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�Estimation: �How Large is the Effect?

Confidence intervals

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Chapter Overview

  • So far, we can only say things like
    • “We have strong evidence that babies prefer the helper toy to the hinderer.”
    • “We have strong evidence facial prototyping dos exist.”
  • We want a method that says
    • “The neutral version would increase the chances that a person agree to become a donor by between 20 and 54 percentage points over the opt in version.”

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Chapter Overview

Estimation tells how large the effect is, through an interval of values.

  • We can be 95% confident that the “true” effect of taking bi-daily aspirin will reduce the rate of heart attacks somewhere between 30% and 50%.
  • “Do you approve of the way the members in Congress are doing their job?” 15% responded approve (results have a margin of sampling error of ± 3.5 percentage points)

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Confidence Intervals

  • These interval estimates of a population parameter are called confidence intervals.
  • We will find confidence intervals three ways.
    • Through a series of tests of significance to see which proportions are plausible values for the parameter.
    • Using the standard deviation of the simulated null distribution to help us determine the width of the interval.
    • Through traditional theory-based methods.

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Statistical Inference – Confidence Intervals

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Exploration: Kissing Right

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Based on a brief article in Nature

  • Onur Güntürkün observed kissing couples in public places (airports, railway stations, beaches and parks) in the United States, Germany and Turkey.
  • The head turning behavior of each couple was recorded for a single kiss, with only the first being counted in instances of multiple kissing.
  • The following criteria had to be met to qualify: lip contact, face-to-face positioning, no hand-held objects (as these might induce a side preference), and an obvious head-turning direction during kissing.
  • Subjects’ ages ranged from about 13–70 years.

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Exploration

As you work through this exploration …

  • Your first test will be one-sided, but after that everything is a two-sided test.
  • The sample proportion stays constant.
  • The hypothesized parameter under the null will change since we are testing to see if different parameters are plausible or not.
  • For small p-values we can rule the parameter out.
  • For large p-values, the parameter is plausible.