-
interval should remain as close to each other as possible.
Consistent with this, the class limits should be located at
multiples of 2, 5, 10, 20, 100 and such other figures. Class
limit may generally be stated in any of the following
forms:

Data Processing
Exclusive type class intervals: They are usually stated as
follows:
10 - 20
20 - 30
30 - 40
40 - 50
The above interval should be read as under;
10 and under 20.
20 and under 30
30 and under 40
40 and under 50

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Thus, under the exclusive type class intervals, the items whose
values are equal to the upper limit of a class are grouped in the
next higher class.
Inclusive type class intervals: They are usually stated as
follows:
11 - 20
21 - 30
31 - 40
41 - 50
In inclusive type class intervals the upper limit of a class
interval is also included in the concerning class interval. Thus,

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an item whose value is 20 will be put in 11 – 20 class
interval. The stated upper limit of the class interval 11 –
20 is 20 but the real limit is 20.99999 and as such 11 – 20
class interval really means 11 and under 21.
When the phenomenon under consideration happens to be
discrete one, then we should adopt inclusive type
classification. But when the phenomenon happens to be a
continuous one capable of being measured in fractions as
well, we can use exclusive type class intervals.
(iii) How to determine the frequency of each class?

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This can be done either by tally sheets or by mechanical
aids. Under the technique of tally sheet, the class groups
are written on a sheet of paper (commonly known as the
tally sheet) and for each item a stroke (usually a small
vertical line) is marked against the class group in which it
falls. The general practice is that after every four small
vertical lines in a class group, the fifth line for the item
falling in the same group, is indicated as horizontal line
through the said four lines and the resulting flower (IIII)
represent five items. All this facilitates the counting of
items in each one of the class groups.

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5. Tabulation: When a mass of data has been assembled, it
becomes necessary for the researcher to arrange the same in
some kind of concise and logical order. This procedure is
referred to as tabulation. Thus, tabulation is the process of
summarizing raw data and displaying the same in compact
form i.e. in the form of statistical tables for further analysis. In
a broader sense, tabulation is an orderly arrangement of data
in columns and rows.
Tabulation is essential because of the following reasons.
(i) It conserves space and reduces explanatory and descriptive
statement to a minimum.
(ii) It facilitates the process of comparison.

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(iii) It facilitates the summation of items and the detection of
errors and omissions.
(iv) It provides a basis for various statistical computations.
Tabulation can be done by hand or by mechanical or
electronic devices. The choice depends on the size and
type of study, cost considerations, time pressures and the
availability of tabulating machines or computers.
Tabulation may also be classified as simple and complex
tabulation. The former type of tabulation gives
information about one or more groups of independent
questions, whereas the latter type of tabulation shows the
division of data in two or more categories and as such is

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designed to give information concerning one or more sets of
inter-related questions. Simple tabulation generally results in
one-way tables which supply answers to questions about one
characteristics of data only. As against this, complex
tabulation usually results in two-way tables, three-way tables
or still higher order tables, also known as manifold tables,
three-way tables or manifold tables are all examples of what is
sometimes described as cross tabulation.
1. Every table should have a clear, concise and adequate title so
as to make the table intelligible.
2. Every table should be given a distinct number to facilitate
easy reference.

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3. The column headings (captions) and the row headings
(stubs) of the table should be clear and brief.
4. The units of measurement under each heading or sub-
heading must always be indicated.
5. Explanatory footnotes, if any, concerning the table should
be placed directly beneath the table, along with the
reference symbols used in the table.
6. Source or sources from where the data in the table have
been obtained must be indicated just below the table.
7. Usually the columns are separated from one another by
lines which make the table more readable and attractive.

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8. There should be thick lines to separate the data under one class
from the data under another class and the lines separating the
sub-divisions of the classes should be comparatively thin
lines.
9. The column may be numbered to facilitate reference.
10. Those column whose data are compared should be kept side
by side.
11. It is generally considered better to approximate figures
before tabulation as the same would reduce unnecessary
details in the table itself.
12. It is important that all column figures be properly aligned.

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13. Abbreviation should be avoided to the extend possible.
14. Miscellaneous and exceptional items, if any, should be
usually placed in the last row of the table.
15. Table should be make a logical, clear, accurate and
simple as possible.
16. Total of rows should normally be placed in the extreme
right column and that of columns should be placed at the
bottom.
17. The arrangement of the categories in a table may be
chronological, geographical, alphabetical or according to
magnitude to facilitate comparison.

