Sample Size Dr Michael R Hyman NMSU Relationship

Sample Size Dr. Michael R. Hyman, NMSU

Relationship Between Sample Size and Error 2

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

Ways to Determine Sample Size • • Blind guess Available budget Bayesian considerations Rules of thumb – Main group – Subgroups n > 100 20 < n < 100 • Standards for comparable studies • Statistical precision 4

Typical Sample Sizes 5

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) 6

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 7

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 8

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. 9

Calculation: Example #1 10

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? 11

Calculation: Example #2 12

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

Sample Size for a Proportion 14

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

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

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