Section 2.1: Taking a Good Sample

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Section 2.1 Taking a Good Sample
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Sampling Design

• Design of a sample refers to the method used to
  collect the data.
• A proper sampling design must start with a sample
  which is representative of the population.

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Key Idea

• If a sample is roughly representative of a
  population, you can estimate that the sample has
  roughly the same proportions as the population.
• If we assume that PA is representative of the
  country, then if we know that 60 of people voted
  in the last presidential election and there are
  12.4 million people in PA we can estimate the
  number of people in PA who voted.

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To get reliable statistics, a sample must
represent the population

• Ex In terms of households who watch tv, the USA
  is not representative of the world. In the USA
  approximately 98.5 of households have a tv but
  its about 13 worldwide.

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Problems with Bad Sampling Designs

• If your sample is created in such a way that it
  would tend to make it unrepresentative, then the
  sample is created using a biased method.

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Examples of Poor Design Methods

• Nonresponse
• Poor wording of question/response bias
• Voluntary response Call-in polls
• Convenience sampling
• Undercoverage

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Need for Randomization

• Salty Soup Sampling from the top (or bottom)
  without first stirring gives a misleading point.
• 1970 Draft Lottery Example

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How large of a random sample do you need for the
sample to be reasonably representative of the
population?

• Most people think you need a large percentage of
  the population but in fact all that really
  matters is the number of people in the sample.
• 100 SU students represents the entire student
  body just as well as 100 voters represents the
  entire electorate of the USA.

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Why? Back to the soup example

• The soup tastes the same whether you use the same
  spoon in a large or small pot.
• This idea determines the balance between how well
  the survey can measure the population and how
  much the survey costs.

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How big of a sample do you need?

• This depends on what youre interested in
  estimating.
• Soup example Are you interested in just tasting
  the broth or more?
• With a categorical variable, youll need at least
  enough subjects to see several respondents in
  each category.

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What do pollsters do in practice?

• Contact respondents by phone using computer
  generated random lists.
• Pollsters list responses in random order to avoid
  biases.