1. Basic Sampling & Review of Statistics

2. Basic Sampling What is a sample?  Selection of a subset of elements from a larger group of objects Why use a sample?  Saves Time Money  Accuracy Lessens non-sampling error

3. Basic Sampling Major definitions  Sample population – entire group of people from whom the researcher needs to obtain information  Sample element -- unit from which information is sought (consumers)  Sampling unit -- elements available for selection during the sampling process (consumers who are in the US at the time of the study)  Sampling frame -- list of all sampling units available for selection to the sample (list of all consumers who are in the US at the time of the study)  Sampling error -- difference between population response and sample response  Non-sampling error – all other errors that emerge during data collection

4. Basic Sampling Procedure for selecting a sample  Define the population – who (or what) we want data from  Identify the sampling frame – those available to get data from  Select a sampling procedure – how we are going to obtain the sample  Determine the sample size (n)  Draw the sample  Collect the data

5. Basic Sampling General Types of Samples  Non-probability – selection of element to be included in final sample is based on judgment of the researcher  Probability – each element of population has a known chance of being selected Selection of element is chosen on the basis of probability  Characteristics of probability samples Calculation of sampling error (+ or - z (  x )) Make inferences to the population as a whole

6. Non-Probability samples Convenience  Sample is defined on the basis of the convenience of the researcher Judgment  Hand-picked sample because elements are thought to be able to provide special insight to the problem at hand Snowball  Respondents are selected on the basis of referrals from other sample elements Often used in more qualitative/ethnographic type studies Quota  Sample chosen such that a specified proportion of elements possessing certain characteristics are approximately the same as the proportion of elements in the universe

7. Probability Samples Simple random sample (SRS)  Assign a number to each sampling unit  Use random number table Systematic Sample  Easy alternative to SRS Stratified sample  Divide population into mutually exclusive strata  Take a SRS from each strata

8. Probability Samples Cluster sample  Divide population into mutually exclusive clusters Select a SRS of clusters One-stage -- measure all members in the cluster Two-stage --measure a SRS within the cluster Area sample  One-stage -- Choose an SRS of blocks in an area; sample everyone on the block  Two-stage -- Choose an SRS of blocks in an area; select an SRS of houses on the block

9. Random Number Table 80147 27404 38749 31272 53703 59853 88288 29540 32340 50499 69466 59448 16059 46226 82283 20995 57976 47035 26741 87624 04973 06042 02837 12450 83611 70130 84015 42358 67330 65857 96833 03905 09246 93224 41290 70534 56244 25672 90829 95360 34881 89760 98565 25268 45158 85488 11382 86815 60516 12855 55839 53444 07514 71861 05378 78270 86152 35949 86556 08178 96428 31677 25932 69725 11787 59044 43831 36354 58785 91492 19927 61180 37422 55580 01105 91088 47699 51308 13923 52635 63057 78675 58380 19264 36613 37681 34477 44090 88692 01769 15655 73998 98969 97496 28472 35545 40885 24863 72929 02174

10. Hypothetical Sample Populations Responden t Number Income ($,000) Education (Years) Yogurt Consumptio n (Cartons/Yea r) Satisfaction Level (1 – 7) City 1568731Madison 260933Milwaukee 36411955Milwaukee 46811714Milwaukee 57211866Madison 67612402Milwaukee 78012217Madison 88412817Madison 98812657Madison 109212447Milwaukee 119613804Other 1210013125Madison 1310414432Milwaukee 1410814564Milwaukee 1511215357Madison 1611616171Other 1712016723Milwaukee 1812417703Milwaukee 1912818807Madison 2013220154Madison

11. Review of Statistics Probability Samples – note that statistical error can be computed when they are used  Thus, need to know about statistics Descriptive statistics  Estimates of descriptions of a population Statistical terms used in sampling  Mean (  or x  x i /n  Variance (  2 or s 2 ) --  x i -x) 2 /n - 1  Standard Deviation (  or s) – Square Root (Variance)

12. Review of Statistics Inferential Statistics  Terms Parameter --  Statistic -- x  Sample Statistics Best estimate of population parameter Why? -- Central Limit Theorem

13. Review of Statistics Central Limit Theorem  Based on the distribution of the means of numerous samples Sampling Distribution of Means  Theorem states: as sample size (n) approaches infinity (gets large), the sampling distribution of means becomes normally distributed with mean (  ) and standard deviation (  √  n) Allows the calculation of sampling error ( s  √  n)  Thus a confidence interval can be calculated

14. Review of Statistics Confidence interval -- tells us how close, based on n and the sampling procedure, how close the sampling mean (x) is to the population mean (  )  Formula: x - z (  x ) < (  ) < x + z (  x )  z-values: 90% -- 1.28 95% -- 1.96 99% -- 2.58

15. Review of Statistics Confidence interval -- interpretation  For the same sampling procedure, 95 out 100 calculated confidence intervals would include the true mean (  )

16. Sample Size Sample size and total error  Larger n increases probability of non-sampling error  Larger n reduces sampling error (  √  n)  Effect on n on total error?  Can pre-determine the level of error (by setting n) Depends mainly on the method of analysis

17. Sample Size Sample size when research objective is estimate a population parameter  CI = x ± z S x  CI = x ± 1.96 (s/ √n)  n = x ± z 2 s 2 / h 2  n = (1.96) 2 s 2 / h 2  n = (3.84) s 2 / h 2 s = expected standard deviation h = absolute precision of the estimate (or with of the desired confidence interval)

18. Sample Size (Sample Exercise) n = (1.96) 2 s 2 / h 2  S = 7.5  h =.50 n = (3.84) (56.25)/.025 n = 216/.025 n = 8640 What if s = 10; h = 1  n = (3.84) (100)/1  n = 384

19. Sample Size (Conclusion) Unaffected by size of universe Affected by  Choice of Desired Precision of Confidence Interval  Estimate of standard deviation

20. Sample Size Sample size estimation  With cross-tabulation based research  Objective is to get a minimum of 25 subjects per cell  Must estimate relationship up front – what is smallest cell <3030+Total Fem.25.35.60 Male.30Small est (.10).40 Total.55.45

21. Sample Size Know smallest cell size should be 25 Calculate Total Sample size 25 is 10% of sample Total Sample size  25 =.10 n  25/.10 = n  250 = n <3030+Total Fem Male25 Total