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6. Graphical Representation: Graphs help to understand the
data easily. All statistical packages, MS Excel, and
OpenOffice.org offer a wide range of graphs. In case of
qualitative data or categorized data, most common graphs are
bar charts and pie charts.
Bar Chart: A bar chart consists of a series of rectangles or
bars. The height of each rectangle is determined by the
frequency of that category.
Pie Chart: A pie chart is used to emphasize relative
proportion or share of each category. It’s a circular chart
divided into sectors, illustrating relative frequencies. The
relative frequency in each category or sector is proportional to
the arc length of that sector or the area of that sector or the

Data Processing
central angle of that sector.
In case of quantitative data, one important chart is histogram
which is a generalization of bar chart. The data is first
summarized in terms of class intervals and each bar represents
a class interval. The width of the bar is proportional to the
width of corresponding class interval. The area of the bar is
proportional to the frequency of corresponding class interval.
After making the class intervals in a quantitative data set, a
pie chart can also be used to read the share of each class
interval.
7. Data Cleaning: This includes checking the data for
consistency and treatment for missing value. Preliminary

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consistency checks are made in editing. Here we check the
consistency in an extensive manner.
Consistency checks look for the data which are not
consistent or outlines. Such data may either be discarded
or replaced by the mean value. However, the researcher
should be careful while doing this. Extreme values or
outlines are not always erroneous.
Missing values are the values which are unknown or not
answered by the respondent. In place of such missing
values, some neutral value may be used. This neutral
value may be the mean of available values. The other
option could be to use the pattern of responses to other

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questions to calculate a suitable substitute to the missing
values.
8. Data Adjusting: Data adjusting is always necessary but it
may improve the quality of analysis sometimes. This
consists of following methods.
(i) Weight-assigning: Each respondent or case is assigned
a weight to reflect its importance relative to other
respondents or cases.
Using this method, the collected sample can be made a
stronger representative of a target population on specific
characteristics. For example, the cases of educated
people could be assigned lower weights in some survey.

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The value 1.0 means unweightage case.
(ii) Variable Respecification: This involves creating new
variables or modifying existing variables. For example, if the
usefulness of a certain product is measured on 10 point scale,
it may be reduced on a 4 point scale – ‘very useful’, ‘useful’,
‘neutral’, ‘not useful’. Ratio of two variables may also be
taken to create a new variable.
Method of dummy variables for respecifying categorical
variables is also very popular. Dummy variable is a variable
which usually takes numerical values based on the
corresponding category in the original variable. For example,
a group of people is divided into smokers and non-smokers.

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We can define a dummy variable taking the value ‘1’ for
smokers and ‘0’ for non-smokers.
(iii) Scale Transformation: Scale transformation done to ensure
the comparability with other scales or to make the data
suitable for analysis. Different type of characteristics are
measured on different scales. For example, attitude variables
are measured on continuous scale, life style variables are
usually measured on a 5 point Likert scale. So the variables
which are measured on different scales, cannot be compared.
A common transformation is subtracting all the values of a
characteristics by corresponding mean and dividing by
corresponding standard deviation.

Data Processing
Some Problems in Preparation Process
We can take up the following two problems of processing the
data for analytical purposes;
(a) The Problem Concerning ‘Don’t Know’ or DK
Responses: While processing the data, the researcher often
comes across some responses that are difficult to handle. One
category of such responses may be ‘Don’t Know’ Response’
or simply DK response. When the DK response group is
small, it is of little significance. But when it is relatively big,
it becomes a matter of major concern in which case the
question arises; Is the question which elicited DK response
useless? The answer depends on two points viz., the
respondent actually may not know the answer or the
researcher may fail in obtaining the appropriate information.

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In the first case the concerned question is said to be alright and
DK response is taken as legitimate DK response. But in the
second case, DK response is more likely to be a failure of the
questioning process.
How DK responses are to be dealt with by researchers? The
best way is to design better type of questions. Good rapport of
interviewers with respondents will result in minimizing DK
responses. But what about the DK responses that have already
taken place? One way to tackle this issue is to estimate the
allocation of DK answers from other data in the questionnaire.
The other way is to keep DK responses as a separate category
in tabulation where we can consider it as a separate reply

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category if DK responses happen to be legitimate, otherwise
we should let the reader make his own decision. Yet another
way is to assume that DK responses occur more or less
randomly and as such we may distribute them among the
other answers in the ratio in which the latter have occurred.
Similar results will be achieved if all DK replies are excluded
from tabulation and that too without inflating the actual
number of other responses.
(b) Use of Percentages: Percentages are often used in data
presentation for they simplify numbers, reducing all of them
to a ‘0’ to ‘100’ range. Through the use of percentages, the
data are reduced in the standard form with base equal to 100

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which fact facilitates relative comparisons. While using
percentages, the following rules should be kept in view by
researchers:
1. Two or more percentages must not be averaged unless each
is weighted by the group size from which it has been
derived.
2. Use of too large percentages should be avoided, since a large
percentage is difficult to understand and tends to confuse,
defeating the very purpose for which percentages are used.
3. Percentages hide the base from which they have been
computed. If this is not kept in view, the real differences
may not be correctly read.

