Sampling Methods 6

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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.

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Sampling Methods 6