Can What Go Wrong?
Sampling and statistics seem simple, but many problems can arise.
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Sample Surveys in the Real World Example: Prediction poll mistake of the 1948 presidential election that proclaimed Thomas Dewey as the winner over Harry Truman.
Types of Errors
There are three types of errors that we will examine. These are ____________errors , ______________ error and ___________ errors. ______________________are errors caused by the act of selecting a sample. They cause sample results to be different from the results of a census.
How Do Sampling Errors Happen?
Improper sampling techniques are used. Sampling errors occur when some groups in the population are left out of the process of choosing the sample.
Sampling Frame list of individuals from which a sample is drawn. So if our sampling frame does not include everyone in the population, the sample will be biased.
Random Sampling Error
This results from chance selection in the simple random sample. The error is due to chance. The best we can do to control this is to select a random sample. ___________________includes only random sampling error
Nonsampling Errors
______________________are errors not related to the act of selecting a sample from the population. They can be present even in a census.
___________________: Refusal to answer survey, subject is not available for survey
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Effects of Data Collection Procedure on Nonsampling errors:
______________Errors: Subject may lie or remember incorrectly, subject may not understand question _______________Errors: Math errors, coding data incorrectly ____________________: It is surprisingly difficult to word questions that are completely clear. _______________: what time of day you call can effect response rate. ______________________: Mail ( low response rate), telephone, personal interview
How to Live with Sampling Errors
Substitute other households for the nonresponsive household
Can help reduce bias
Alternative to Simple Random Sampling
__________________ Divide sampling frame into groups of individuals called strata. Take SRS in each stratum. _______________is made up of a group of individuals based on some similarity (location, age, income, etc.)
Weight the responses
Example: Number of males and females in the sample may differ, weighting can account for differences.
Can also account for differences by race, age, household size
Helps correct bias But it Increases variability
Current Survey
2007 Population Primary Sampling Units (PSU's)
Stratified Random Sampling Design
Step 1: Divide the sampling frame into groups of units called strata.
The strata are chosen using some characteristic of the units already known (i.e.: race, gender, location, etc.). The strata are chosen to be of special interest in these groups within the population. (Note: strata is plural, stratum is singular.)
Step 2: Take a separate simple random sample in each stratum and combine these to make up the stratified random sample.
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Example: Males and Females
The class has been separated into males and females. There are 17 males and 23 females.
Take an SRS of size 5 from the males. Take an SRS of size 5 from the females.
More Sampling Designs
Cluster sampling: Divide population into clusters. Select one or more cluster and include everyone in sample.
Example: SC has 46 counties. Select 5 counties at random, use all household in each selected county as sample.
Combine these two samples to form our stratified random sample (stratified by gender).
Systematic sampling: Take every nth item from the sampling frame.
Example: Take every 10th towel from a roll of paper towels
More Complex Sample Designs
Multistage Sampling Design: This type of sampling is used to select a sample from a very large population where certain groups and subgroups are available.
Example of a Multistage Sample
Suppose we wish to obtain a sample of people in the United States. 1) Randomly select a few states (SRS) 2) Randomly select a few counties (SRS) 3) Randomly select a few neighborhoods (SRS) 4) Randomly select people (SRS)
Probability Sample
Probability Sample: A sample chosen in such a way that we know what samples are possible and what chance, or probability, each possible sample has to be chosen (not all need be equally probable).
Simple random and stratified random sampling all fall into the category of probability samples.
Questions to ask before you believe a poll
1. 2. 3. 4. 5. 6. 7. 8. Who carried out the survey? What was the population? How was the sample selected? How large was the sample? What was the response rate? How were the subjects contacted? When was the survey conducted? What questions were asked?
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Summary
Using good random sampling techniques we avoid biased sampling. Use sample size to determine margin of error at given confidence level. Avoid, but be aware of non-sampling errors.
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