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# Chapter 4

Chapter 4. Sampling and Generalizability. CHAPTER OVERVIEW. Populations and Samples Probability Sampling Strategies Nonprobability Sampling Strategies Sampling, Sample Size, and Sampling Error. POPULATIONS AND SAMPLES. Inferential method is based on inferring from a sample to a population

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## Chapter 4

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1. Chapter 4 Sampling and Generalizability

2. CHAPTER OVERVIEW • Populations and Samples • Probability Sampling Strategies • Nonprobability Sampling Strategies • Sampling, Sample Size, and Sampling Error

3. POPULATIONS AND SAMPLES • 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

4. 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

5. 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

6. CHOOSING A SIMPLE RANDOM SAMPLE • Define the population • List all members of the population • Assign numbers to each member of the population • Use criterion to select a sample

7. 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 • Select a starting point • The first two digit number is 68 (not used) • The next number, 48, is used • Continue until sample is complete

8. 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!!

9. USING THE COMPUTER TO GENERATE RANDOM SAMPLES Those not selected have a diagonal line through the case (or record) number. There are ten participants selected in this example. The example uses SPSS, but any capable data analysis tool can produce a random sample.

10. SYSTEMATIC SAMPLING • Divide the population by the size of the desired sample: e.g., 50/10 = 5 • Select a starting point at random: e.g., 43 = Heather • Select every 5th name from the starting point

11. 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

12. 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)

13. STRATIFICATION ON MORE THAN ONE FACTOR

14. 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

15. 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

16. Summary of the different types of probability and nonprobability strategies

17. 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

18. 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

19. 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

20. HAVE WE MET THE OBJECTIVES? CAN YOU: • Apply the following concepts? • Population • Sample • Random • Generalization (generalizability) • Differentiate between probability and nonprobability sampling techniques?

21. OBJECTIVES, CONTINUEDCAN YOU: • Identify four (4) probability sampling strategies? • Simple Random Sampling • Systematic Sampling • Stratified Sampling • Cluster Sampling • Identify two (2) nonprobability sampling strategies? • Convenience Sampling • Quota Sampling

22. OBJECTIVES, CONTINUEDCAN YOU: • Explain sampling error? • List ways researchers can reduce sampling error • Summarize the effect of sample size on sampling error

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