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Sampling

Sampling. Research Process and Design Spring 2006 Class #9 (Week 10). Today’s objectives. To answer any questions you have To describe various sampling approaches To introduce sampling theory and the central limit theorem To discuss concept of standard error and confidence intervals.

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Sampling

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  1. Sampling Research Process and Design Spring 2006 Class #9 (Week 10)

  2. Today’s objectives • To answer any questions you have • To describe various sampling approaches • To introduce sampling theory and the central limit theorem • To discuss concept of standard error and confidence intervals Research Process and Design (Umbach)

  3. Quality perspective (Groves, et al., p. 48) Measurement Representation _ Y Target Population m1 Construct Coverage Error Validity _ yc Measurement Yi Sampling Frame Sampling Error Measurement Error _ ys Sample Response yi Nonresponse Error Processing Error _ yr Respondents Edited Response yip Adjustment Error Postsurvey Adjustments _ yrw _ yprw Survey Statistic Research Process and Design (Umbach)

  4. Representation definitions • Target population - a group of elements or cases that conform to specific criteria; and we intend to generalize the results of the research • Sample frame- a subset of the population; list from which a sample is drawn • Sample - subjects selected from a larger group of people • Respondents – Those successfully measured Research Process and Design (Umbach)

  5. Discussion questions (from Light, Singer, and Willett) • Why do we sample? Why not study the entire population? • What is the ultimate goal of sampling? • What factors should we consider when determining who to sample? Research Process and Design (Umbach)

  6. Nonobservational error • Coverage error • Gap between the target population and the sampling frame • The result of not allowing all members of the survey population to have an equal or nonzero chance of being sampled for participation • People that can never be sampled (telephone survey/no telephone) • Exists before the sample is drawn • Sampling error • Gap between the sampling frame and the sample • The result of surveying only some, and not all, elements of the survey population Research Process and Design (Umbach)

  7. Nonobservational error (continued) • Nonresponse error • Gap between the sample and the respondent pool • People who respond are different than sampled individuals who do not respond in a way relevant to the study • Adjustment error • Statistical adjustments may introduce error in the form of bias or variance Research Process and Design (Umbach)

  8. Two sampling approaches • Probability sample • Each element in the sampling frame has a known and nonzero probability of being selected • Probabilities do not need to be equal • E.g., simple random sample, cluster sample • Non-probability sample • The probability of being selected is unknown Research Process and Design (Umbach)

  9. Non-probability samples • Common terms • Convenience • Purposeful • Snowball • Always to be avoided! • “ … there is no direct theoretical support for using them to describe the characteristics of the larger frame population.” Groves et al. p. 95 Research Process and Design (Umbach)

  10. Probability samples • Simple random • Finite population correction • Cluster • Design effect • Stratified random • Proportionate allocation • Disproportionate allocation What are the strengths and weaknesess of each? Research Process and Design (Umbach)

  11. Group research proposals • What is your population? • How will you sample? • Who will you study? • How will you get access to these people? Research Process and Design (Umbach)

  12. Commonly asked questions? • What do researchers mean when they say “p<.05”? • What is a margin of error of + 3%? • What is a standard error? • How do I determine how large my sample should be? Answers to these questions and more will be covered this week and next!!! Research Process and Design (Umbach)

  13. Probability samples and standard errors • Random selection • Human influence is removed from the selection process • E.g., dice, random number generator • Probability samples use random selection to draw a subset of the sampling frame • Sampling error arises because of this • Standard errors allow us to quantify this error Research Process and Design (Umbach)

  14. Laws of Sampling Theory • Whenever a random sample is taken from a population there will be sampling error. • If sample is truly random, then characteristics of sample will be an unbiased estimate of population characteristics. • As sample size increases, the range (the size) of sampling error decreases. Research Process and Design (Umbach)

  15. Central Limit Theorem • The sampling distribution, or the distribution of the sampling error for any sample drawn from a given population, approximates a normal curve. • Standard error - standard deviation of the sample estimates of means that would be formed if an infinite number of samples. Research Process and Design (Umbach)

  16. Standard error • Relies on the concept of repeated samples from a population • Due to chance, the means of these samples will vary around the population mean • We can measure this variance and determine how much the typical sample will deviate from the population mean (i.e., the standard deviation or SD) • This SD is the standard error (SE) • http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html Research Process and Design (Umbach)

  17. Standard errors • Standard error of the mean: • s is the SD from our sample; n is sample size • We can see that as n increases, SE decreases • Different formulas for different statistics (proportions, comparing two means, etc.), but they have a similar form Research Process and Design (Umbach)

  18. Confidence Intervals • The range within which the parameter in question could be expected to be included a specified percentage of the time if procedure were to be repeated. C = Z statistic associated with the confidence level; 1.96 corresponds to the .95%, 2.33 corresponds to the 98% level, and 2.58 corresponds to the 99% confidence level Research Process and Design (Umbach)

  19. Standard errors • Confidence intervals (CI) use SE and tell us the precision of our estimates • 95% CI for a mean = • Very specific definition: if we calculated similar CIs on 100 similar samples, 95% of them would bracket the population parameter • Does not mean there is a 95% probability that population parameter falls in your CI – either it does or it doesn’t • http://www.ruf.rice.edu/~lane/stat_sim/conf_interval/ Research Process and Design (Umbach)

  20. Standard errors • Margin of error in polls is a confidence interval, usually a 95% CI Research Process and Design (Umbach)

  21. How large a sample? • Usually depends on resources • When doing surveys, don’t forget to take into account nonresponse • Sample size calculator (courtesy of Mike Valiga, ACT) Can be found at http://www.uiowa.edu/~c07b209/SampleSize_CI_calc.xls • Countless websites (e.g., http://www.surveysystem.com/sscalc.htm) Research Process and Design (Umbach)

  22. For next week… • Hypothesis testing and inferential statistics • Readings for next week: • Jaeger – Chapters 7-10 • Assignment due: One page description of method. Bring 3 copies to class. Research Process and Design (Umbach)

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