Marketing Research Module 8 Sampling Design Finalsize

8/14/2019 Marketing Research Module 8 Sampling Design Finalsize

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Ch apter Twelv e

Sampling:Final and Initial SampleSize Determination

12-1 2007 Prentice Hall


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2007 Prentice Hall 12-2

Cha pter Ou tl ine1) Overview

2) Definitions and Symbols

3) The Sampling Distribution

4) Statistical Approaches to Determining Sample Size

5) Confidence Intervals

i. Sample Size Determination: Means

ii. Sample Size Determination: Proportions

6) Multiple Characteristics and Parameters

7) Other Probability Sampling Techniques


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Ch apter O utl ine8) Adjusting the Statistically Determined Sample Size

9) Non-response Issues in Sampling

i. Improving the Response Rates

ii. Adjusting for Non-response

10) International Marketing Research

11) Ethics in Marketing Research

12) Summary


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Defi niti ons a nd S ymbo ls Para mete r: Aparameteris a summary description of a

fixed characteristic or measure of the target population. Aparameter denotes the true value which would be obtained ifa census rather than a sample was undertaken.

Statistic : Astatistic is a summary description of acharacteristic or measure of the sample. The sample statisticis used as an estimate of the population parameter.

Fin ite Pop ulat ion Corre ction : Thefini te popu la tioncorrection (fpc) is a correction for overestimation of thevariance of a population parameter, e.g., a mean orproportion, when the sample size is 10% or more of thepopulation size.


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Defi niti ons a nd S ymbo ls Pr eci sio n le vel : When estimating a population

parameter by using a sample statistic, the pr eci si onlevel is the desired size of the estimating interval.This is the maximum permissible difference betweenthe sample statistic and the population parameter.

Confidence interval : The co nfide nce in ter va l isthe range into which the true population parameterwill fall, assuming a given level of confidence.

Co nfiden ce leve l: The confidence level is theprobability that a confidence interval will include thepopulation parameter.


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Sym bol s f or Po pula ti on andSam pl e Var ia blesTable 12.1

Va r ia b l e P o pu l a t i o n Sam p l eM e a n XP ropo r t i o n

p

Va r i ance 2 s 2 S t anda rd d ev i a t io n sS i ze N nS t anda rd e r r o r o f t he m ean x S x S t anda rd e r r o r o f t he p ropo r t i o n p S p S t anda rd i z ed v a r i a t e ( z ) (X - ) / ( X -X ) / SCoe f fi ci en t o f va r i a t i on (C ) / S / X

__

_

_

_


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Calculation of the confidence interval involves determining a

distance below ( ) and above ( ) the population mean ( ),which contains a specified area of the normal curve (Figure12.1).

The z values corresponding to and may be calculated as

where = -zand = +z. Therefore, the lower value of is

and the upper value of is

Th e Conf ide nc e Int erval Appro achXL XU X

X

zL =

XL

-

x

zU =XU -

x

XL = -zx

XU = +zx

z Uz L

X



Th e Conf ide nc e Int erval Appro achNote that is estimated by . The confidence interval is given by

We can now set a 95% confidence interval around the sample mean of$182. As a first step, we compute the standard error of the mean:

From Table 2 in the Appendix of Statistical Tables, it can be seen thatthe central 95% of the normal distribution lies within + 1.96 zvalues.The 95% confidence interval is given by

+ 1.96

= 182.00 + 1.96(3.18)

= 182.00 + 6.23

Thus the 95% confidence interval ranges from $175.77 to $188.23.The probability of finding the true population mean to be within$175.77 and $188.23 is 95%.

XX zx

x=n

= 55/ 300 = 3.18

X x



95 % Co nfi den ce Inter va lFigure 12.1

XL_ XU

_X_

0.475 0.475



Sam pl e Size Determi nat ion forMeans and Pr opor ti onsTable 12.2

`Steps Means Proportions

1. Specify the level of precision D = $5.00 D = p - = 0.05

2. Specify the confidence level (CL) CL = 95% CL = 95%

3. Determine the z value associated with CL z value is 1.96 z value is 1.96

4. Determine the standard deviation of thepopulation Estimate : = 55 Estimate : = 0.64

5. Determine the sample size using theformula for the standard error

n = 2z2/D2 = 465 n = (1-) z2/D2 = 355

6. If the sample size represents 10% of thepopulation, apply the finite populationcorrection

nc = nN/(N+n-1) nc = nN/(N+n-1)

7. If necessary, reestimate the confidenceinterval by employing s to estimate

= zsx= p zsp

8. If precision is specified in relative ratherthan absolute terms, determine the samplesize by substituting for D.

D = Rn = C2z2/R2

D = Rn = z2(1-)/(R2)

_



Sam pl e Size fo r Esti mat ingMult iple Par am et ersVariable

Mean Household Monthly Expense OnDepartment store shopping Clothes Gifts

Confidence level 95% 95% 95%

z value 1.96 1.96 1.96

Precision level (D) $5 $5 $4

Standard deviation of thepopulation ()

$55 $40 $30

Required sample size (n) 465 246 217

Table 12.3



Adjus ting the St at is tic all yDeterm ined Sam ple SizeIn cid en ce rate refers to the rate of occurrence or thepercentage, of persons eligible to participate in the study.

In general, if there are c qualifying factors with anincidence of Q1, Q2, Q3, ...QC,each expressed as aproportion:

Incidence rate = Q1 x Q2 x Q3....x QC

Initial sample size = Final sample size

.



