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

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 Sample Error

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 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

12 Calculation: Example #2

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

14 Sample Size for a Proportion

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.

16 Calculating Sample Size at the 95% Confidence Level 753   )24)( (  )035(. )4 )(. 6(.) ( n 4.q 6.p 2 2   

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