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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e. Chapter 6: Samples and Populations. HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 3/31/2014, Spring 2014. CHAPTER OBJECTIVES. 6 .1. Distinguish between populations and samples. 6 .2.

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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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  1. Fox/Levin/Forde, Elementary Statistics in Social Research, 12e • Chapter 6: Samples and Populations HLTH 300 Biostatistics for Public Health Practice,Raul Cruz-Cano, Ph.D. 3/31/2014, Spring 2014

  2. CHAPTER OBJECTIVES 6.1 • Distinguish between populations and samples 6.2 • Describe the methods of random and nonrandom sampling 6.3 • Understand the concept of sampling error • Understand the characteristics of the sampling distribution of means 6.4 6.5 • Calculate confidence intervals

  3. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 6.1 Distinguish between populations and samples

  4. 6.1 Populations and Samples Population (or universe) – a group of a set of individuals that share at least one characteristic Sample – a small number of individuals from the population Social researchers generally are not able to measure an entire population • Limited by time and resources Sampling allows researchers to generalize Population sample

  5. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 6.2 Describe the methods of random and nonrandom sampling

  6. 6.2 Sampling Random Sampling Nonrandom Sampling vs. Every member of the population has the same chance of being included Every member of the population does not have the same chance of being included

  7. 6.2 Nonrandom Sampling • Accidental or Convenience • The sample is based on what is convenient for the researcher • Quota • The sample is drawn in proportion to the population • Judgment or Purposive • The sample is drawn according to logic, common sense, or judgment

  8. 6.2 Random Sampling • Simple Random • Similar to drawing numbers from a hat • Systematic • Every nth member is included • Stratified • Divides the population into homogenous subgroups and then samples • Cluster or Multistage • Samples are drawn at different levels

  9. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 6.3 Understand the concept of sampling error

  10. 6.3 Sampling Error By chance alone, we can always expect some difference between a sample and the population from which it is drawn We use different symbols for samples as compared to populations

  11. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 6.4 Understand the characteristics of the sampling distribution of means

  12. 6.4 Sampling Distribution of Means A frequency distribution of a large number of random sample means that have been drawn from the same population Characteristics of the Sampling Distribution of Means: • The sampling distribution of means approximates a normal curve • The mean of the sample distribution of means (the mean of means) is equal to the true population mean • The standard deviation of a sampling distribution of means is smaller than the standard deviation of the population

  13. 6.4 Figure 6.3

  14. 6.4 If you have enough data then this is true regardless of the distribution of X! Figure 6.4

  15. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 6.5 Calculate confidence intervals

  16. 6.5 Figure 6.6

  17. 6.5 Standard Error of the Mean The standard deviation of the sampling distribution of means

  18. 6.5 Confidence Intervals The range of mean values within which the population mean is likely to fall • Confidence intervals can be calculated at different levels: How sure do you want to be?

  19. Figure 6.8

  20. 6.5 The t Distribution Rarely do we actually know the standard deviation of the population • This makes it impossible to calculate the standard error of the mean • But we can estimate it:

  21. 6.5 The t Distribution Continued • When we use the sample standard deviation (and not the population standard deviation) the distribution is not normal • We have to use the t distribution instead of the z distribution • The value of t can be found in Table C

  22. 6.5 Figure 6.9

  23. Small Sample Size Example Basically, we just follow the steps in pages 201-203 Find sample mean from raw data (Chapter 3) Calculate standard deviation of the sample from raw data (Chapter 4) Estimate standard error of the mean: divide 2) by SQRT(N-1) Determine t (use Table C in page 552) Obtain Margin of Error: Multiply 3) by 4) Add and subtract 5) from 1) Let’s find CI for data in Problem 12

  24. Large Sample Size Example We just follow the steps in pages 204-206 (We will concentrate in the cases where sample mean and standard deviation are given, hence we begin in Step 3) Find sample mean from frequency table(Chapter 3) Calculate standard deviation of the sample from a frequency table (Chapter 4) Estimate standard error of the mean: divide 2) by SQRT(N-1) Determine t(use closest of the last rows of Table C in page 552) Obtain Margin of Error: Multiply 3) by 4) Add and subtract 5) from 1) Let’s solve Problem 21

  25. 6.5 Estimating Proportions The same rationality is used to estimate population proportions • The only difference is that we use the z distribution as opposed to the t distribution used to estimate population means In other words, you just need the proportion to find the sample mean and standard error of the proportion

  26. Proportion Examples We just follow the steps in pages 208-209 Estimate standard error of the mean (previous slide = 1 formula in page 207) Determine t(use last row of Table C in page 552) Obtain Margin of Error: Multiply 1) by 2) Add and subtract 3) from the given p Let’s solve Problem 34!

  27. More Examples Problem 9, 26 and 29

  28. CI’s can be used for hypothesis testing for a single variable vs. a constant

  29. HW#6 Problem 13, 27 and 30

  30. CHAPTER SUMMARY • Samples are drawn from populations and can be used to generalize findings 6.1 • Several forms of random and nonrandom sampling methods are used in the social sciences 6.2 • Due to random chance, the sample will differ from the population. This is referred to as sampling error 6.3 • The sampling distribution of means has several important characteristics that allow researchers to generalize their findings 6.4 • The specific method used to calculate a confidence interval is determined by whether the researcher knows the population standard deviation and whether means or proportions are being estimated 6.5

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