chapter12.ppt 211KB Dec 31 1997 01:06:16 PM
Chapter XII
Sampling:
Final and Initial Sample Size
Determination
Chapter Outline
1) 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
8) 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) Internet and Computer Applications
13) Focus On Burke
14) Summary
15) Key Terms and Concepts
16) Acronyms
Table 12.1
Variable
Symbols for Population
and Sample
Variables Sample
Population
Mean
µ
-X
Proportion
p
Variance
2
s
Standard deviation
s
Size
N
n
Standard error of the mean
x
Sx
Standard error of the proportion
Standardized
variate (z)
(X-µ)/
Coefficient of variation (C)
-
p
(X-X)/S
/µ
2
-
Sp
-S/X
95% Confidence Interval
Figure 12.1
0.475
_
XL
0.475
_
X
_
XU
Table 12.2
Sample Size Determination
for Means and Proportions
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%
z value is 1.96
z value is 1.96
Estimate : = 55
Estimate : = 0.64
3. Determine the z value associated with CL
4. Determine the standard deviation of the
population
5. Determine the sample size using the
formula for the standard error
n = z /D = 465
2
2
n = (1-) z /D = 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)
- = zx
= p zs p
D = Rµ
2 2
2
n = C z /R
D = R
2
2
n = z (1-)/(R )
7. If necessary, reestimate the confidence
interval by employing s to estimate
8. If precision is specified in relative rather
than absolute terms, determine the sample
size by substituting for D.
2
2
2
s
Table 12.3
Sample Size For Estimating
Multiple Parameters
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
Fig. 12.2
Improving Response Rates
Methods of Improving
Response Rates
Reducing
Refusals
Reducing
Not-at-Homes
Prior
Motivating Incentives Questionnaire Follow-Up Other
Design
Facilitators
Notification Respondents
and
Administration
Callbacks
RIP 12.1
Arbitron Responds to Low Response Rates
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.
2.
3.
4.
5.
6.
Maximize the effectiveness of placement/follow-up calls.
Make materials more appealing and easy to complete.
Increase Arbitron name awareness.
Improve survey participant rewards.
Optimize the arrival of respondent materials.
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.
RIP 12.2
Exit Polling of Voters
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.
RIP 12.2 Contd.
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 noncompliant pollsters allow VRS to obtain margins of error close to 3 to
4%.
Table 12.4
Use of Trend Analysis in
Adjusting for Non-response
Percentage Response
Average Dollar
Expenditure
Percentage of Previous
Wave’s Response
First Mailing
12
412
__
Second Mailing
18
325
79
Third Mailing
13
277
85
Nonresponse
(57)
(230)
91
Total
100
275
Figure 12A.1
Finding Probabilities Corresponding
to Known Values
Area is 0.3413
Area between µ and µ + 1 = 0.3431
Area between µ and µ + 2 = 0.4772
Area between µ and µ + 3 = 0.4986
µ-3
µ-2
µ-1
µ
µ+1
µ+2
µ+3
35
40
45
50
55
60
65
-3
-2
-1
0
+1
+2
+3
Z Scale
(µ=50, =5)
Z Scale
Figure 12A.2
Finding Values Corresponding to
Known Probabilities
Area is 0.500
Area is 0.450
Area is 0.050
X
50
X Scale
Z Scale
-Z
0
Finding Values Corresponding to Known
Fig. 12A.3 Probabilities: Confidence Interval
Area is 0.475
Area is 0.475
Area is 0.025
X
Area is 0.025
X Scale
50
Z Scale
-Z
0
-Z
RIP 12.3
Opinion Place Bases Its Opinions on 1000
Respondents
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.
RIP 12.3 Contd.
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).
Sampling:
Final and Initial Sample Size
Determination
Chapter Outline
1) 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
8) 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) Internet and Computer Applications
13) Focus On Burke
14) Summary
15) Key Terms and Concepts
16) Acronyms
Table 12.1
Variable
Symbols for Population
and Sample
Variables Sample
Population
Mean
µ
-X
Proportion
p
Variance
2
s
Standard deviation
s
Size
N
n
Standard error of the mean
x
Sx
Standard error of the proportion
Standardized
variate (z)
(X-µ)/
Coefficient of variation (C)
-
p
(X-X)/S
/µ
2
-
Sp
-S/X
95% Confidence Interval
Figure 12.1
0.475
_
XL
0.475
_
X
_
XU
Table 12.2
Sample Size Determination
for Means and Proportions
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%
z value is 1.96
z value is 1.96
Estimate : = 55
Estimate : = 0.64
3. Determine the z value associated with CL
4. Determine the standard deviation of the
population
5. Determine the sample size using the
formula for the standard error
n = z /D = 465
2
2
n = (1-) z /D = 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)
- = zx
= p zs p
D = Rµ
2 2
2
n = C z /R
D = R
2
2
n = z (1-)/(R )
7. If necessary, reestimate the confidence
interval by employing s to estimate
8. If precision is specified in relative rather
than absolute terms, determine the sample
size by substituting for D.
2
2
2
s
Table 12.3
Sample Size For Estimating
Multiple Parameters
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
Fig. 12.2
Improving Response Rates
Methods of Improving
Response Rates
Reducing
Refusals
Reducing
Not-at-Homes
Prior
Motivating Incentives Questionnaire Follow-Up Other
Design
Facilitators
Notification Respondents
and
Administration
Callbacks
RIP 12.1
Arbitron Responds to Low Response Rates
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.
2.
3.
4.
5.
6.
Maximize the effectiveness of placement/follow-up calls.
Make materials more appealing and easy to complete.
Increase Arbitron name awareness.
Improve survey participant rewards.
Optimize the arrival of respondent materials.
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.
RIP 12.2
Exit Polling of Voters
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.
RIP 12.2 Contd.
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 noncompliant pollsters allow VRS to obtain margins of error close to 3 to
4%.
Table 12.4
Use of Trend Analysis in
Adjusting for Non-response
Percentage Response
Average Dollar
Expenditure
Percentage of Previous
Wave’s Response
First Mailing
12
412
__
Second Mailing
18
325
79
Third Mailing
13
277
85
Nonresponse
(57)
(230)
91
Total
100
275
Figure 12A.1
Finding Probabilities Corresponding
to Known Values
Area is 0.3413
Area between µ and µ + 1 = 0.3431
Area between µ and µ + 2 = 0.4772
Area between µ and µ + 3 = 0.4986
µ-3
µ-2
µ-1
µ
µ+1
µ+2
µ+3
35
40
45
50
55
60
65
-3
-2
-1
0
+1
+2
+3
Z Scale
(µ=50, =5)
Z Scale
Figure 12A.2
Finding Values Corresponding to
Known Probabilities
Area is 0.500
Area is 0.450
Area is 0.050
X
50
X Scale
Z Scale
-Z
0
Finding Values Corresponding to Known
Fig. 12A.3 Probabilities: Confidence Interval
Area is 0.475
Area is 0.475
Area is 0.025
X
Area is 0.025
X Scale
50
Z Scale
-Z
0
-Z
RIP 12.3
Opinion Place Bases Its Opinions on 1000
Respondents
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.
RIP 12.3 Contd.
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).