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SAMPLING METHODS
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Why Sampling
The basis logic behind sampling is that, in mostcases, the underlying patterns in a population
become clear after a certain section or sub-
group has been examined, thus making a
complete census unnecessary.
In simple, this is the basic idea behind
sampling- by studying a sub-group of a
population, the characteristics of the populationcan be ascertained.
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The benefits derived from
sampling
Reduced costs
Reduced time
Greater accuracy
Greater flexibility of scope
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Sampling Frame
Population
Sampling Frame
Sampling Unit
Sampling Element
Sampling Method
Sample Size
Sampling Plan
Sample
Selection
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Population
This is not the entire population of a givengeographical area, but the pre-defined set ofpotential respondents (elements) in ageographical area.
For example, a population may be defined as allmothers who buy branded baby food in a givenarea
or "all teenagers who watch MTV in the country"or
all adult males who have heard about or use the
AQUAFRESH brand oftoothpaste orall MBA students for the Research Methodolo
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Primary Group of Population MBA students
and statistics students
Secondary Group of Population or Alternative
population Undergraduate managementstudents, libraries of business schools and
statistics, teacher who teach this subject
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Sampling Frame
This is a subset of the defined target
population, from which we can realistically
select a sample for our research.
Census list, Telephonic directories, lists of
subscribers to magazines, members of an
association (example HRD
Association/AIMA) and database ofcustomers maintained by various
corporations are all examples of sampling
frame.
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Sampling Element
In the preceding study on refrigerators,
assuming that the household is identified as
the sampling unit, who should be interviewed
the housewife, the head of the household, orthe entire family?
The number of people in a household is
determined, and a random number is chosen
to selected a particular person as a
respondent.
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The Sample Size Calculation
It is not a formula alone that determines sample size in actual
marketing research. Sampling in practice is based on science,
but is also an art.
The basic assumptions made while computing sample sizes
through the use of formulae are sometimes not met in practice.
At other times, there are other factors which are influential in
increasing or decreasing sample sizes obtained through theuse of formulae.
In simple sense one percent of the population considered for
research is the sample size
For now, remember that sample size is decided based on
use of formulae,
experience of similar studies,
time and budget constraints,
output or analysis requirements,
number of segments of the target population,
number of centres where the study is conducted, etc.
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There are two formulas depending on variable type, used for computing
sample size for a study. The first is used when the critical variable studied
is an interval-scaled one.
We will study only this formula
Formula for Sample Size Calculation when Estimating Means
(for Continuous or Interval Scaled Variables)
The formula for computing n, the sample size required to do the study, is
Z s
n = ----------
e
Let us examine one by one what the quantities Z,s, and e represent.
2
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Z :The Z value represents the Z score from the standard
normal distribution for the confidence level desired by theresearcher. For example, a 95 percent confidence level
would indicate (from a standard normal distribution for a 2-
sided probability value of 0.95) a z score of 1.96. Similarly, if
the researcher desires a 90 percent confidence level, the
corresponding z score would be 1.645 (again, from the
standard normal distribution, for a 2 sided probability of
0.90).
Generally, 90 or 95 percent confidence is adequate for most
marketing research studies. A 100 percent confidence level
is not practical, as it means we have to take a census of theentire population, instead of using a sample.
We will use z = 1.96, equivalent to a 95 percent confidence
level, in our example.
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s : The s represents the population standard deviation for the variable whichwe are trying to measure from the study. By definition, this is an unknownquantity, since we have not taken a sample yet. So, the question of knowing thevalue ofs, the sample standard deviation, does not arise.
However, we can use a rough estimate of the sample standard deviation for thevariable being measured. This estimate can be obtained in the following ways
If past studies have measured this variable, we can use the standard deviationof the variable from one of the studies from the recent past. It serves as a goodapproximation.
A very small sample can be taken as a test or pilot sample, only for the purposeof roughly estimating the sample standard deviation of the concerned variable.
If the minimum and maximum values of the variable can be estimated, then therange of the variables values is known. Range = Maximum value Minimumvalue. Assuming that in practically all variables, 99.7 percent of the values of the
variables would lie within + 3 standard deviations of the mean, we could get anapproximate value of the standard deviation by dividing the range by 6.
The logic of this is that Range is equal to 6 standard deviations for most variables.Therefore, Range, when divided by 6, should give a fairly good estimate of thestandard deviation.
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e : The third value required for calculating the sample size required for the
study is e, called tolerable error in estimating the variable in question. This can be
decided only by the researcher or his sponsor for the study. The lower the
tolerance, the higher will be the sample size. The higher the tolerable error, the
smaller will be the sample size required.
Now, let us take an example of the use of the above formula, to see how it works.
Let us assume we are doing a customer satisfaction study for a washing machine.
