2.4 Sampling

1. 2.4 Sampling • To Get a perfect set of data, we would survey every person in the population • Census: Obtaining information from an entire population • Difficult to do… • Limited Resources • Process is destructive and would be foolish • Sample should be representative of the population

2. Bias in Sampling • Bias: Systematically leading the researcher to an outcome • Selection Bias • Measurement Bias • Response Bias • Non-response Bias

3. Selection BiasUndercoverage • When some part of the population is systematically excluded • Telephone surveys exclude people without telephones or those people who aren’t at home in the evenings, etc. • Self-Selected (volunteers): Only those with an interest in the topic complete the survey (like calling in to radio station, etc.)

4. Measurement Bias • Data don’t represent the true population due to some sort of measurement error

5. Response Bias • Produces values that systematically differ from the true population in some way… • The way questions are worded on a survey • Appearance or Behavior of the person asking the question • The group or organization conducting the study • People have a tendency to lie when asked about illegal behavior or unpopular beliefs

6. Non-Response Bias • Occurs when responses are not obtained from everyone in the sample • Those without an opinion either way don’t return the survey • Mail Surveys are least expensive, but have the worst response rates • Telephone surveys are more costly but have a better response rate • Personal Interviews are very expensive, but have the best response rate

7. Random Sampling • Simple Random Sampling (SRS) • Systematic Sampling • Sampling with replacement • Sampling without replacement • Stratified Random Sampling • Multi-Stage Sampling • Cluster Sampling • Convenience Sampling

8. Sample Size • Represented by n • The best way to solve all issues in AP Stats… • Increase the Sample Size

9. Simple Random Sampling • Every person in the population has an equal chance of being drawn. • Best Way: “Put them in a hat, shake them up, draw them out” • Drawbacks: mixing must be adequate and process can be tedious • Sampling Frame: Create a List of all objects/individuals in the population • Use a Random number generator or digitable to select the sample

10. Random Sampling • It is possible for sampling to be random, without being SRS… • Selecting 64 NFL Football Players • Random Sampling does not guarantee that the sample will be representative… • We have to rely on our methods being adequate choices for the sample

11. Systematic Sampling • Random– but there is a well-defined pattern to the selection • Randomly select one of the first 10 names in the phone book, then select every 10th name after that to be in the sample.

12. Sampling • With Replacement… • Put Names/Numbers back into the hat • Allows for the possibility for an item or individual to appear more than once in the sample • Rarely Used in practice • Without Replacement… • Don’t put the names/numbers back into the hat • Used More often • When the sample size is small relative to the population size (which is typical), there is little practical difference between replacement and without replacement

13. Stratified Random Sampling • Used when the entire population can be divided into a set of non-overlapping groups (strata) • Used when it is important to obtain information about characteristics of the individual strata • Can produce more accurate results because each strata may be more homogeneous than the entire population

14. Cluster Sampling • Sampling pre-existing groups • Census the Entire Population of the Cluster • Cluster vs. Stratified Sampling • Makes life easier by breaking it down

15. Multi-Stage Sampling • Sampling that combine several methods • Breaks down the groups – makes life a little easier

16. Convenience Sampling • Obtaining a Sample any way you can • Easy for the researcher • Lots of bias! • Avoid This Technique!