Mr Chapter 5 Sampling

7/25/2019 Mr Chapter 5 Sampling

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Welcome to Powerpoint slides

forChapter 5

Sampling Methods:

Theory and Practice

Marketing Research

Text and Cases

byRajendra Nargundkar

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Basic Terminology in Sampling

Sampling lement: This is the unit about whichinformation is sought by the marketing researcher for

further analysis and action.

The most common sampling element in marketing

research is a human respondent who could be a

consumer, a potential consumer, a dealer or a person

exposed to an adertisement, etc.

!ut some other possible elements for a study could be

companies, families or households, retail stores and so

on. "


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Pop!lation: This is not the entire population

of a gien geographical area, but the pre#

defined set of potential respondents

$elements% in a geographical area.

&or example, a population may be defined as'all mothers who buy branded baby food in a

gien area' or 'all teenagers who watch

(T) in the country' or ' all adult males who

hae heard about or use the *+*&R-/brand of toothpaste' or similar definitions in

line with the study being done.

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Sampling "rame

This is a subset of the defined target population,

from which we can realistically select a sample

for our research.

&or example, we may use a telephone directory

of (umbai as a sampling frame to represent the

target population defined as 'the adult residents

of (umbai'.


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2biously, there would be a number of elements$people% who fit our population definition, but do

not figure in the telephone directory. imilarly,

some who hae moed out of (umbai recently

would still be listed.

Thus, a sampling frame is usually a practical

listing of the population, or a definition of theelements or areas which can be used for the

sampling exercise.

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Sampling #nit

4f indiidual respondents form the sample elements,

and if we directly select some indiiduals in a single

step, the sampling !nitis also the element. That is,

both the unit and the element are the same.

!ut in most marketing research, there is a multi#

stage selection.

&or example, we may first select areas or blocks in a

city or town. These form the first stage ampling

nits.

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Then, we may select specific streets within

a block or area, and these are called secondstage sampling units.

Then we may select apartments or houses #

the third stage sampling units.

*t the last stage, we reach the indiidual

sampling element # the respondent wewanted to meet.

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The Sample Si$e Calc!lation

4t is not a formula alone that determines sample

si7e in actual marketing research. ampling in

practice is based on science, but is also an art.

The basic assumptions made while computing

sample si7es through the use of formulae are

sometimes not met in practice. *t other times,

there are other factors which are influential in

increasing or decreasing sample si7es obtained

through the use of formulae.

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&or now, remember that sample si7e isdecided based on

!se of form!lae%

experience of similar st!dies% time and &!dget constraints%

o!tp!t or analysis re'!irements%

n!m&er of segments of the target

pop!lation%n!m&er of centres where the st!dy is

cond!cted% etc(

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There are two formulas depending on ariable type,

used for computing sample si7e for a study. Thefirst is used when the critical ariable studied is an

interal#scaled one.

"orm!la for Sample Si$e Calc!lation when

stimating Means)for Contin!o!s or *nter+al Scaled ,aria&les-

The formula for computing n;, the sample si7e

re sn ? ##########

e

"

1@


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Aet us examine one by one what the

;, s;, and e; represent. Be

will then apply the same to an exampleto see how it works in practice.

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. :The >; alue represents the > score from the

standard normal distribution for the confidenceleel desired by the researcher. &or example, a

93 percent confidence leel would indicate

$from a standard normal distribution for a "#

sided probability alue of @.93% a 7; score of

1.95. imilarly, if the researcher desires a 9@

percent confidence leel, the corresponding 7;

score would be 1.53 $again, from the standardnormal distribution, for a "; sided probability of

@.9@%.

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Cenerally, 9@ or 93 percent confidenceis ade


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s : The s; represents the population standarddeiation for the ariable which we are trying tomeasure from the study. !y definition, this is anunknown


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4f past studies hae measured this ariable, wecan use the standard deiation of the ariable fromone of the studies from the recent past. 4t seres as agood approximation.

* ery small sample can be taken as a test or pilotsample, only for the purpose of roughly estimatingthe sample standard deiation of the concernedariable.

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4f the minimum and maximum alues of the

ariable can be estimated, then the range of theariable;s alues is known. Range ? (aximumalue = (inimum alue. *ssuming that in

practically all ariables, 99.6 percent of the aluesof the ariables would lie within D 0 standarddeiations of the mean, we could get anapproximate alue of the standard deiation bydiiding the range by 5.

The logic of this is that Range is e


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e : The third alue re


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Aet us assume we are doing a customer satisfaction

study for a washing machine. Be are measuringsatisfaction on a scale of 1 to 1@. 1 represents 'Not

at all satisfied', and 1@ represents 'Eompletely

atisfied'. The scale would look like this on a


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C!stomer Satisfaction Scale

Be will assume that the


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Be will apply the formula discussed for sample si7e

calculation, and check for its usefulness.