We are measuring satisfaction on a scale of 1 to 10. 1 represents "Not at all
satisfied", and 10 represents "Completely Satisfied". The scale would look like thison a questionnaire
Customer Satisfaction Scale
We will assume that the questionnaire consists only of 7-8 questions, all of them
using this 10-point scale. Therefore, the variable we are trying to measure or
estimate through the survey, is Customer Satisfaction, which is being measured on
a 10 point interval scale.
1 2 3 4 5 6 7 8 9 10
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We will apply the formula discussed for sample size calculation, and check
for its usefulness.
Zs is the formula, for variables which arecontinuous, or scaled.
Z Let us assume we want a 95 percent confidence level in our
estimate of customer satisfaction level from the study. Then, from the
standard normal distribution tables, (for a 2-sided probability value of 0.95),
the Z value is 1.96.
s Let us assume that such a customer satisfaction study was not
conducted in the past by us. We have no idea of the standard deviation
of the variable Customer Satisfaction. We can then use the rough
approximation of Range divided by 6 to estimate the sample standard
deviation.
In this case, the lowest value of customer satisfaction is 1, and the
highest value is 10. Thus, the Range of values for this variable is 101 =
9. Therefore, the estimated sample standard deviation becomes 9/6 =
1.5. We will use this value of 1.5, as s in our formula.
e
2
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e The tolerable error is expressed in the sameunits as the variable being measured or estimated by
the study. Thus, we have to decide how much error (on
a scale of 1 to 10) we can tolerate in the estimate of
average customer satisfaction. Let us say, we put the
value at + 0.5. That means we are putting the value ofe as 0.5. This means, we would like our estimate of
customer satisfaction to be within 0.5 of the actual
value, with a confidence level of 95 percent (decided
earlier while setting the z value).
contd.
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Slide 10
ow, we have all 3 values required for calculating
n, the sample size. So let us calculate n.
n = Z s 2
1.96 x 1.5 2e 0.5
= (1.96 x 3)2
= 34.57 or 35 (approximately)
Therefore, a sample size of 35 would give us an
estimate of customer satisfaction measured on a 110point scale, with 95 percent confidence level, an
error level maintained within + 0.5 of the actual
alue.
If we were to tighten our tolerance level of error (e)
to + 0.25 instead of + 0.5, we would have to take a
sample of higher size.
n would then be equal to
1.96 x 1.52
= ( 1.96 x 6 ) 2 = 138.3
0.25
= 138 (approximately)
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Sampling Method
Probability
Random
Stratified
Snowball
Judgmental
Quota
Convenience
Non-probability
Cluster
Systematic
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Probability
If we wish to use simple
random sampling we could
make a list of all the
population say 100employees. Then, an
identification number could be
allotted to each employee.
We could then write these
100 numbers on small piecesof paper, one number on
each. Shuffling these folded
pieces of paper, we can draw
5 pieces out of the 100, and
use these employees as oursample.
1.Random
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2.Stratified coati
This is a special case of
simple random sampling.
In this case, the totalpopulation is divided into
strata that are internally
homogeneous with
respect to thecharacteristic being
studied and as distinct as
possible from the other
strata. This could be
based on age or area
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2.Stratified
For example India has four different regions
can be selected as north, south, east and west
in the state.
Select randomly the sample.
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Probability
Systematic sampling is very
similar to Simple Random
Sampling, and easier to practice.Just as we do in a simple
random sample, we start with a
list of all sampling units or
respondents in the population.
We first compute the sample size
required, based on a formula andselect the required sample.
3.Systematic
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Systematic Sampling
Once the sample size (n) is decided, we divide
the total population into (N n) parts, where n
is the sample size required. From the first part
of sampling units, we pick one at random.Thereafter, we pick every (N n) th item from the
remaining parts.
To illustrate, say we have a population of 600
students, for some research. We need asample of 15 out of these.
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Systematic Sampling
We divide the list into 300/15 = 20 parts. Out of
the first 20 students, we choose any one at
random. Let us say, we choose student number
7 (all students are listed). Thereafter, wechoose student numbers 7+20, 7+20+20,
7+20+20+20 and so on in a systematic
sampling plan. Therefore, the selected students
will be numbers 7, 27, 47, 87, 107, 127, 147,167, 187, 207, 227, 247, 267, and 287 All
these 15 students will comprise our total sample
for the study.
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Cluster
A list of all available clusters should be
prepared
All clusters should be numbered
A sample of clusters (number to be decided byresearcher) should be randomly drawn.
All sampling units/elements such as
households in the selected clusters should bechosen to be a part of the sample.
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Probability
A cluster is a group of
sampling units or elements,
which can be identified, listedand a sample of which can be
chosen. Theoretically, a
cluster could be on the basis
of any criterion. But in
practice, clusters tend to befound either in terms of
geographical areas, or
membership of some groups
such as a church, a club, or a
social organization.
