CHAPTER OVERVIEW

• Populations and Samples• Probability Sampling Strategies• Nonprobability Sampling Strategies• Sampling, Sample Size, and

Sampling Error

SAMPLES AND POPULATIONS

• Inferential method is based on inferring from a sample to a population

• Sample—a representative subset of the population

• Population—the entire set of participants of interest

• Generalizability—the ability to infer population characteristics based on the sample

CHOOSING A REPRESENTATIVE SAMPLE

• Probability sampling—the likelihood of any member of the population being selected is known

• Nonprobability sampling--the likelihood of any member of the population being selected is unknown

PROBABILITY SAMPLING STRATEGIES

• Simple random sampling– Each member of the population has

an equal and independent chance of being chosen

– The sample should be very representative of the population

1. Jane 18. Steve 35. Fred

2. Bill 19. Sam 36. Mike

3. Harriet 20. Marvin 37. Doug

4. Leni 21. Ed. T. 38. Ed M.

5. Micah 22. Jerry 39. Tom

6. Sara 23. Chitra 40. Mike G.

7. Terri 24. Clenna 41. Nathan

8. Joan 25. Misty 42. Peggy

9. Jim 26. Cindy 43. Heather

10. Terrill 27. Sy 44. Debbie

11. Susie 28. Phyllis 45. Cheryl

12. Nona 29. Jerry 46. Wes

13. Doug 30. Harry 47. Genna

14. John S. 31. Dana 48. Ellie

15. Bruce A.

32. Bruce M.

49. Alex

16. Larry 33. Daphne 50. John D.

17. Bob 34. Phil

1. Define the population

2. List all members of population

3. Assign numbers to each member of population

4. Use criterion to select sample

CHOOSING A SIMPLE RANDOM SAMPLE

1. Select a starting point

2. The first two digit number is 68 (not used)

3. The next number, 48, is used

4. Continue until sample is complete

23157 48559 01837 25993

05545 50430

10537 43508

14871 03650 32404 36223

38976 49751 94051 75853

97312 17618 99755 30870

11742 69183 44339 47512

43361 82859 11016 45623

93806 04338

38268 04491

49540 31181 08429 84187

36768 76233 37948 21569

  

USING A TABLE OF RANDOM NUMBERS

KEYS TO SUCCESS IN SIMPLE RANDOM SAMPLING

• Distribution of numbers in table is random

• Members of population are listed randomly

• Selection criterion should not be related to factor of interest!!

USING SPSS TO GENERATE RANDOM SAMPLES

1. Be sure that you’re in a data file

2. Click Data > Select Cases

3. Click Random sample of Cases

4. Click the Sample Button

5. Define Sample Sizea. Click Continueb. Click OK (in next

dialog box)

1. Divide the population by the size of the desired sample: e.g., 50/10 = 5

2. Select a starting point at random: e.g., 43 = Heather

3. Select every 5th name from the starting point

SYSTEMATIC SAMPLING1. Jane 18. Steve 35. Fred

2. Bill 19. Sam 36. Mike

3. Harriet 20. Marvin 37. Doug

4. Leni 21. Ed. T. 38. Ed M.

5. Micah 22. Jerry 39. Tom

6. Sara 23. Chitra 40. Mike G.

7. Terri 24. Clenna 41. Nathan

8. Joan 25. Misty 42. Peggy

9. Jim 26. Cindy 43. Heather

10. Terrill 27. Sy 44. Debbie

11. Susie 28. Phyllis 45. Cheryl

12. Nona 29. Jerry 46. Wes

13. Doug 30. Harry 47. Genna

14. John S. 31. Dana 48. Ellie

15. Bruce A.

32. Bruce M.

49. Alex

16. Larry 33. Daphne 50. John D.

17. Bob 34. Phil

STRATIFIED SAMPLING• The goal of sampling is to select a

sample that is representative of the population

• But suppose—– That people in the population differ

systematically along some characteristic? – And this characteristic relates to the

factors being studied?• Then stratified sampling is one

solution

STRATIFIED SAMPLING

• The characteristic(s) of interest are identified (e.g., gender)

• The individuals in the population are listed separately according to their classification (e.g., females and males)

• The proportional representation of each class is determined (e.g., 40% females & 60% males)

• A random sample is selected that reflects the proportions in the population, (e.g., 4 females & 6 males)

STRATIFICATION ON MORE THAN ONE FACTOR      

     

Grade

Location 1 3 5 Total

Rural1,200[120]

1,200[120]

600[60]

3,000[300]

Urban2,800[280]

2,800[280]

1,400[140]

7,000[700]

Total4,000[400]

4,000[400]

2,000[200]

10,000[1000]

CLUSTER SAMPLING

• Instead of randomly selecting individuals– Units (groups) of individuals are identified– A random sample of units is then selected– All individuals in each unit are assigned to

one of the treatment conditions

• Units must be homogeneous in order to avoid bias

NONPROBABILITY SAMPLING STRATEGIES• Convenience sampling

– Captive or easily sampled population– Not random– Weak representativeness

• Quota sampling– Proportional stratified sampling is desired

but not possible– Participants with the characteristic of

interest are non-randomly selected until a set quota is met

SAMPLES, SAMPLE SIZE, AND SAMPLING ERROR• Sampling error = difference

between sample and population characteristics

• Reducing sampling error is the goal of any sampling technique

• As sample size increases, sampling error decreases

HOW BIG IS BIG?

• The goal is to select a representative sample—– Larger samples are usually more

representative– But larger samples are also more

expensive – And larger samples ignore the power

of scientific inference

ESTIMATING SAMPLE SIZE• Generally, larger samples are needed

when– Variability within each group is great– Differences between groups are smaller

• Because– As a group becomes more diverse, more data

points are needed to represent the group– As the difference between groups becomes

smaller, more participants are needed to reach “critical mass” to detect the difference