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 $decided earlier while setting the 7;
alue%.
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Now, we hae all 0 alues re
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imilarly, for any change in the estimate of s; or
the alue of >; we choose to set, the alue of n;,the sample si7e, would change.
4n general, sample si7e would increase if
Istandard deiation s; is higherIconfidence leel re
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The major things to remember in the aboe
formula are that
1>; alue is set based on the confidence leel
we desire.
"s; alue is estimated from past studiesinoling the same ariable, or from the
approximate formula of Range, if we can
estimate the range of alues for the ariable in
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"orm!la for Sample Si$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@@
00
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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.
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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.
88
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.
9@
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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.
90
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
9
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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.