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Sampling

Sampling. Probability Sampling Nonprobability Sampling. Probability Sampling. Sampling element Population Target population Sampling frame Sampling ratio.

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Sampling

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  1. Sampling Probability Sampling Nonprobability Sampling

  2. Probability Sampling • Sampling element • Population • Target population • Sampling frame • Sampling ratio

  3. There is a classic Jimmy Stewart movie, Magic Town, about "Grandview," a small town in the Midwest that is a perfect statistical microcosm of the United States, a place where the citizens' opinions match perfectly with Gallup polls of the entire nation. A pollster (Jimmy Stewart), secretly uses surveys from this "mathematical miracle" as a shortcut to predicting public opinion. Instead of collecting a national sample, he can more quickly and cheaply collect surveys from this single small town. The character played by Jane Wyman, a newspaper editor, finds out what is going on and publishes her discovery. As a result the national media descend upon the town, which becomes, overnight, "the public opinion capital of the U.S."

  4. Probability Sampling

  5. Sampling Distribution

  6. Probability Sampling • Random sample • Sampling error • Four Ways to Sample Randomly • Simple Random • Systematic • Stratified Sampling • Cluster Sampling

  7. Random Sample Variation Component • Sampling Error: Sample size Component

  8. R Session data=c(1,1,0,0,0,0,1,1,0,1,1,0,1,1,1,0) population.mean=mean(data) #samples of size 5 a.sample=sample(x=data,size=5,replace=FALSE) a.mean=mean(a.sample) #another sample b.sample=sample(data,5,FALSE) b.mean=mean(b.sample) #Distribution of sample mean #We need to sample lots of times sim.runs=100 mean.sample=NA for (i in 1:sim.runs){ sample.data=sample(data,5,FALSE) mean.sample[i]=mean(sample.data) } hist(mean.sample,breaks=4)

  9. Sampling Distribution and Sampling Error Let’s first see what mathematics has to say. According to Law of Large Numbers: As sample size increases (approaches to ) sample mean approaches to population mean, in mathematical symbols According to Central Limit Theorem As the number of samples (not the sample size, this time) increases then sample mean has a normal distribution with mean andstandarddeviation. Mathematically we say,

  10. Sampling and Confidence x Confidence information is in z. can be replacedby.

  11. Important Concepts in Sampling The value of z depends on confidence Sampling error Margin of Error FinitePopulationCorrectionFactor Next: Sample size

  12. Other Probability Sampling Designs

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