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4. Percentage decreases can never exceed 100 percent and as
such for calculating the percentage of decrease, the higher
figure should invariably be taken as the base.
5. Percentages should generally be worked out in the direction of
the causal-factor in case of two-dimension tables and for this
purpose we must select the more significant factor out of the
two given factors as the causal factor.
Missing Value and Outliers
Missing values are the observations which the researcher plan
to collect but could not collect or lost due to some reason.
Many statistical tools cannot be employed when the data set
has one or more missing values. In data collection through

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asking questions ‘Don’t Know’ response may also creep
the problem of missing values. Utmost care should be
taken by the researcher to avoid the missing values in the
data set. Most common methods to deal with the problem
of missing value while conducting the analysis is either to
leave the observation, if possible, or to replace the missing
value by the arithmetic mean of other collected
observation.
Outliers are the observations which are quite different to
other observations in the data set. Although all the
statistical techniques can be employed when the data set
has outliers, their interpretations may be misleading. The

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most common reason of outliers being present in the data
set is the recording error. This error should be corrected
while editing and cleaning the data. Consider an example
of survey of 100 customers in a mall.
If few bulk customers purchasing very large amount are
among the 100 surveyed customers. In this survey having
outlier may not be posing any error as bulk customers are
always there in the mall along with small customers.
However, in a similar survey at a nearby grocery shop on
a day when there is strike in the mall may include some
bulk customers which could be misleading. Thus outliers

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should not be ignored as they might have some relevant
information or pose to a serious risk.
Before detecting the outliers, we need to define them first.
Commonly, an observation with a value that is more than
3 standard deviations from the mean is considered as an
outlier. A scatter plot can also be helpful in identifying the
outliers. After identifying an outlier, the researcher has to
decide what to do with it. The researcher may like to
delete it or modify the value of it or retain it as it is. It
depends on the knowledge about the cause of that outlier.

Data Processing
Types of Analysis
As stated earlier, by analysis we mean that computation of
certain indices or measures along with searching for
patterns of relationship that exist among the data groups.
Analysis, particularly in case of survey of experimental
data, involves estimating the values of unknown
parameters of the population and testing of hypotheses for
drawing inferences. Analysis may, therefore, be
categorized as descriptive analysis is largely the study of
the distributions of one or more variables involved in the
study. In this context we work out various measures that
show the size and shape of a distribution(s)along with the

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study of measuring relationships between two or more
variables.
We may as well talk of correlation analysis and causal
analysis. Correlation analysis studies the joint variation of
two or more variables for determining the amount of
correlation between two or more variables. Casual analysis is
concerned with the study of how one or more variables affect
changes in another variable. It is thus a study of functional
relationship existing between two or more variables. This
analysis can be termed as regression analysis. Casual analysis
is concerned relatively more important in experimental
researches, whereas in most social and business researches our

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interest lies in understanding and controlling relationship
between variables then with determining cause per se and as
such we consider correlation analysis as relatively more
important.
In modern times, with the availability of computer facilities,
there has been a rapid development of multivariate analysis.
Usually the following analyses are involved when we make a
reference of multivariate analysis:
(a) Multiple regression Analysis: This analysis is adopted when
the researcher has one dependent variable which is presumed
to be a function of two or more independent variables. The

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objective of this analysis is to make a prediction about the
dependent variable based on its covariance with all the
concerned independent variables.
(b) Multiple Discriminate Analysis: This analysis is
appropriate when the researcher has a single dependent
variable that cannot be measured, but can be classified into
two or more groups on the basis of some attribute. The object
of this analysis happens to be to predict an entity’s possibility
of belonging to a particular group based on several predictor
variables.
(c) Multivariate Analysis of Variance (Multi-ANOVA): This

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analysis is an extension of two-way ANOVA, wherein the
ration of among group variance to within group variance is
worked out on set of variance.
(d) Canonical Analysis: This analysis can be used in case of
both measurable and non-measurable variables from their
joint covariance with a set of independent variables.
Inferential analysis is concerned with the various tests of
significance for testing hypothesis in order to determine with
what validity data can be said to indicate some conclusion or
conclusions. It is also concerned with the estimation of
population values. It is mainly on the basis of inferential
analysis that the task of interpretation is performed.

Data Processing
Thank You!

Marketing Research PPT - III

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