Understanding Sampling Methods and Protecting Against Bias

1. Section 4.2 Random Sampling

2. Quiz 4.1 – 4.2 -- no notes

3. Is bias in our sampling method good or bad? Explain.

4. If sample selection bias is present in a sampling method, samples tend to result in estimates of population parameters that systematically are too high or too low.

5. Protecting Against Bias • Selecting your sample by chance is the only methodguaranteed to be unbiased.

6. Protecting Against Bias Probability sample: each unit in population has fixed probability of being in the sample

7. Types of Probability Samples

8. Types of Probability Samples • Simple Random Sample (SRS)

9. Types of Probability Samples • Simple Random Sample (SRS) • Stratified Random Sample

10. Types of Probability Samples • Simple Random Sample (SRS) • Stratified Random Sample • Cluster Sample

11. Types of Probability Samples • Simple Random Sample (SRS) • Stratified Random Sample • Cluster Sample • Two-Stage Cluster Sample

12. Types of Probability Samples Simple Random Sample (SRS) Stratified Random Sample Cluster Sample Two-Stage Cluster Sample Systematic Sampling with Random Start

13. Simple Random Sample • Simple random sampling: all possible samples of a given fixed size are equally likely.

14. Simple Random Sample • Simple random sampling: all possible samples of a given fixed size are equally likely. • all units have the same chance of belonging to the sample

15. Simple Random Sample • Simple random sampling: all possible samples of a given fixed size are equally likely. • all units have the same chance of belonging to the sample • all possible pairs of units have the same chance of belonging to the sample

16. Simple Random Sample • Simple random sampling: all possible samples of a given fixed size are equally likely. • all units have the same chance of belonging to the sample • all possible pairs of units have the same chance of belonging to the sample • all possible triples of units have the same chance, and so on

17. Choosing a Simple Random Sample Steps: 1.  Start with a list of all the units in the population (list is known as a sampling frame).

18. Choosing a Simple Random Sample Steps: 1.  Start with a list of all the units in the population (list is known as a frame). 2.  Number the units in the list.

19. Choosing a Simple Random Sample Steps: 1.  Start with a list of all the units in the population (list is known as a frame). 2.  Number the units in the list. 3.  Use a random number table or generator to choose units from the numbered list, one at a time, until you have as many as you need

20. Choosing a Simple Random Sample • random number table: see page 828

21. Choosing a Simple Random Sample random number generator (calculator): To generate random integers between 0 and 99: • Press MATH • Arrow right to select PRB • Arrow down to select 5: randInt( • Enter expression randInt( 0, 99) • Press ENTER to generate as many integers as needed

22. Choosing a Simple Random Sample Display 4.8, page 240

23. Stratified Random Sampling Steps: •  Divide the units of the entire sampling frame into non-overlapping subgroups. -- Make strata as different as possible

24. Stratified Random Sampling Steps: •  Divide the units of the entire sampling frame into non-overlapping subgroups. -- Make strata as different as possible • Take a simple random sample from each subgroup -- Allocate units in sample proportionally to number of units in the strata

25. Stratified Random Sampling

26. Stratified Random Sampling 32 Females 16 Males

27. Why Stratify? • Easier to sample in smaller, compact groups than in one large population

28. Why Stratify? • Easier to sample in smaller, compact groups than in one large population • Coverage of each stratum is ensured

29. Why Stratify? • Easier to sample in smaller, compact groups than in one large population • Coverage of each stratum is ensured • Precision of results may be improved. • Fundamental statistical reason for stratification

30. Problems?? May encounter problems using simple random samples and stratified random samples. Sampling individual units from population one at a time is often: • too costly • too time consuming • simply not possible if a good frame is not available

31. Solution • Form larger sampling units out of groups of population units

32. Cluster Sampling Steps: • Create a numbered list of all the clusters in your population.

33. Cluster Sampling Steps: • Create a numbered list of all the clusters in your population. • Take a simple random sample of clusters.

34. Cluster Sampling Steps: • Create a numbered list of all the clusters in your population. • Take a simple random sample of clusters. • Obtain data on each individual in each cluster in your SRS

35. Cluster Sampling

36. Two-Stage Cluster Sampling Steps: • Create a numbered list of all the clusters in your population, and then take a simple random sample of clusters.

37. Two-Stage Cluster Sampling Steps: • Create a numbered list of all the clusters in your population, and then take a simple random sample of clusters. • Create a numbered list of all the individuals in each cluster already selected, and then take an SRS from each cluster

38. Two-Stage Cluster Sampling

39. Cluster vs Two-Stage Cluster Uses SRS once Uses SRS twice

40. Systematic Sampling with Random Start Steps: •  By a method such as counting off, divide your population into groups of the size you want for your sample.

41. Systematic Sampling with Random Start Steps: •  By a method such as counting off, divide your population into groups of the size you want for your sample. • Use a chance method to choose one of the groups for your sample

42. Systematic Sampling with Random Start

43. To select students to explainhomework problems, a teacher has students count off by 5’s. She then randomly selects an integer from 1 through 5. Every student who counted off that integer is asked to explain a problem. What type of sampling plan is this? A. cluster B. two-stage cluster C. simple random D. stratified random E. systematic with random start

44. To select students to explainhomework problems, a teacher has students count off by 5’s. She then randomly selects an integer from 1 through 5. Every student who counted off that integer is asked to explain a problem. What type of sampling plan is this? A. cluster B. two-stage cluster C. simple random D. stratified random E. systematic with random start

45. Questions? Selecting your sample by chance is the only methodguaranteed to be unbiased

46. Fathom Activity 4.2a Complete steps 1 and 2 before you come to class tomorrow.