4. ClusterExample testing the fill of bottles
It is time consuming to pull
individual bottles. It is expensive
to waste an entire cartons of 12bottles to just test one bottle. If we
would like to test 240 bottles, we
could randomly select 20 cartons,
test all 12 bottles within each
carton. This reduces the time and
expense required.
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Cluster
Let us assume that a study is to be conducted in the city of Mumbai to
determine the perception of second-year students about job opportunities in
the field of International jobs.
Second year marketing students may be approached in all the 25 odd
business schools in the city. But this is time consuming so, each of the
classes of the second-year students in the various business schools maybe treated as a stratum. (Instead Number each business school or group
them according to areas)
From the numbered B-Schools select according to the required sample size
or
From the area cluster select from each area cluster the required samplesize
N P b bilit S li
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Non-Probability Sampling
Techniques
In reality, because of various difficulties involved in
obtaining reliable lists of the desired target population, it
is difficult to use a textbook probability sampling
prescription. Therefore, some compromises could be
made, or approximately probability-type of samplingprocedures may be used. Some of the non-probabilistic
techniques may also be used explicitly in cases where it
is not feasible to use probability based methods.
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Non-probability
Also referred to as availability
sampling, convenience sampling
is a method by which therespondents are selected on the
basis of the interviewers
convenience or on the basis of
availability.
For example students could be
used as a sample by a marketingresearcher who lives in a college
town. They (the students) need
not be representative of the
target population for the study,
for the product being researched.
Other examples of
convenience sampling
includes on-the-streetinterviews, or any other
meetings, or from employees
of one office block or factory.
Another common example of
convenience sampling is theone by TV reporters who
catch any person passing by
and interview him on the
street.
1. Convenience 1. Convenience
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2. Quota
This method, quota sampling, is very similar to stratified randomsampling. The first step of deciding on the strata, or segmentswhich the population is divided into, is actually the same.
The second step, of calculating a total sample size, and allocating it
to the various strata, is also the same. The major difference is that,random selection of respondents is not strictly adhered to. Moreliberty is given to the field worker to select enough respondents tocomplete the segment wise quota.
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Quota
In practice, unless there are untrained field workers, orthe field supervision is lax, the results produced by aquota sample could be very similar to the one producedby a stratified random sample. But there is no
guarantee that it would be similar. In practice, many researchers use quota sampling,
because it saves time, compared with stratified randomsampling. For example, if a household is locked, aquota sample would permit the field worker to use a
substitute household in the same apartment block. Butwith a stratified random sample, he would be expectedto make a second or third attempt at different times ofthe day to contact the same locked household. Thiswould increase the time taken to complete the required
quota.
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Non-probability
This is another variant of
convenience sampling, where
the units are selected on thebasis of the interviewers
judgement to ensure a better
quality of response.
For example, the interviewees
may be experts in a field.
This technique is used when
the population being sought is
a small one, and chances offinding them by traditional
means are low. For example,
to find owners of Mercedes
Benz cars in a city, we may
go to one or two, and askthem if they know anyone
else who owns one. They in
turn are asked for more
names of owners.
3. Judgemental 4. Snowball
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Types of Errors in Marketing Research
Any research study has an error margin associated with it. No method is
foolproof, as we will see, including a census. This is because there are two
major types of errors associated with a research study. These are called
Sampling Error or Random Error
Non-sampling or Human Error
Sampling ErrorThis is the error which occurs due to the selection of some units and non-
selection of other units into the sample. It is controllable if the selection of
sample is done in a random, unbiased way. In other words, if a probability
sampling technique is used, it is possible to control this error. In general,
this error reduces as sample size increases.
contd
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Non-sampling ErrorThis is the effect of various errors in doing the study, by the interviewer,
data entry operator or the researcher himself. Handling a large quantity of
data is not an easy job, and errors may creep in at any stage of the
researcher. The data entry person may interchange the column of yes
and no responses while entering or compiling data, or the interviewer may
cheat by not filling up the questionnaire in the field, and instead, fudge the
data. Or, the respondent may say one thing, but another may be recorded
by mistake. These errors are usually proportionate to the sample size.
That is, the larger the sample size, the larger the non-sampling error. Also,
it is difficult to estimate the size of non-sampling error. But we can use
some controls on the quality of manpower, and supervise effectively tominimize it.
contd...
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Total Error
1. This is the total of sampling error + non-sampling error.
2. Out of this, the sampling error can be estimated in the case ofprobability samples, but not in the case of non-probability samples.
3. Non-sampling errors can be controlled through hiring better field
workers, qualified data entry persons, and good control procedures
throughout the project.
4. One important outcome of this discussion of errors is that the total
error is usually unknown. But, we may have to live with higher non-
sampling error in our attempt to reduce sampling error by increasing
the sample size of the study, not to mention the higher cost of a largersample.
5. Therefore, it is worthwhile to optimise total error by optimising the
sample size, rather than going blindly for the largest possible sample
size.