Dr. Michael R. Hyman, NMSU

Sample Size

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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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