The Language of Statistical Decision Making

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The Language of Statistical Decision Making

• Lecture 2
• Section 1.3
• Fri, Jan 18, 2008

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Case Study 1

• Study Men Enjoy Watching Bad Guys Suffer

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Populations and Samples

• Population
• Sample
• Statistical inference

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Samples and Inferences
Population
5
Samples and Inferences
Population
Take Sample
Sample
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Samples and Inferences
Population
Take Sample
Make Observations
Sample
Data
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Samples and Inferences
Population
Inference
Draw an Inference
Take Sample
Make Observations
Sample
Data
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Samples and Inferences
Population
Inference
Draw an Inference
Take Sample
Make Observations
Sample
Data
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Hypotheses

• Hypothesis
• A hypothesis is often a statement that is
  proposed to explain something that is known to be
  true.

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Hypotheses

• The Null Hypothesis The conventional belief
  about the population, or the status quo, or the
  neutral position.
• It receives the benefit of the doubt.
• The Alternative (Research) Hypothesis An
  alternative to the null hypothesis.
• It bears the burden of proof.
• Typically, the researchers are trying to prove
  the alternative hypothesis.

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Hypothesis Testing
Population
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Hypothesis Testing
Null Hypothesis
Population
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Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
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Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
Sample
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Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
Sample
Evidence
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Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
Which Hypothesis Is Supported?
Sample
Evidence
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Hypothesis Testing
Null Hypothesis
Population
The evidence may support the Null Hypothesis
Sample
Evidence
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Hypothesis Testing
Null Hypothesis
Population
if any discrepancy can be attributed to chance
Sample
Evidence
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Hypothesis Testing
Population
Alternative Hypothesis
The evidence will support the Alternative Hypothes
is
Sample
Evidence
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Hypothesis Testing
Population
Alternative Hypothesis
if the discrepancy cannot be attributed to chance
Sample
Evidence
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Statistical Significance

• The data are called statistically significant if
  their deviation from what would be expected under
  the null hypothesis is too great to be attributed
  to chance.
• Example The incidence of cancer in one
  community is 8 and in another community it is
  10. Can the difference be attributed to chance?

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Case Study 1 Man or Woman?

• Suppose we are not told a subjects sex, but we
  are told that the subject felt empathy for the
  cheater.
• Would we guess that the subject is a man or a
  woman?
• Why?
• Would we necessarily be correct?