Chapter XII
Chapter XII
Sampling:
Sampling:
Final and Initial Sample Size
Final and Initial Sample Size
Determination
Chapter Outline
Chapter Outline
1) Overview
2) Definitions and Symbols
2) Definitions and Symbols
3) The Sampling Distribution
4) Statistical approaches to Determining Sample Size
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
6) Multiple Characteristics and Parameters
8) Adjusting the Statistically Determined Sample Size
8) Adjusting the Statistically Determined Sample Size
9) Non-response Issues in Sampling
9) Non-response Issues in Sampling
i. Improving the Response Rates
i. Improving the Response Rates
ii. Adjusting for Non-response
ii. Adjusting for Non-response
10) International Marketing Research
11) Ethics in Marketing Research
11) Ethics in Marketing Research
12) Internet and Computer Applications
13) Focus On Burke
13) Focus On Burke
14) Summary
14) Summary
15) Key Terms and Concepts
15) Key Terms and Concepts
Symbols for Population
Symbols for Population
and Sample Variables
and Sample Variables
Table 12.1
Table 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
Standardized
variate (z) (X-µ)/ (X-X)/S
Coefficient of variation (C) /µ S/X
-
-95% Confidence Interval
[image:5.720.29.647.91.450.2]95% Confidence Interval
Figure 12.1
Figure 12.1
X
L_
X
U_
X
_
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 the
population Estimate : = 55 Estimate : = 0.64
5. Determine the sample size using the
formula for the standard error n =
2z2/D2 = 465 n = (1-) z2/D2 = 355
6. If the sample size represents 10% of the population, apply the finite population correction
nc = nN/(N+n-1) nc = nN/(N+n-1)
7. If necessary, reestimate the confidence
interval by employing s to estimate = zx = p
zss p
8. If precision is specified in relative rather than absolute terms, determine the sample size by substituting for D.
D = Rµ
n = C2z2/R2 D = R
n = z2(1-)/(R2)
Sample Size Determination
Sample Size Determination
for Means and Proportions
for Means and Proportions
Table 12.2
Table 12.2
Variable
Mean 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 the
population () $55 $40 $30
Required sample size (n) 465 246 217
Sample Size For Estimating
Sample Size For Estimating
Multiple Parameters
[image:7.720.36.693.95.449.2]Multiple Parameters
Table 12.3
Methods of Improving Response Rates
Improving Response Rates
[image:8.720.24.712.36.510.2]Improving Response Rates
Fig. 12.2
Fig. 12.2
Reducing Refusals
Reducing Not-at-Homes
Prior
Notification
Motivating Respondents
Incentives Questionnaire Design
and
Administration
Follow-Up Other
Facilitators
Arbitron Responds to Low Response Rates
RIP 12.1
RIP 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.
Exit Polling of Voters
Exit Polling of Voters
RIP 12.2
RIP 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.
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.
Percentage Response Average Dollar
Expenditure 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 in
Use of Trend Analysis in
Adjusting for Non-response
[image:12.720.22.702.86.432.2]Adjusting for Non-response
Table 12.4
Finding Probabilities Corresponding
Finding Probabilities Corresponding
to Known Values
[image:13.720.38.698.28.455.2]to Known Values
Figure 12A.1
Figure 12A.1
Z Scale
µ-3 µ-2 µ-1 µ µ+1 µ+2 µ+3
35 -3 40 -2 45 -1 50 0 55 +1 60 +2 65 +3
(µ=50, =5)
Z Scale
Area is 0.3413
Area between µ and µ + 1 = 0.3431
Area between µ and µ + 2 = 0.4772
Finding Values Corresponding to
Finding Values Corresponding to
Known Probabilities
[image:14.720.43.702.30.504.2]Known Probabilities
Figure 12A.2
Figure 12A.2
Area is 0.500
Area is 0.450
Area is 0.050
X
50
X Scale
-Z
0
Area is 0.475
Area is 0.475
X
50
X Scale
-Z
0
Z Scale
Area is 0.025
Finding Values Corresponding to Known
Finding Values Corresponding to Known
Probabilities: Confidence Interval
[image:15.720.29.698.33.500.2]Probabilities: Confidence Interval
Fig. 12A.3
Fig. 12A.3
Area is 0.025
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 12.3
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).
