Sampling Sampling is used instead of a census Limited Limited Time Reduce Error Only method feasible if element is destroyed or contaminated Definitions Population universe parent population aggregate of all elements from who information is needed defined prior to selection of the sample how we define group we are pulling sample from Extent Basically geography but may include other elements e g NAICS code geography Element object that possesses information sought who Sampling Unit Element or elements available for selection at some stage in the sampling process Elements and sampling unit may be the same one stage UG alumni 90 99 living in the U S Elements and sampling unit may differ multiple stage Sampling Frame Representation of the elements of the target population set of instructions for identifying elements or list of all the sampling units available for selection may have multiple frames what you pull your information from i e phonebook Time Time period when sampling took place Basic Steps Define the target population all definitions Determine the sampling frame Select a sampling technique Determine the sample size Select the sample elements Nonprobability Sampling Types 1 Convenience Sample Subjects are convenient No measure of sampling error Cannot make definitive or conclusive statements about the results 2 Judgment Purposive Sample An expert believes particular elements will provide relevant info No sampling error not definitive Quality depends on who is sampled Text page 511 bellwether precincts selected in voting behavior research 3 Quota Sample special type of purposive what we are doing Obtain a sample that is similar to the population on some pre specified control characteristics Cell Assignment up to date The right control characteristics Number of control characteristics interviewer bias Can provide definitive answers 4 Snowball Sample Initial group of respondents selected randomly Subsequent respondent are selected from referrals or information provided by initial respondents Useful if incidence rate is low Chapter 16 Probability Sampling Probability Sampling Each element has a fixed probabilistic chance of being selected the probability is known and the sample elements are selected by means of mechanical decision rules Trade off between sampling cost and precision Guarantees No but researcher can assess sampling error 1 Simple Random Sampling A known and equal chance of inclusion Every combination of n population elements is as likely to occur as any other n elements Example Use lists of random numbers p 752 by themselves and also in combination with telephone prefixes Random Digit Dialing RDD 2 Stratified Sampling What we are Doing Population divided into mutually exclusive just 1 group and exhaustive strata have to put EVERYONE in a group Simple random sample of elements is chosen independently from each strata Individual strata are homogeneous high school education income 20K etc Every possible combination is not possible Representation increase precision hold cost 3 Cluster Sampling Grade School Count off by 5 Population divided into mutually exclusive and exhaustive clusters Simple random sample of clusters is selected Details One stage Two stage Area Sampling Clusters are to be as heterogeneous as the population use all elements in selected subsets sample of elements is selected probabilistically from subsets Systematic sampling sampling of blocks every ith element Statistical inference Definitions Statistical Inference Process of generalizing sample results to the population Sampling Distribution Distribution of the values of a sample statistic computed for each possible sample that could be drawn Normal Distribution Bell Shaped Symmetrical Centl equal Central Limit Theorem Population Normal sampling distribution of the mean normal for all n Population Non Normal Income sampling distribution of mean becomes normal as n increases Mean of sampling distribution is population mean Standard deviation of sampling distribution is pop Standard dev square root of n standard error of the mean Importance of C L T standard deviation indicates spread of distribution Standard deviation of sampling distribution is known Confidence Interval Mean X bar or Z sx Determining Sample Size Importance of the decision Factors Nature of the Research Number of variables Nature of analysis including confidence intervals Sample Sizes used in similar studies Incidence rate Completion Rates Resource Constraints Sampling Procedures Components Parameter Statistic Characteristic summary description of a target population true value that would be obtained from a census Characteristic summary description of summary Symbols Population Sample Size of group s N n Mean u X bar over it Variance o 2 s 2 Std Dev o s Yes 3 14 p No 1 3 14 1 p or q Dispersion of Sampling distribution Standard error of the mean Random error associated with estimate Variance unknown is o square root of n Variance known is s square root of n Degree of Confidence Desired 90 95 99 99 9 Desired precision of error 95 z 1 96 round to 2 for these calculations Standard Error ox or s x bar Confidence Precision Or 35 Total precision 70 Half precision D 35 Unknown o need to estimate past study that is similar pilot study for a normally distributed variable the range is 3 standard deviations estimate range and divide by 6 Control Characteristics Women Men 29 5 5 16 4 6 46 22 Women 53 78 Men 23 161 includes post bacs and non degree UG students