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Dr. Michael R. Hyman, NMSU
Sample Size
(Click icon for audio)
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Relationship Between Sample Size and Error
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Determine Size for Probability Sample—Practical Issues
• Financial
• Statistical
• Managerial (how confident needed)
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Ways to Determine Sample Size
• Blind guess
• Available budget
• Bayesian considerations
• Rules of thumb– Main group n > 100– Subgroups 20 < n < 100
• Standards for comparable studies
• Statistical precision
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Typical Sample Sizes
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Statistical Precision
Must know:
• Variability of population and individual stratum
• Acceptable level of sampling error
• Needed level of confidence
• Type of distribution (if non-normal)
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Online Sampling Calculators
From DSS Research:
• Sample Sizehttp://www.dssresearch.com/toolkit/sscalc/size.asp
• Sample Errorhttp://www.dssresearch.com/toolkit/secalc/error.asp
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Sample Size Formula
2
Ezs
n
where:n = sample sizez = confidence interval in standard error unitss = standard error of the meanE = acceptable magnitude of error
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Sample Size Formula:Example #1
Suppose a survey researcher, studying expenditures on lipstick, wishes to have a 95% confident level (Z) and a range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00.
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2
E
zsn
2
00.2
00.2996.1
2
00.2
84.56
242.28 808
Calculation: Example #1
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Suppose, in the same example as the one before, the range of error (E) is acceptable at $4.00. By how much is sample size is reduced?
Sample Size Formula:Example #2
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2
E
zsn
2
00.4
00.2996.1
2
00.4
84.56
221.14 202
Calculation: Example #2
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99% Confidence
Calculating Sample Size
1389
265.372
253.74
2
2)29)(57.2(n
2
347 6325.18 2
453.74
2
4)29)(57.2(n
2
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2
2
EpqZ
n
Sample Size for a Proportion
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2
2
Epqz
nWhere:
n = number of items in samples
Z2 = square of confidence interval in standard error units
p = estimated proportion of success
q = (1-p) or estimated the proportion of failures
E2 = square of maximum allowance for error between true proportion and sample proportion, or zsp squared.
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Calculating Sample Size at the 95% Confidence Level
753001225.
922.
001225
)24)(.8416.3(
)035( .)4)(.6(.)96 1. (
n4.q
6.p2
2
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