Statistical Significance

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Statistical Significance

• Generalizing From Samples

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Generalizing From Samples

• Sample error (Confidence intervals)
• Confidence levels
• Significance levels

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Sample Error AKA Confidence Intervals

• Are a RANGE OF VALUES within which the population
  parameter most likely falls
• Are expressed as
• Parameter Statistic ? ___
• Or, statistic (sampling error is ____ )

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Sample Error Example
Table 1
Support For Tax Levy ()
For 45
Against 40
Undecided 15
Total 1200
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Sample Error Example, cont.

• 45 percent of the respondents indicated that, if
  the election were to be held today, they would
  vote for the levy (The poll has a 3 sampling
  error)

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Sample Error Example, cont.

• If the election were to be held today, the For
  the levy side would carry 45 percent (? 3) of
  the votes

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Sample Error

• Is affected by sample size (larger samples
  provide smaller sample errors, see White, Table
  7.3, pg. 197)
• Can be calculated, if we are able to specify our
  desired confidence level

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Confidence Level A Probability Statement

• A.K.A. likelihood
• In both of the previous cases, the statement
  means that the true percentage of levy
  supporters in the population is MOST LIKELY
  (PROBABLY) somewhere between 42 and 48
  (Remember, sample had 45 For, with a 3 error
  rate)

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Confidence Level How Likely???

• The likelihood (probability) that the sample is
  representative of the population
• The likelihood that we can safely infer from the
  sample to the population

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Confidence Level

• Is used with univariate measures (percentages,
  typicality, dispersion)
• Is affected by sample size (larger samples permit
  higher confidence)
• Usually, we wish to be at least 95 confident
• That our sample is representative
• That the population parameter falls within the
  sample error

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Confidence Level Example

• If the election were to be held today, it is 95
  likely that the For the levy side would carry
  45 (? 3) of the votes

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Statistical Significance

• Is used with bi- and multi- variate analysis
  (summary association measures, crosstabulations)
• Is not synonymous with importance (confusing the
  two is a common error)
• Is a tool used to help us decide whether or not
  it is likely that we are wrong if we decide that
  a sample is representative of the population

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Calculating Statistical Significance

• There are many measures, etc.
• Most work by calculating the size of the
  difference between what is actually found in a
  sample and what one would expect to find in a
  sample were the sample results due simply to the
  luck of the draw

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Interpreting Statistical Significance

• It is the likelihood that we are wrong (in error)
  if we conclude that the sample is representative
  of the population
• Usually, we want our findings to be significant
  at least at the .05 level (Closer to zero is
  better!)

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Presenting Significance Summary Association

• At bottom of table
• There are various formats

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