Determining Sample Size; How to Calculate Survey Sample Size
Analysis of sample size in consumer surveys · Formula for sample size for the mean n0 - the sample...
Transcript of Analysis of sample size in consumer surveys · Formula for sample size for the mean n0 - the sample...
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Analysis of sample size
in consumer surveys
GfK Polonia, 2013, Poland
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1. Introduction
a. Theoretical aspects
b. Sample size in the DG ECFIN Consumer Survey
2. Quality measures vs. sample size
a. Sample size - analysis of impact
b. Effective sample size - analysis of impact
c. Additional analysis
3. Summary and conclusions
4. References.
Agenda
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1. Introduction
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Sample size: Theoretical aspects
Main aspects of determining the size of a sample
the purpose of the study
population size
sampling error (the level of precision)
the confidence level
the degree of variability in the main measured attributes
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Sample size: Theoretical aspects
Ways of determining the size of a sample
using or conducting a census survey
transfer a sample size from a similar study
using published tables
applying of formulas to calculate a sample size
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Sample size: Theoretical aspects, formulas
Representative sample for proportions in large populations (W. G. Cochran)
n0 - the sample size
Z2 - the abscissa of the normal curve that cuts off an area α at the tails
e - the acceptable sampling error
p - the estimated proportion of an attribute that is present in the population
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Sample size: Theoretical aspects, formulas
Finite population correction for proportions
n0 - the initial sample size
n - adjusted sample size
N - the population size.
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Sample size: Theoretical aspects, formulas
Simplified formula for proportions* (Taro Yamane)
n - the sample size
N - the population size
e - the acceptable sampling error
* 95% confidence level and p = 0.5 are assumed
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Sample size: Theoretical aspects, formulas
Formula for sample size for the mean
n0 - the sample size
Z - the abscissa of the normal curve that cuts off an area σ at the tails
e - the acceptable sampling error
σ2 - the variance of an attribute in the population
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Sample size: Theoretical aspects
Margin of sampling error was calculated for 95% confidence interval, 50% fraction and infinite population
Dependence of sampling error on sample size
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Sample size in the DG ECFIN Consumer Survey
Sample sizes in the survey
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Sample size in the DG ECFIN Consumer Survey
Effective sample sizes in the survey
0
500
1000
1500
2000
2500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Effective sample size
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2. Quality measures vs. sample size
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Quality measures
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Sample size - analysis of impact on quality measures
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Sample size - analysis of impact on quality measures
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Sample size - analysis of impact on quality measures
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Sample size - analysis of impact on quality measures
sample size
correlation BCS with
ref.series
(moving average)
MCD_1
(moving average)
MCD_2
(moving average)
500 34.0 2.90 1.69
800, 500 33.3 2.49 1.47
1000, 800, 500 58.9 2.34 1.36
1020, 1000, 800 59.0 2.37 1.38
1200, 1020, 1000, 800 65.9 2.14 1.24
1500, 1200, 1020, 1000 63.6 2.29 1.30
1661, 1500, 1200, 1020 59.1 2.25 1.26
1850, 1661, 1500, 1200 54.1 2.19 1.22
2000, 1850, 1661, 1500 52.1 2.28 1.26
2100, 2000, 1850, 1661 56.4 2.09 1.17
2350, 2100, 2000, 1850 53.4 2.12 1.18
3300, 2350, 2100, 2000 59.9 2.08 1.17
Quality measures as moving averages for cumulated countries’ samples
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Sample size - analysis of impact on quality measures
Tendency of changes in the quality of data along with the increase of
sample size
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Sample size - analysis of impact on quality measures
Tendency of changes in the quality of data along with the increase of
sample size
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Effective sample size - analysis of impact on quality measures
0
10
20
30
40
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70
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100
0 500 1000 1500 2000 2500
corr
elat
ion
BC
S w
ith
ref
ere
nce
se
ries
Effective sample size
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Effective sample size - analysis of impact on quality measures
0
0.5
1
1.5
2
2.5
3
3.5
4
0 500 1000 1500 2000 2500
MC
D 1
Effective sample size
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Effective sample size - analysis of impact on quality measures
0
0.5
1
1.5
2
2.5
0 500 1000 1500 2000 2500
Effective sample size
MC
D 2
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Tendency of changes in the quality of data along with the increase of
effective sample size
Effective sample size - analysis of impact on quality measures
0
10
20
30
40
50
60
70
80
90
100
0 500 1000 1500 2000 2500
Sample size (cumulated groups)
corr
elat
ion
BC
S w
ith
ref
eren
ce s
erie
s
Effective sample size (moving averages)
corr
elat
ion
BC
S w
ith
ref
eren
ce s
erie
s
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Tendency of changes in the quality of data along with the increase of
effective sample size
Effective sample size - analysis of impact on quality measures
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 500 1000 1500 2000 2500
Effective sample size (moving averages)
MC
D 2
MC
D 1
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Sample size and correlation BCS with reference series for 3 types of
sampling frames
Additional analysis
telephone SF individual SF not classified SF
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Sample size and MCD 1 for 3 types of sampling frames
Additional analysis
telephone SF individual SF not classified SF
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Sample size and MCD 2 for 3 types of sampling frames
Additional analysis
telephone SF individual SF not classified SF
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3. Summary and conclusions
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Main findings
• Both sample size and effective sample size have moderate impact on
quality measures
• Although tendencies are slight they are quite clear and coherent for all
MCD1 and MCD2 measures. Picture for correlation is not so clear.
• Effect of sample size on data volatility and consistency with reference
series is clear as tendency
• Impact of effective sample size on MCD1, MCD2 is achieved also as a
trend, and for the major part of the ESS range – rather strong
• the ESS impact on correlation BCS with reference series is also clear
except the behavior of few biggest samples. It should be probably
analyzed in connection with other factors that influence the quality
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Recommendations
• Revise the way of determining the sample size in the
survey
• Verify the sampling error based on conducted sample
size
• Consider possibility of increase of sample size in some
countries
• Compare similar sample sizes and their likely effects on
data quality
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4. References
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References
1. Glossary of Statistical Terms OECD
2. Särndal, Carl-Erik; Swensson, Bengt; Wretman, (2003). Model assisted
survey sampling. Springer. (Retrieved 2 2011)
3. Israel, Glen D. (1992) Determining Sample Size, Agricultural Education and
Communication Department, University of Florida, IFAS Extension, PEOD6
(Reviewed 2013)
4. Turner, Anthony G. Sampling frames and master samples. United Nations
Secretariat. Retrieved 12/11/2012.
5. Data source: Metadata_checked_by_partners - Consumers.xlsx
6. Cochran, W. G. (1963). Sampling Techniques, 2nd Ed., New York: John
Wiley and Sons, Inc.
7. Kish, Leslie. (1965). Survey Sampling. New York: John Wiley and Sons, Inc.
8. Sudman, Seymour. (1976). Applied Sampling. New York: Academic Press.
9. Yamane, Taro. (1967). Statistics: An Introductory Analysis, 2nd Edition, New
York: Harper and Row.
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