>s is the formula, for ariables which are

continuous, or scaled.

. Aet us assume we want a 93 percent

confidence leel in our estimate of customer

satisfaction leel from the study. Then, from the

standard normal distribution tables, $for a "#sidedprobability alue of @.93%, the > alue is 1.95.

e

"

"@


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s Aet us assume that such a customer

satisfaction study was not conducted in the

past by us. Be hae no idea of the standard

deiation of the ariable FEustomer

atisfactionG. Be can then use the rough

approximation of Range diided by 5 to

estimate the sample standard deiation.

4n this case, the lowest alue of customer

satisfaction is 1, and the highest alue is 1@.

Thus, the Range of alues for this ariable is1@=1 ? 9. Therefore, the estimated sample

standard deiation becomes 9H5 ? 1.3. Be will

use this alue of 1.3, as s; in our formula."1


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e The tolerable error is expressed in the

same units as the ariable being measured or

estimated by the study. Thus, we hae to decide

how much error $on a scale of 1 to 1@% we can

tolerate in the estimate of aerage customersatisfaction. Aet us say, we put the alue at D

@.3. That means we are putting the alue of e;

as @.3. This means, we would like our estimate

of customer satisfaction to be within @.3 of theactual alue, with a confidence leel of 93

percent $decided earlier while setting the 7;

alue%.

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Now, we hae all 0 alues re


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"


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imilarly, for any change in the estimate of s; or

the alue of >; we choose to set, the alue of n;,the sample si7e, would change.

4n general, sample si7e would increase if

Istandard deiation s; is higherIconfidence leel re


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The major things to remember in the aboe

formula are that

1>; alue is set based on the confidence leel

we desire.

"s; alue is estimated from past studiesinoling the same ariable, or from the

approximate formula of Range, if we can

estimate the range of alues for the ariable in


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"orm!la for Sample Si$e Calc!lation when

stimating Proportions

4n cases where the ariable being estimated is aproportion or a percentage, a ariation of the

formula mentioned earlier should be used.

uch ariables are typically found in


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/ere, the formula is

>

n ? p< ####e

Aet us look at the meaning of each

of the terms on the right hand side

of the formula.

"

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1p2 is the fre


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2nly after doing the study will we hae our true

estimate of p;, the proportion of users in the

population. 4t is similar to the problem

mentioned earlier $in the estimation of means

for continuous ariables% when we used an

estimate of s; before doing the actual study,only for the purpose of computing sample si7e.

. : >; is the confidence leel#related alue of

the standard normal ariable, as discussed in

the earlier section. 4t is e


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e : e; is once again, the tolerable leel of errorin estimating p; that the researcher has to decide.

4f we decide that we can tolerate only a 0 percent

error, e; has to be expressed in terms of the same

units as p;. o, a 0 percent tolerable error would

translate into e ? @.@0 because p; is a proportion,

with alues ranging from @ to 1 only.


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-xample of se of &ormula for Lromotions

Aet us plug in some numbers of see how the

formula works. *ssuming we are trying to

estimate the proportion of the population who use

our toothpaste brand *+*, let us assume thatwe want confidence leel of 93 percent in our

results $which means $Z?1.95%, and FeG is @.@0. as

discussed aboe. p, from preious studies or

from prior knowledge, is estimated as @."3 for thepurpose of sample si7e determination .

0"


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n? $@."3% [email protected]% $ "58.%

? 8@@

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/ere, like in the earlier formula, the sample si7e

is higher if

The confidence le+el is higher

The error tolerance is lower

!ut, the relationship between sample si7e and

estimated p; is somewhat different. The sample

si7e increases as p; increases from @ to @.3, butdecreases thereafter, as p; increases from @.3 to

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1. Thus, other things being e


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This also gies us an easy way out of

estimating the alue of p;, if past

information is not aailable. Be can

simply set the alue of p; to @.3, becausethat will gie us the maximum sample

si7e. This could be an oerestimated

sample si7e, but it can neer

underestimate sample si7e.

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3imitations of "orm!lae

4!m&er of Centres

(ost studies deal with multiple locations spreadacross the country. 4f the data is to be analysedseparately for each geographical segment, theoerall sample si7e obtained from the formula hasto be split into these geographical centres orsegments. 4n such cases, we may interene, and

fix a minimum sample si7e for each centre H city.

