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Statistical Sampling

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Statistical Sampling

Part I – Introduction

This video is designed to accompany

pages 41-76

in

Making Sense of Uncertainty

Activities for Teaching Statistical Reasoning

Van-Griner Publishing Company

Goal of Sampling

- To make inferences about a population from what we know about our sample data …
- Not something we can do perfectly…
- But it is something we can do scientifically.

Scientifically?

- Basically we want to be able to estimate numbers in the population that we don’t know, using numbers we do know from our sample.
- And we want to be able to say something mathematically meaningful about how much confidence we have in our estimation procedure.

Data Collection

- Once the sample is determined, data may be collected a variety of ways.
- Survey Monkey is a popular, free on-line survey tool.
- Even if the sample is taken the right way, there is the additional issue of the integrity of the data measurements.

Common Sense First

Sampling from Biased Lists

1936 Literary Digest poll that forecast Landon would defeat FDR by 57% to 43%.

The Digest used lists of telephone and automobile owners to select their sample, which targeted middle- and upper-class citizens who voted for Landon.

The lower classes voted for Roosevelt.

“If you had to do it over again, would you have children?”

- Voluntary Response
- Ann Landers had 10,000 responses and about 70% said “NO!”
- Wise follow-up by Landers
- “People who are contented are rarely motivated to write and tell me how happy they are. Anger, hostility and resentment are often the fuel that moves people to action.”

- Hints at an understanding of the bias in voluntary response “surveys.”

So How Bad Was the Bias?

Follow-up

Newsday commissioned a nationwide poll of 1373 parents and used “statistical sampling.”

Found that 91% would have children again!

Push Polls

- Intentional Bias
- 2000 Republican Primaries
- Bush camp asked voters in South Carolina:
- "Would you be more likely or less likely to vote for John McCain for president if you knew he had fathered an illegitimate black child?"

- Push Polls “push” respondents in a certain direction.
- Inferences with push poll data are nonsense.

Briefly Said

Biased samples tend to systematically favor certain outcomes.

With biased samples you can’t say anything meaningful about how good your estimates are.

The science of statistics is about what you can say when you take samples the right way.

Avoiding biased samples is just good common sense, whereas making meaningful statements from proper samples is the business of statistical science.