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The Language of Statistical Decision Making

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Title: The Language of Statistical Decision Making


1
The Language of Statistical Decision Making
  • Lecture 1
  • Section 1.3
  • Fri, Sep 1, 2006

2
I Dont Feel Your Pain!
  • Study Men Enjoy Watching Bad Guys Suffer

3
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?

4
Populations and Samples
  • Population
  • Sample
  • Statistical inference

5
Samples and Inferences
Population
6
Samples and Inferences
Population
Take Sample
Sample
7
Samples and Inferences
Population
Take Sample
Make Observations
Sample
Data
8
Samples and Inferences
Population
Inference
Draw an Inference
Take Sample
Make Observations
Sample
Data
9
Samples and Inferences
Population
Inference
Draw an Inference
Take Sample
Make Observations
Sample
Data
10
Hypotheses
  • Hypothesis
  • A hypothesis is often a statement that is
    proposed to explain something that is known to be
    true.

11
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.

12
Hypothesis Testing
Population
13
Hypothesis Testing
Null Hypothesis
Population
14
Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
15
Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
Sample
16
Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
Sample
Evidence
17
Hypothesis Testing
Null Hypothesis
Population
Alternative Hypothesis
Which Hypothesis Is Supported?
Sample
Evidence
18
Hypothesis Testing
Null Hypothesis
Population
The evidence may support the Null Hypothesis
Sample
Evidence
19
Hypothesis Testing
Null Hypothesis
Population
if any discrepancy can be attributed to chance
Sample
Evidence
20
Hypothesis Testing
Population
Alternative Hypothesis
The evidence will support the Alternative Hypothes
is
Sample
Evidence
21
Hypothesis Testing
Population
Alternative Hypothesis
if the discrepancy cannot be attributed to chance
Sample
Evidence
22
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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