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M!ltiple !estions

Mifferent arieties and scales of ariables are used in a


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Cell Si$e in 6nalysis

ust as there are segments in geographical

terms, one may want to analyse data by othersegments, one or two segments at a time. &orexample, we may be interested in analysing thecombined effect of income and age on someariable of interest.

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There may be 3 income categories among ourrespondents, and age categories. This creates a

table with 3x, or "@ cells. Now, een thoughthe oerall sample si7e was ade


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Time and B!dget Constraints

(any a time, a study has to be done


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The Role of xperience in 7eterminationof Sample Si$e

Cien the many limitations in using formulae

to determine the FrightG sample si7e, pastexperience of conducting marketing researchstudies is often used to moderate or adjust thenumbers crunched out by the formulae.

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Be will now discuss some of the commonly usedsampling techni


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Pro&a&ility Sampling Techni'!es

These are techni


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The other major distinguishing feature

of probability sampling methods is that

they are unbiased. The scheme of

selection of units from the targetpopulation is pre#specified, and then

the sample is selected according to the

scheme. Not according to any biases

or preferences of the researcher.

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4n practice, there are


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Simple Random Sampling

This techni


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4f we wish to use simple random

samplingwe could make a list of all 1@@

employees. Then, a number could be

allotted to each employee. Be could then

write these 1@@ numbers on small piecesof paper, one number on each. huffling

these folded pieces of paper, we can draw

3 pieces out of the 1@@, and use these

employees as our sample.

8

Thi t d h th i l ti l


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This appears ery easy to do when there is a relatiely

small number of people to pick from. !ut when we

deal with typical marketing research problems, the

numbers are


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!ut it is possible to use modifications of the basictechni


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Lractically, the oerall sample si7e is first calculated,

using a formula of the type discussed earlier, or based

on judgement and experience. This oerall sample is

then diided into sub#samples for each stratum orsegment. There are two ways of doing this# called

proportionate satisfaction, and disproportionate

stratification. Be will illustrate, based on our example

of three age#based strata.

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Total Sample si$e for Proportionate Stratified

Samples.

&irst, to compute the oerall sample si7e for proportionatestratified sample, we hae to use a modified formula,

iisw

e

z

"

3"


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instead of the earlier formula discussed at the

beginning of this chapter. The pre#condition for using

this formula is that we need to know the standard

deiation $estimated% of the concerned ariable for

each of the strata 1,

",

0, etc.

Be also hae to assign a weight to each stratum,

which is Bi in the formula aboe. B

i is generally

calculated as a proportion of number of people in

stratum i; to the number of people in all the strata. 4nother words,

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where Ni is the population of stratum i;, and N; is

the total population targeted & or the study.

&or calculating the weights, therefore, we must haeat least an estimate of the distribution of our target

population among the strata. Be also need i, the

standard deiation of the ariable being estimated,

for each stratum. These are not always easy to get.

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/oweer, we will illustrate, assuming we are trying to

gather data for a customer satisfaction study for a T)

channel. Ae us assume we want to know the oerall

customer satisfaction leel among three age groups#

below "3, "3 to @, for an entertainment channel such

*s ony. Be want to determine the customersatisfaction 2n a 6#point scale, 1 being Aow

satisfaction leel, and 6 being /igh satisfaction leel.

2ur formula for total sample si7e, we recall, is

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Be will now assume that

Z? 1.95 $assuming 93 per cent confidence leel%e? @.@3 $tolerable error on the 6#point scale%

Be will assume that for the three age#based strata, the

weights and standard deiations are known or can be

calculated. * rough estimate of the standard deiations

$overall% is gien by the formula $RangeH5%.

Range is 6#1?5 because the maximum alue of the rating

can be 6, and minimum is 1.

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( ) ( ) ( ) ( ) ( ) ( )[ ] ""

6.@.@[email protected].@".10.@@3.@

95.1++

=n

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This is the total sample si7e re


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To split this total sample of 1008 into

proportionately stratified sub#samples, we simply

use the same weights as determined earlier. Thus,the sample si7e for stratum 1 $below "3 age group%

would be

1008 x B1? 1008 x @.0 ? @1

&or stratum ", it would be1008 x B"? 1008 x @.0 ? @1

&or stratum 0 $aboe @ age group%, it would be

1008 x B0? 1008 x @. ? 305 $approx.%

Thus, we would take a sample of @1, @1 and 305

from each of the three strata. The total sample si7e

is maintained at 1008.5@


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7isproportionate Stratified Sampling

2ne of the keys to effectie sampling is to take asample as largeor as small as re


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*s an illustration $though exaggerated%,if we know that all the population is of

exactly the same characteristics, then asample si7e of 1 is enough to tell us thecharacteristics of the entire population.

