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Sample Size

Sample Size. Relationship Between Sample Size and Error. Determine Size for Probability Sample—Practical Issues. Financial Statistical Managerial (how confident needed). Ways to Determine Sample Size. Blind guess Available budget Bayesian considerations Rules of thumb

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Sample Size

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  1. Sample Size Dr. Michael R. Hyman, NMSU

  2. Relationship Between Sample Size and Error

  3. Determine Size for Probability Sample—Practical Issues • Financial • Statistical • Managerial (how confident needed)

  4. 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

  5. Typical Sample Sizes

  6. 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)

  7. Online Sampling Calculators From DSS Research: • Sample Size http://www.dssresearch.com/toolkit/sscalc/size.asp • Sample Error http://www.dssresearch.com/toolkit/secalc/error.asp

  8. Sample Size Formula where: n = sample size z = confidence interval in standard error units s = standard error of the mean E = acceptable magnitude of error

  9. 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.

  10. Calculation: Example #1

  11. Sample Size Formula:Example #2 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?

  12. Calculation: Example #2

  13. 2 2 é ù é ù ( 2 . 57 )( 29 ) ( 2 . 57 )( 29 ) = = n n ê ú ê ú 4 2 ë û ë û 2 2 é ù é ù 74 . 53 74 . 53 = = ê ú ê ú 4 2 ë û ë û ] [ [ ] 2 2 = = 6325 18 . 37 . 265 = = 347 1389 Calculating Sample Size 99% Confidence

  14. Sample Size for a Proportion

  15. 2 z pq = n 2 E Where: 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.

  16. = p . 6 2 ( 96 )(. 1. ) (. 6 4 ) = n = ( . 035 ) 2 q . 4 ( 3 . 8416 )(. 24 ) = 001225 . 922 = . 001225 = 753 Calculating Sample Size at the 95% Confidence Level

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