In unit 1, our task was to summarize the information in a sample. There was no consideration of the source of the data. We didn’t ask “what population did these data come from?”, “how was the data obtained?”, nor “was random sampling used”? In unit 1, Summarizing Data: Now, let’s step back.Consider the source of our “sample.” It’s a population, but what population? Is the sample “representative?” Can we use the conclusions drawn from our sample to say anything about the source population from which the sample came?The 1948 Gallup PollSampling FramesTo Construct a Sampling Frame RequiresTarget PopulationExample – an NIH Funded Randomized TrialNow You Try …Example of Simple Random SamplingThe following is true for the population of size N=6Sampling ProcedureCalculation for Each Sample (1) QuotaLimitations of a Non-Probability Sampling PlanThus, we need to solve for the number of equally likely samples! How many Equally Likely Samples Are there? a. Simple Random Sampling With ReplacementExample – How many equally likely samples are there?PopulationSampling PlanWhat if the Order of the Sample Doesn’t Matter?Example of an Unordered Sample – Example – How many equally likely samples are there?PopulationSampling PlanSimple Random Sampling WITHOUT ReplacementIF Order DOES MatterIF Order Does NOT Matterb. How to Select a Simple Random Sample WITHOUT ReplacementWith each row, if the required digits are > N, PASS BYWith each row, if the required digits are a repeat of a previous selection, PASS BYRepeat “Step 5” a total of n=30 times, which is your desired sample size.Remarks on Simple Random Samplinga. Systematic SamplingRemarks on Systematic SamplingRemarks on Stratified Sampling Stratumc. Multi-Stage Sampling10. The Nationwide Inpatient Survey (NIS)Sampling Designs Can Be Quite Complex All discharges All dischargesPubHlth 540 – Fall 2011 3. Populations and Samples Page 1 of 36 Nature Sample Observation/ Data Relationships/ Modeling Analysis/ Synthesis Population/ Unit 3 Populations and Samples “To all the ladies present and some of those absent” - Jerzy Neyman The collection of all individuals with HIV infection and the collection of all individuals with exposure to mercury are examples of populations about which we wish to make inferences. A census is one way to obtain information about a population but is usually impractical because it requires the collection of data for every individual in the population. Instead, typically, we study a fraction of the population called a sample. If the sample is representative of the population, then quantities computed from available data in the sample are reasonable estimates of the corresponding, but unavailable, quantities in the population. A sample is not a replica of the population of interest. Thus, the goal of sampling is to obtain a representative sample such that the inferences drawn from the sample are in error by as little as possible.PubHlth 540 – Fall 2011 3. Populations and Samples Page 2 of 36 Nature Sample Observation/ Data Relationships/ Modeling Analysis/ Synthesis Population/ Table of Contents Topics 1. Unit Roadmap ………………………………………………………. 2. Learning Objectives …………………………………………………. 3. A Feeling for Populations v Samples ………………………………... 4. Target Populations, Sampled Populations, Sampling Frames ………. 5. On Making Inferences from a Sample ……………………..……… 6. Simple Random Sampling ………………….………………..………. 7. Some Non-Probability Sampling Plans ……………………….…….. 8. More on Simple Random Sampling ……..………………………….. a. Sampling WITH v WITHOUT replacement …………….… b. How to select a simple random sample ……………………... 9. Some Other Probability Sampling Plans ………………………..…… a. Systematic ………………………………………………..….. b. Stratified ……………………………………………………… C. Multi-stage …………………………………………………… 10. The Nationwide Inpatient Survey (NIS) …………………………... 3 4 5 8 11 13 16 19 20 28 31 31 33 35 36PubHlth 540 – Fall 2011 3. Populations and Samples Page 3 of 36 Nature Sample Observation/ Data Relationships/ Modeling Analysis/ Synthesis Population/ 1. Unit Roadmap Nature/ Populations Unit 3. Populations and Samples Sample Representative - Glance again at the roadmap at the footer of this page. We’re headed to estimation and hypothesis tests of data in samples. We hope that the conclusions drawn from these reasonably apply to the population as well. For this to be possible at all, the sample must be representative. Minimum Variance – A conclusion drawn from a sample will differ from the reality of the population. This is sampling error. An additional goal of sampling is to obtain a sample for which sampling error is minimized. Observation/ Data Relationships Modeling Analysis/ SynthesisPubHlth 540 – Fall 2011 3. Populations and Samples Page 4 of 36 Nature Sample Observation/ Data Relationships/ Modeling Analysis/ Synthesis Population/ 2. Learning Objectives When you have finished this unit, you should be able to:  Explain the distinction between target population, sampled population, and sample.  Explain why it is important that a sample should be representative of the population from which it is taken.  Explain the rationale for choosing a sampling method that minimizes sampling error.  Distinguish non-probability versus probability samples.  Define simple random sampling.  Distinguish sampling with versus without replacement.  Explain the rationale for systematic, stratified, and multi-stage sampling methods.  Define systematic, stratified, and