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 method guaranteed 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 explain homework 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 explain homework 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 method guaranteed to be unbiased

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