Transcript Sampling II / SPSS index review

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
– +/- 1.96 Standard Errors contains 95% of outcomes
– +/- 2.58 Standard Errors contains 99% of outcomes
Sampling Distribution
.95  95% of all sample outcomes (from infinite
number of samples) will be within this window
0.95
True Population
Parameter
-1.96
 Standard Errors
5% of the time, you would get a
weird finding this different from
the true parameter
1.96
Probability Theory IV
• From sampling distribution to our single sample
– IF: 95% of sample statistics (assuming an infinite
number of samples) fall within +/- 1.96 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?