2. Dr. Michael R. Hyman, NMSU Sample Size (Click icon for audio)

3. 2 Relationship Between Sample Size and Error

4. 3 Determine Size for Probability Sample—Practical Issues Financial Statistical Managerial (how confident needed)

5. 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

6. 5 Typical Sample Sizes

7. 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)

8. 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

9. 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

10. 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.

11. 10 Calculation: Example #1

12. 11 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

13. 12 Calculation: Example #2

14. 13 99% Confidence Calculating Sample Size  1389  265.37 2  2 53.74 2        2 )29)(57.2( n 2         347   6325.18 2  4 53.74 2        4 )29)(57.2( n 2       

15. 14 Sample Size for a Proportion

16. 15 2 2 E pqz n  Where: n = number of items in samples Z 2 = square of confidence interval in standard error units p = estimated proportion of success q = (1-p) or estimated the proportion of failures E 2 = square of maximum allowance for error between true proportion and sample proportion, or zs p squared.

17. 16 Calculating Sample Size at the 95% Confidence Level 753  001225. 922.  001225 )24)(.8416.3(  )035(. )4 )(. 6(.) 96 1. ( n 4.q 6.p 2 2   

18. 17