Im pr ovi ng Response Ra tesFig. 12.2

PriorNot ific at ion Mo tivat ingResp ond ent s Incent ives Quest io nnai reDesignandAd mini st rat io n

Fol l ow-U p OtherFac il itators

Ca llback s

Met hod s of Im pro vi ngResp onse Rat es

Reduci ngRefusal s ReducingNot -at -Homes


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Arbi tr on Responds to Lo wResp ons e Ra tesArbitron, a major marketing research supplier, was trying to improveresponse rates in order to get more meaningful results from its surveys.Arbitron created a special cross-functional team of employees to work onthe response rate problem. Their method was named the breakthroughmethod, and the whole Arbitron system concerning the response rateswas put in question and changed. The team suggested six majorstrategies for improving response rates:

1. Maximize the effectiveness of placement/follow-up calls.2. Make materials more appealing and easy to complete.3. Increase Arbitron name awareness.4. Improve survey participant rewards.5. Optimize the arrival of respondent materials.

6. Increase usability of returned diaries.

Eighty initiatives were launched to implement these six strategies. As aresult, response rates improved significantly. However, in spite of thoseencouraging results, people at Arbitron remain very cautious. They knowthat they are not done yet and that it is an everyday fight to keep thoseresponse rates high.



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Adj us ti ng for Nonr espo nse Subsamp lin g of Nonres po nden ts the researcher

contacts a subsample of the nonrespondents, usually

by means of telephone or personal interviews.

In repl ace men t, the nonrespondents in the currentsurvey are replaced with nonrespondents from anearlier, similar survey. The researcher attempts tocontact these nonrespondents from the earlier surveyand administer the current survey questionnaire tothem, possibly by offering a suitable incentive.



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Adj us ti ng for Nonr espo nse In su bst itut ion, the researcher substitutes for

nonrespondents other elements from the sampling

frame that are expected to respond. The samplingframe is divided into subgroups that are internallyhomogeneous in terms of respondent characteristicsbut heterogeneous in terms of response rates. Thesesubgroups are then used to identify substitutes who aresimilar to particular nonrespondents but dissimilar torespondents already in the sample.



Ad ju sti ng f or No nr es ponse Sub jecti ve Est ima tes When it is no longer feasible

to increase the response rate by subsampling,replacement, or substitution, it may be possible to

arrive at subjective estimates of the nature and effectof nonresponse bias. This involves evaluating the likelyeffects of nonresponse based on experience andavailable information.

Tren d anal ysi s is an attempt to discern a trendbetween early and late respondents. This trend isprojected to nonrespondents to estimate where theystand on the characteristic of interest.


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Adj us ti ng for Nonr espo nse Wei ghti ng attempts to account for nonresponse by

assigning differential weights to the data depending

on the response rates. For example, in a survey the

response rates were 85, 70, and 40%, respectively,for the high-, medium-, and low income groups. In

analyzing the data, these subgroups are assigned

weights inversely proportional to their response rates.

That is, the weights assigned would be (100/85),(100/70), and (100/40), respectively, for the high-,

medium-, and low-income groups.



Adju sti ng f or No nr esp onse Imp uta tio n involves imputing, or assigning, the

characteristic of interest to the nonrespondents

based on the similarity of the variables available forboth nonrespondents and respondents. Forexample, a respondent who does not report brandusage may be imputed the usage of a respondent

with similar demographic characteristics.



Finding Proba bi lit ies Co rr espondi ngto Known Values

-3 -2 -1 +1 +2 +335

-3

40

-2

45

-1

50

0

55

+1

60

+2

65

+3

Area is 0.3413

Z Scale

Figure 12A.1

Z Sc ale(=50, =5)

Area between and + 1 = 0.3431




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Finding Proba bi lit ies Co rr espondi ngto Known ValuesArea is 0.500Area is 0.450

Area is 0.050

X 50X Scale

-Z 0

Z Scale

Figure 12A.2


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Finding Value s Cor respo nding to Kno wnPr oba bil it ies : Confidenc e In terva lArea is 0.475Area is 0.475

X 50X Scale

-Z 0

Z Scale

Area is 0.025

Fig. 12A.3

Area is 0.025

-Z


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Marketing research firms are now turning to the Web to conduct

online research. Recently, four leading market researchcompanies (ASI Market Research, Custom Research, Inc.,M/A/R/C Research, and Roper Search Worldwide) partnered withDigital Marketing Services (DMS), Dallas, to conduct customresearch on AOL.

DMS and AOL will conduct online surveys on AOL's Opinion Place,with an average base of 1,000 respondents by survey. Thissample size was determined based on statistical considerations aswell as sample sizes used in similar research conducted by

traditional methods. AOL will give reward points (that can betraded in for prizes) to respondents. Users will not have to submittheir e-mail addresses. The surveys will help measure response toadvertisers' online campaigns. The primary objective of thisresearch is to gauge consumers' attitudes and other subjectiveinformation that can help media buyers plan their campaigns.

Opinio n Pla ce Bases It s Opini onson 100 0 Res ponde nt s


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200 i ll

Another advantage of online surveys is that you aresure to reach your target (sample control) and that theyare quicker to turn around than traditional surveys likemall intercepts or in-home interviews. They also are

cheaper (DMS charges $20,000 for an online survey,while it costs between $30,000 and $40,000 to conducta mall-intercept survey of 1,000 respondents).

on 10 00 R espon den ts

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Marketing Research Module 8 Sampling Design Finalsize