5"

*t the other extreme if the population is extremely


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*t the other extreme, if the population is extremelyariable, each unit haing its own differentcharacteristics, we would need a ery large sample

to accurately represent the population. (ostpopulations do not fall into extreme 7ones, andgenerally strata or segments consist of units thatare similar to each other.

Bhen doing stratified sampling, we wouldprobably go for disproportionate stratified samplesif the ariability of the ariable being estimated is

different from segment to segment. 4f theariability is the same, we could take aproportionate stratified sample. Be measureariability by the standard deiation of the

population stratum or segment. 50


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The formula for the total sample si7e calculation

is $for disproportionate sampling%

? 1"6" $approx.%

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Thus, we see that compared to the proportionatestratified sample, si7e for the same leel of tolerable

error $e% and 7 $1.95,93 per cent confidence leel% is

smaller. 4n general, we will note that disproportionate

stratified samples tend to be more efficient $lower

sample si7es are obtained%, than proportionate

stratified samples, because we allocate sample si7e

according to the ariability in the strata.

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Be hae yet to allocate the sub#samples to the strata


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Be hae yet to allocate the sub samples to the strata.

Be will now do that. The criterion for doing so would

!e to do it in proportion to the ariation in a gien

stratum, compared to the total ariation in all strata4n other words

4n our three strata,

ni? sample si7e for stratum i

n ? total sample si7e 1"6" $calculated aboe%Ni? proportion of population belonging to stratumi

Si? tandard deiation of the ariable $customer

satisfaction% in stratum i)55


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Thus, the sample is diided into the three age groups

in proportion to the ariation in customer satisfaction,

and not in proportion to the number of respondents ineach stratum.

&or example, the below "3 segment has the largest

sample si7e of 3@0, een though it has only @.0 or 0@

percent of the population. 4f we had gone for

proportionate stratified sampling, this segment would

hae got a sample si7e of @.0 x 1"6" ? 08" only. Thiswould hae been under#representatie for this

segment.

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Be hae discussed the pros and cons of


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Be hae discussed the pros and cons of

proportionate and disproportionate stratified

sampling in these two sections. The reason for

such an extensie discussion is because manyof the


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Be now moe on to a discussion of otherprobabilistic methods of sampling.

Cl!ster Sampling 9 6rea Sampling

* major difference between preiously discussedmethods of sampling and cluster sampling is thata group of objects H units for sampling is selectedin cluster sampling.

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* cluster is a group of sampling units or

elements, which can be identified, listed and asample of which can be chosen.Theoretically, a cluster could be on the basisof any criterion. !ut in practice, clusters tendto be found either in terms of geographicalareas, or membership of some groups such asa church, a club, or a social organisation.

Bhen the clusters are selected on the basis of

geographical area, it is also called *reaampling.

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4f cluster sampling is only a single stage

procedure, then

1. * list of all aailable clusters should beprepared.

". *ll clusters should be numbered.0. * sample of clusters $number to be decided

by researcher% should be randomly drawn.. *ll sampling units H elements such as

households in the selected clusters should bechosen to be a part of the sample.

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Lractically, most of the time, " or more stages


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Lractically, most of the time, " or more stages

of sampling takes place. 2ut of the clusters

selected in the first stage, a sample of units

$households% is generally taken, because thenumber of people in a cluster is usually too

large for sampling purposes.

2ne problem with cluster sampling is that the

members of a cluster tend to be similar = for

example, people liing in a block or

neighbourhood come from the same socio#economic backgroundP hae similar tastes,

buying behaiour, etc.

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4n general, cluster sampling is statistically

inferior to simple random sampling and

stratified random sampling. 4ts sample tends tobe less representatie than the other two

methods. 4n other words, it produces more

sampling error for the same sample si7e, when

compared to the other two methods.!ut on the positie side, the cost of cluster

sampling is also usually lower. o, the

researcher may be able to justify using this

techni


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ystematic sampling is ery similar to imple Random

ampling, and easier to practice. ust as we do in asimple random sample, we start with a list of all sampling

units or respondents in the population. Be first compute

the sample si7e re


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To illustrate, say we hae a population of0@@ students, for some research. Be need

a sample of 13 out of these. The

sampling fraction is 13H0@@ which means

1 out of eery "@ students will beselected, on an aerage.

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Be diide the list into 0@@H13 ? "@ parts. 2ut

of the first "@ students, we choose any one at

random. Aet us say, we choose student

number 6 $all students are listed%. Thereafter,

we choose student numbers 6D"@, 6D"@D"@,

6D"@D"@D"@ and so on in a systematicsampling plan. Therefore, the selected

students will be numbers 6, "6, 6, 56, 86,

1@6, 1"6, 16, 156, 186, "16, "06, "36, "66

and "96. *ll these 13 students will compriseour total sample for the study.

