Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 7: Sampling

1. Slides to accompany Weathington, Cunningham & Pittenger (2010), Chapter 7: Sampling

2. Objectives • Samples, in general • Probability sampling • Probability sampling methods • Nonprobability sampling • Central Limit Theorem • Applications of CLT • Sources of bias and error

3. Why Worry about Sampling? • Don’t worry, just appreciate it • Objective sampling helps us avoid the Idols of the Cave • Improving external validity of our conclusions • “Good” sampling allows us to make comparisons and predictions from our data

4. Samples... • …are (hopefully) valid representatives of the population you are studying • …can grant you better (more objective, empirical) data than you will find in anecdotes • …allow you to avoid reliance on one person’s opinions, perspectives, and biases

5. Probability Examples • Probability of Heads in one flip of a fair coin: p(H) = 1/2; p(T)=1/2=.5 • p(H and T) in two flips = 2/4=.5 • p(correct answer on 4-option mc question) = .25 • Pr. of choosing a woman in a single random selection from a class of 223 students with 150 women: p(w)=150/223=.673

6. Probability Sampling • Random: each outcome has an equal probability of occurring, every time • Every time I flip a coin, the probability is .5 that it will be H or T • Random sampling depends on this independence of outcomes • Law of large numbers: On average, a large selection of items will have the same characteristics as those in the population

7. Populations and Samples • Target vs. sampling population • Target: (universe) e.g. all depressed persons • Sampling: (accessible) all diagnosed as depressed • Sampling Frame (all who can be reached) • Subject (participant pool) – (willing to participate) • Descriptive data helps us compare our sample against the population • External validity depends largely on representativeness in sampling

8. Probability Sampling Characteristics • Each population member has an equal chance of being a potential sample member • No systematic exclusions • Sampling procedures are based on a protocol • Prevents bias effects on sample selection • Probability of any specific sample can be calculated • Helps connect results with population

9. Simple Random Sampling • Each population member has equal probability of selection to the sample • If selection is random, the sample of any size should represent the population from which it was chosen • Random numbers are in tables and Excel-type computer programs

10. Simple Random Sampling: How-To • Generate a list of possible participants (population) in Microsoft Excel • In the next column insert the function “=RAND()” • Creates a random number between 0 and 1 • Sort both columns by the random numbers • Select the first N individuals for your sample

11. Sequential/Systematic Sampling • Random is not always practical • All sampling population members are listed and each kth member is selected to the sample k = sampling interval = Population size desired sample N

12. Stratified Sampling • Good option when sample needs to include subgroups from a population • Based on gender, age, education, etc. • Size of subgroups in final sample must be equivalent to size in population • Can use simple random or sequential sampling to fill each relative subgroup

13. Cluster Sampling • Good option when participants are already in groups that cannot be easily separated • e.g., Study of coaching’s impact on different sports teams • Instead of randomly selecting team members, you randomly select teams • If need certain subgroup representation, this may limit your option of teams

14. Nonprobability Sampling • Sampling based on some other factor besides probability • May be more convenient • May not be as representative • Can’t establish probabilities associated with sample membership • Can still be useful if treated with caution

15. Convenience Sampling • “Person” on the street approach • Sampling from easy to find population members (a “special” subset) • Sample determined in part by researcher’s sampling method • Not by probability • Can bias/distort results • Sometimes the only option

16. Snowball Sampling • Good for cohort studies or when trying to reach a dispersed population • Using one cohort member to find others, and so on... • Pros: Good for research on difficult populations to reach (e.g., homeless) • Cons: No representative sample guarantee

17. Central Limit Theorem Refers to distribution of characteristics within the probability samples • As N (sample size) increases, the shape of the sampling distribution of means will approach a normal distribution • µM = µ (mean of sample means =pop mean) • σM = σ/√n (SEM)

18. CLT • Sampling Distribution Shape • Figure 7.4  Note how the M becomes closer to µ as N increases • µM = mean of means = (sum of all sample means)/(number of samples) • M = unbiased estimate of µ • σM = std. dev. of the sampling distribution of M • As n increases, distribution of sample means will cluster closer to µ more accurate estimate

20. CLT • If we use probability sampling, M = unbiased estimate of µ • M becomes a better estimate of µ when n increases • We can determine the probability of obtaining various M

21. Standard Error of the Mean • Represents uncertainty of how well M represents µ • SEM = SD of sampling distribution of means σ/ √n (n = sample size) http://www.miniwebtool.com/standard-error-calculator/ • SEM is affected by: • σ as this decreases, SEM decreases • n as this increases, SEM decreases (1/√n) • M is best estimate of µ when SEM is low

22. Applying CLT • Reliability of a sample mean (M) • Use SEM to calculate confidence intervals around M (see Fig 7.4, p 212) • There will be variability among sample M, but a CI can help you determine the expected range • Adequacy of a sample size (n)

23. Confidence Intervals • In a normal distribution, 68% of M within 1 SEM of µ, 95% within 1.96 SEM of, 99% within 2.58 SEM • Can use CI to predict other M • 95% CI = 95% of future sample M should fall within this range

24. Sources of Bias and Error • Bias: nonrandom, systematic factors that may make M differ from µ • Could be controlled • Error: random events that have the same effect, but cannot be controlled • Figure 7.7 is a good illustration • Ideally, µ’ = µ, but not in these examples • Possible nonsampling biases at work

26. Bias and Error • If the sampling is random, then even if there is a nonsampling bias present, µM = µ’ • Sampling bias: systematic selection bias while sampling • Total error = M - µ • Sum of effects from nonsampling bias, sampling bias, and sampling error

27. What is Next? • **instructor to provide details