1. Agenda Review Exam I Sampling Start Probabilities

2. Exam I Ex1 Written + Ex1 MC = raw score (Raw score / 86) = raw percent Raw percent + 6 = final recorded = Exam1% Distribution 5 F, 5D, 6C, 8B, 3A Mean = 76, Median = 78

3. Distribution of Exam 1 Scores

4. Short Essay questions Pillars + Study Nominal vs. Operational definition Validity vs. Reliability Anonymity vs. Confidentiality

5. Why Draw A Sample? Why not just the get the whole enchilada? – Pragmatic reasons – The true population is typically “unknowable” When done right, a small proportion of the population works just fine…

6. Types of Sampling Probability Sampling – Based on the principles of probability theory – Elements of the population have some known probability (typically equal odds) of selection Non-probability sampling – Elements in the population have unknown odds of selection Make it very difficult to generalize findings back to the population of interest

7. Non-Probability Sampling Reliance on available subjects Purposive/judgmental sampling Snowball sampling Quota sampling Informants

8. Probability Sampling Terminology – Element – Population – Sample – Sampling Frame – Parameter vs. Statistic

9. Probability Sampling Advantages – Avoids both conscious and unconscious bias – By using probability theory, we can judge the accuracy of our findings There is ALWAYS ERROR in any sample No sample perfectly reflects the entire population Key issue = How much error is likely in our specific sample?

10. EPSEM Equal Probability of SElection Method – Most common form of probability sampling – All elements in the population have an equal chance of being selected for the sample AKA, “Simple Random Sample”

11. Probability Theory A branch of mathematics that allows us to gauge how well our sample statistics reflect the true population parameters. Based on HYPOTHETICAL distributions – What would happen if we took an infinite number of unbiased (EPSEM) samples from a population and plotted the results? Some “weird” findings just by chance (large errors) Findings closer to the true parameter more likely (small errors)

12. Probability Theory II Hypothetical distributions are called: – Sampling distributions – Probability distributions Sampling/probability distributions exist for any kind of sample outcome you can imagine – Percent, mean, mean difference… – ALL OF THEM PRODUCE “KNOWN” ESTIMATES OF ERROR How sample outcomes will be distributed around the true population parameter

13. Probability Theory III Standard deviation = how far a case typically falls from the mean of a distribution – Measure of dispersion Standard error – The standard deviation of a sampling/probability distribution KEY POINT: standard deviations of a sampling distribution always contain the same percent of sample outcomes – +/-1 Standard Error contains 68% of outcomes – +/- 1.96 Standard Errors contains 95% of outcomes – +/- 2.58 Standard Errors contains 99% of outcomes

14. Probability Theory IV The sampling distribution therefore tells us generally how sampling error is distributed around a population parameter – 68% of sample outcomes will be within one standard error of the true population parameter OR – There a 68% chance that a particular sample outcome falls within one standard error of the population parameter – There a 95% chance that a particular sample outcome falls within two standard errors (1.96) of the population parameter This logic is what we use to calculate our specific error

15. .95 means that this window contains 95% of all sample outcomes—OR, there is a 95% chance of getting an outcome in this window 0.95 -1.961.96.025  Standard Errors  Sampling Distribution

16. Getting estimates of error for a specific sample outcome The error for a particular sample depends upon… Sample Size  larger samples = less error Dispersion/homogeneity in the sample  greater homogeneity = less error

17. Estimation Point Estimate: Value of a sample statistic used to estimate a population parameter Confidence Interval: A range of values around the point estimate Confidence Interval Point Estimate Confidence Limit (Lower) Confidence Limit (Upper).58.546.614

18. Confidence Intervals – We can calculate a “confidence interval” around a sample finding We can be 95%, 99% (or whatever) certain that some sample finding is within +/- points/units – We are 99% confident that 77%, +/- 4 %, of UMD students would car splash professor Maahs with a puddle if they drove by and had the opportunity » OR, We are 99% sure that between 73% and 81% of UMD students…. – Based on our sample findings, we are 95% confident that average age of Duluth homeowners is between 36.5 and 41.5 years old » Or, 39 years old, +/- 2.5 years

19. Calculating a confidence interval Step 1: Choose a confidence level: – 95% confident means going out +/- 1.96 standard errors – 99% confident means going out +/- 2.58 standard errors – How many standard errors would you have to go out to be 68% confident? KEY: Extend logic from what would happen with infinite number of samples to “odds of obtaining a sample finding within 1, 1.96, or 2.58 standard errors of population parameter”

20. Calculating a confidence interval Step 2: figuring out what a standard error is “worth” for your situation – Sample size (N) – Some estimate of dispersion – There are formulas for every situation Babbie  The “Binomial” – Used for agree/disagree survey questions (% agree)

21. Example CNN Poll (CNN.com; Feb 20, 2009): Slight majority thinks stimulus package will improve economy “The White House's economic stimulus plan isn't a surefire winner with the American public, but a majority does think the recovery plan will help. According to a new poll, fifty-three percent said the plan will improve economic conditions, while 44 percent said it won't stimulate the economy.” “On an individual level, there was less hope for improvement. According to the poll, 67 percent said it would not help them personally.” “The Poll was conducted Wednesday and Thursday (Feb 18-19, 2009), with 1,046 people questioned by telephone. The survey's sampling error is plus or minus 3 percentage points.”

22. Estimation – POINT ESTIMATES (another way of saying sample statistics) – CONFIDENCE INTERVAL a.k.a. “MARGIN OF ERROR” Indicates that over the long run, 95 percent of the time, the true pop. value will fall within a range of +/- 3 “… but a majority does think the recovery plan will help, according to a new poll. Fifty- three percent said the plan will improve economic conditions, while 44 percent said it won't stimulate the economy. …. The Poll was conducted Wednesday and Thursday (Feb 18-19, 2009), with 1,046 people questioned by telephone. The survey's sampling error is plus or minus 3 percentage points.

23. Confidence Intervals for Proportions Sample point estimate (convert % to a proportion): – “Fifty-three percent said the plan will improve economic conditions…” – 0.53 Sample size (N) = 1,046 Formula in Babbie (p.217) – Numerator = (your proportion) (1- proportion) – 95% confidence level (replicating results from article)

24. Example 1: Estimate for the economic recovery poll p =.53 (53% think it will help) 95% confidence interval = 1.96 standard errors N = 1046 (sample size) What happens when we… – Recalculate for N = 10,000 – Back to original, but change confidence level to 99%