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4n an ordered list according to the criterion of

interest, systematic sampling produces a more

representatie sample than simple random sampling.&or example, if all students were arranged in

ascending order of age, a systematic sample would

produce a sample consisting of all age groups.

/oweer, a potential drawback also exists. 4f the list

is drawn up such that eery "@thstudent were similar

on the characteristic we are estimating, either by

chance or design, then systematic samples can go

ery wrong. o a list should be examined to see that

there is no cyclicality which coincides with our

sampling interal.69

M!ltistage or Com&ination Sampling


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*s the name indicates, in this type of sampling, we do not

choose the final sample in one stage. Be combine two or

more stages, and sometimes " or more different methods ofprobability sampling.

Be hae already talked about "#stage *rea amples while

discussing Eluster ampling. sually, multi#stage methods

hae to be used when doing research on a national scale.Be may diide the national#leel target population for our

surey into clusters or some such units. &or example, we

may diide 4ndia into 3 metro clusters, "@ class * towns,

"@@ class ! towns, and take our first stage sample as 1metro, 0 class * towns, and 1@ class ! towns, based on our

sampling plan.

8@

4n the second stage, we may choose a stratified


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g , y

sample based on household income and age of

respondent. 4n such a case, we are using a two stage

sampling plan, which is a combination of Elusterampling, and tratified Random ampling.

4f we go on sampling by geographical area based

clusters in all the stages, it could be a 0 or stage

cluster sample.

uch combination sampling plans are fre


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4on8Pro&a&ility Sampling Techni'!es

Be hae so far discussed probability samplingtechni


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The major difference is that in non#probability techni


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There are four major non#probability

sampling techni


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p g

The first method,


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4n practice, unless there areuntrained field workers, or thefield superision is lax, theresults produced by a


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4n practice, many researchers use


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!dgement Sampling

This is not used often, as it is difficult to justify.

The method relies only on the judgement of the

researcher as to who should be in the sample.

4t obiously suffers from a researcher bias. 4f a

different researcher were to do the same study,

he is likely to select an entirely different kind of

sample.

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Con+enience Sampling


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p g

This is employed usually in pre#testing of


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2ther examples of coneniencesampling includes on#the#street

interiews, or any other meetings, or

from employees of one office blockor factory. *nother common

example of conenience sampling is

the one by T) reporters who catch

any person passing by and interiew

him on the street.

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Snow&all Sampling

This techni


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4t would appear from our discussion of sampling that it

is not possible to do a census in marketing research.trictly speaking, it is possible to do one if the

population si7e is small. &or example, if "@@ solar

cooker owners exist in a town, it may be possible to

meet all of them, if their addresses were aailable, orcould be obtained.

4n some cases, like a surey of distributors or dealers,

or een industrial buyers, it may make sense to do a

census if it is feasible. Larticularly if opinions or

buying behaiour of respondents in a small population

are likely to be widely diergent.9"


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!ut in most cases, if populations are

reasonably large or ery large, it makeslittle sense to do a census. 2ne major

reason is that it may simply take too long.

Mata may arrie too late for decision#

making. 4naccuracies also are likely to be a

function of the olume of data collected.

Be will discuss these in the next section

under the subject Fampling and Non#sampling -rrorsG.

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T f i M k ti R h


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Types of rrors in Marketing Research

*ny research study has an error margin associatedwith 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 =

Iampling -rror or Random -rror

INon#sampling or /uman -rror

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Sampling rror

This is the error which occurs due to theselection of some units and non#selection

of other units into the sample. 4t is

controllable if the selection of sample isdone in a random, unbiased way. 4n other

words, if a probability sampling

techni


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4on8sampling rror

This is the effect of arious errors in doing the study, by the

interiewer, data entry operator or the researcher himself./andling a large


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Total rror

1. This is the total of sampling error D non#

sampling error.

". 2ut of this, the sampling error can be

estimated in the case of probability samples, but

not in the case of non#probability samples.

0. Non#sampling errors can be controlled

through hiring better field workers,


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. 2ne important outcome of this discussion

of errors is that the total error is usually

unknown. !ut, we may hae to lie with

higher non#sampling error in our attempt to

reduce sampling error by increasing the

sample si7e of the study, not to mention the

higher cost of a larger sample.

3. Therefore, it is worthwhile to optimise

total error by optimising the sample si7e,

rather than going blindly for the largestpossible sample si7e.

Documents

Mr Chapter 5 Sampling