Sampling-big picture Want to estimate a characteristic of population (population parameter). Estimate a corresponding sample statistic Sample must be representative of population on variable(s) of interest Sampling error is probability of getting an un-representative sample by chance Sample may be biased if not drawn properly

Sampling Always define study population first Use element/unit/extent/time for complete definition element - who is interviewed sampling unit - basic unit containing elements extent - limit population (often spatially) time - fix population in time

Examples element, unit, extent, time Adults 12 and older in vehicles entering Yogi Bear Park between July 1 and Aug 31, 1998 Teenagers (13-18) in households in Lansing, MI during May 1996

Steps in Sampling Define study population Specify sampling frame and unit Specify sampling method Determine sample size Specify sampling plan Choose sample

Sampling methods Probability vs non-probability ( Does each element of population have known chance of being selected?) Simple random sample or Systematic sample (equal probability) (choose every nth element ) Stratified vs Cluster Sample group elements and sample from groups –stratified: choose some from every group –cluster: only some groups sampled

Non-probability sampling Convenience Judgement Purposive Quota Snowball

Prob or Non-prob Sample? Project/generalize results to population - prob Quantitative estimate of sampling error - prob Accuracy needed & relative magnitude of sampling vs other kinds of errors Homo- or hetero-geneous population Overall Costs vs benefits

Stratify vs Cluster Stratify to ensure enough samples from subgroups & to lower sampling error Cluster primarily to reduce costs of gathering the data Form homogeneous groups when stratifying, heterogeneous when clustering Proportionate vs disproportionate sample Stratification variables

Sample size Based on four factors Cost/budget Accuracy desired variance in popln on variable of interest subgroup analysis planned Formula: n= Z 2  2 / e 2 n= sample size Z indicates confidence level (95% = 1.96)  = standard deviation of variable in population e = sampling error

Sampling error formula n = Z 2  2 / e 2 1. Solve for e to express error as a function of sample size, confidence level, and variance: e = (Z *  ) / SQRT ( n ) 2. For binomial,  = sqrt (p(1-p)), where p is proportion for “yes” in the population Generate numbers in binomial sampling error table as: [1.96 *sqrt( p * (1-p)) ]/ sqrt (n)

Sampling errors for binomial (95% confidence interval) percent distribution in population

Computing 95% confidence interval N= 100, sample mean = 46%, use p= 50/50, sampling error from table = 10% 95% CI is 46% + or - 10% = (36, 56) N=1,000 sample mean =22% sampling error from table = 2.5% 95% CI is 22% + or - 2.5% = (19.5, 24.5)