Chapter XIIChapter XII

Sampling: Sampling: Final and Initial Sample Size Final and Initial Sample Size

DeterminationDetermination

Chapter OutlineChapter Outline1) Overview

2) Definitions and Symbols2) Definitions and Symbols

3) The Sampling Distribution

4) Statistical approaches to Determining Sample Size4) Statistical approaches to Determining Sample Size

5) Confidence Intervals

i. Sample Size Determination: Means

ii. Sample Size Determination: Proportions

6) Multiple Characteristics and Parameters6) Multiple Characteristics and Parameters

7) Other Probability Sampling Techniques

8) Adjusting the Statistically Determined Sample Size8) Adjusting the Statistically Determined Sample Size

9) Non-response Issues in Sampling9) Non-response Issues in Sampling

i. Improving the Response Ratesi. Improving the Response Rates

ii. Adjusting for Non-responseii. Adjusting for Non-response

10) International Marketing Research

11) Ethics in Marketing Research11) Ethics in Marketing Research

12) Internet and Computer Applications

13) Focus On Burke13) Focus On Burke

14) Summary14) Summary

15) Key Terms and Concepts15) Key Terms and Concepts

16) Acronyms

Symbols for Population Symbols for Population and Sample Variablesand Sample Variables

Table 12.1Table 12.1

Variable Population Sample

Mean µ X

Proportion p

Variance 2 s2

Standard deviation s

Size N n

Standard error of the mean x

Sx

Standard error of the proportion p

Sp

Standardizedvariate (z)

(X-µ)/ (X-X)/S

Coefficient of variation (C) /µ S/X

- -

--

-

95% Confidence Interval95% Confidence IntervalFigure 12.1Figure 12.1

XL

_XU

_X_

0.475 0.475

Steps Means Proportions

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

= p zssp

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

D = Rµn = C2z2/R2

D = R

n = z2(1-)/(R2)

Sample Size Determination Sample Size Determination for Means and Proportionsfor Means and Proportions

Table 12.2Table 12.2

- -

VariableMean Household Monthly Expense On

Department 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

Sample Size For Estimating Sample Size For Estimating Multiple ParametersMultiple Parameters

Table 12.3Table 12.3

Methods of ImprovingResponse Rates

Improving Response RatesImproving Response RatesFig. 12.2Fig. 12.2

ReducingRefusals

ReducingNot-at-Homes

PriorNotification

MotivatingRespondents

Incentives Questionnaire Designand Administration

Follow-Up OtherFacilitators

Callbacks

Arbitron Responds to Low Response RatesRIP 12.1RIP 12.1

Arbitron, a major marketing research supplier, was trying to improve response rates in order to get more meaningful results from its surveys. Arbitron created a special cross-functional team of employees to work on the response rate problem. Their method was named the “breakthrough method” and the whole Arbitron system concerning the response rates was put in question and changed. The team suggested six major strategies 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 a result, response rates improved significantly. However, in spite of those encouraging results, people at Arbitron remain very cautious. They know that they are not done yet and that it is an everyday fight to keep those response rates high.

Exit Polling of VotersExit Polling of VotersRIP 12.2RIP 12.2

Warren Mitofsky, executive director of Voter Research and Surveys (VRS), states that planning exit interviews for a presidential election begins two years before the big day. The New York City-based staff of 22 grows to 60 during an election year; on election day, it blossoms to 6,000 workers who conduct exit interviews at 1,500 polling places.

VRS workers give voters a list of about 25 questions. Certain issues are well-known determinants of a voter’s choice, whereas other questions deal with last-minute events such as political scandals. The questions are written at the last possible moment. The questionnaire is designed to determine not only for whom people voted but on what basis.

Uncooperative pollsters are a problem among exit polling. VRS workers are told to record a basic demographic profile for non-compliers. From this demographic data, a voter profile is developed to replace the uncooperative pollster using the method of substitution. Age, sex, race, and residence are strong indicators of how Americans vote. For example, younger voters are more likely to be swayed by moral issues whereas older voters are more likely to consider a candidate’s personal qualities. Thus, VRS substitutes for non-respondents for other potential respondents who are similar in age, sex, race, and residence. The broad coverage of exit interviews and the substitution technique for non-compliant pollsters allow VRS to obtain margins of error close to 3 to 4%.

RIP 12.2 Contd.RIP 12.2 Contd.

Percentage Response Average DollarExpenditure

Percentage of PreviousWave’s Response

First Mailing 12 412 __

Second Mailing 18 325 79

Third Mailing 13 277 85

Nonresponse (57) (230) 91

Total 100 275

Use of Trend Analysis inUse of Trend Analysis inAdjusting for Non-responseAdjusting for Non-response

Table 12.4Table 12.4

Finding Probabilities Corresponding Finding Probabilities Corresponding to Known Valuesto Known Values

Figure 12A.1Figure 12A.1

Z Scaleµ-3 µ-2 µ-1 µ µ+1 µ+2 µ+335

-3

40

-2

45

-1

50

0

55

+1

60

+2

65

+3

(µ=50, =5)

Z Scale

Area is 0.3413Area between µ and µ + 1 = 0.3431Area between µ and µ + 2 = 0.4772Area between µ and µ + 3 = 0.4986

Finding Values Corresponding to Finding Values Corresponding to Known ProbabilitiesKnown Probabilities

Figure 12A.2Figure 12A.2

Area is 0.500Area is 0.450

Area is 0.050

X 50X Scale

-Z 0Z Scale

Area is 0.475Area is 0.475

X 50X Scale

-Z 0Z Scale

Area is 0.025

Finding Values Corresponding to Known Finding Values Corresponding to Known Probabilities: Confidence IntervalProbabilities: Confidence IntervalFig. 12A.3Fig. 12A.3

Area is 0.025

-Z

Marketing research firms are now turning to the Web to conduct online research. Recently, four leading market research companies (ASI Market Research, Custom Research Inc., M/A/R/C Research and Roper Search Worldwide) partnered with Digital Marketing Services (DMS), Dallas, to conduct custom research on AOL.DMS and AOL will conduct online surveys on AOL's Opinion Place, with an average base of 1,000 respondents by survey. This sample size was determined based on statistical considerations as well as sample sizes used in similar research conducted by traditional methods. AOL will give rewards points (that can be traded in for prizes) to respondents. Users will not have to submit their e-mail addresses. The surveys will help measure response to advertiser's online campaigns. The primary objective of these researches is to gauge consumers' attitudes and other subjective information that can help media buyers plan their campaigns.

Opinion Place Bases Its Opinions on 1000 Respondents

RIP 12.3RIP 12.3

Another advantage of online surveys is that you are sure to reach your target (sample control) and that they are quicker to turn around than traditional surveys like mall intercepts or home interviews. They also are cheaper (DMS charges $20,000 for an online survey, while it costs between $30,000 and $40,000 to conduct a mall-intercept survey of 1,000 respondents).

RIP 12.3 ContdRIP 12.3 Contd..