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…

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

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

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?

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 (random) 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) Population parameter is most likely outcome (top of curve)

Probability Theory II Hypothetical distributions are called: – Sampling distributions Because they are based on drawing an infinite # of samples – Probability distributions Because they tell us the probability of obtaining particular sample outcomes Sampling/probability distributions exist for any kind of sample outcome you can imagine – ALL OF THEM PRODUCE “KNOWN” ESTIMATES OF ERROR

Probability Theory III Standard error – The standard deviation of a sampling/probability distribution KEY POINT: standard deviations for normal (bell shaped) sampling distribution always contain the same percent of sample outcomes – +/-1 Standard Error contains 68% of outcomes – +/ Standard Errors contains 95% of outcomes – +/ Standard Errors contains 99% of outcomes

Sampling Distribution.95  95% of all sample outcomes (from infinite number of samples) will be within this window  Standard Errors  5% of the time, you would get a weird finding this different from the true parameter True Population Parameter

Probability Theory IV From sampling distribution to our single sample – IF: 95% of sample statistics (assuming an infinite number of samples) fall within +/ standard errors of the true population parameter – Then, there is a 95% chance that our single statistic falls within 1.96 standard errors of the population parameter SO- we “go out” 1.96 (or 2.58 for 99% confidence) standard errors to create a confidence interval

Calculating what one standard error is “worth” for your sample outcome The calculations always include – Sample size (N) – Some estimate of dispersion – There are formulas for every situation Babbie  The “Binomial” – Used for agree/disagree questions (% agree) in polling data

Example: Feb 12, 2009 Gallup Poll On Darwin’s Birthday, Only 4 in 10 Believe in Evolution: Belief drops to 24% among frequent church attendees “PRINCETON, NJ -- On the eve of the 200th anniversary of Charles Darwin's birth, a new Gallup Poll shows that only 39% of Americans say they "believe in the theory of evolution," while a quarter say they do not believe in the theory, and another 36% don't have an opinion either way. These attitudes are strongly related to education and, to an even greater degree, religiosity.” Survey Methods “Results are based on telephone interviews with 1,018 national adults, aged 18 and older, conducted Feb. 6-7, 2009, as part of Gallup Poll Daily tracking. For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is X percentage points.” CAN YOU CALCULATE THEIR MARGIN OF ERROR?

Confidence Intervals for Proportions Sample point estimate (convert % to a proportion): – “39% of Americans say they ‘believe in the theory of evolution,’ while…”  estimate is.39 Formula in Babbie (p.217): P (1-P) N 95% confidence level  1.96 standard errors

What happens when… Still using 39%... – Change the sample size to 100 – Use original sample size, but change confidence level to 68% Use the original sample size, but assume the percentage is 96% rather than 39%

Types of Probability Sampling EPSEM SYSTEMATIC (every Kth element) Stratified Cluster Disproportionate (oversample) + weighting

Composite Measures Why use composite (adding indicators up) as opposed to a single indicator of a concept? Index – Typically adding yes/no (coded as 0/1) or ordinal scales (codes as 1-4) together “Simple Summated Index” SPSS review/demo– or, just do the assignment?