ttests

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t-tests Confidence Intervals
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What Does Difference Mean?

• The t-test is to determine if there is a
  difference between two measures.
• A sample and a population?
• Two independent samples?
• Related Samples?

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Statistical Analysis
Control group mean
Treatment group mean
Is there a difference?
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What Does Difference Mean?
Medium variability
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What Does Difference Mean?
Medium variability
High variability
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What Does Difference Mean?
Medium variability
High variability
Low variability
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What Does Difference Mean?
The mean difference is the same for all three
cases.
Medium variability
High variability
Low variability
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What Does Difference Mean?
Medium variability
High variability
Which one shows the greatest difference?
Low variability
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What Does Difference Mean?

• A statistical difference is a function of the
  difference between means relative to the
  variability.
• A small difference between means with large
  variability could be due to chance.
• Like a signal-to-noise ratio.

Which one shows the greatest difference?
Low variability
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Steps in Hypothesis Testing

• Establish hypotheses to be tested
• State a criterion for making a decision or
  identify a and critical values
• Collect and describe sample data.
• Do the math using inferential statistics
• Make a statistical decision

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Errors in Hypothesis Tests

• Type I Error ?- Rejecting a null hypothesis
  that is true
• Type II Error ? - Failing to reject a null
  hypothesis that is false.

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Outcomes in Hypothesis Testing
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(No Transcript)
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Decisions in Hypothesis Testing
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Graphical Representation of Statistical Power
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Statistical Power, a, and ß

• Power 1-ß
• Explanations for Type I errors - a
• An unusual sample
• Something other than our manipulation produced a
  difference in the means
• Explanations for Type II errors - ß
• An unusual sample in the opposite direction
• The change was too small to detect
• There was too much variability in the sample

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The t statistic
The objective in the hypothesis testing process
is to have large t values as an aid in the
decision making process.
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Impact of Sample Size and Standard Deviation on
Statistical Power
Power is also impacted by difference between the
means and a
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Types of t tests

• One sample t tests
• Related samples t tests
• Repeated measures
• Matched groups
• Independent samples t tests

?
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Related Samples t tests
df n - 1
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Independent Samples t tests
df n - 2
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Estimated Standard Error of the Difference
Between Two Groups
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Confidence Intervals

• A tool for making estimations about populations
  based on sample data
• More useful than t-tests in that they answer
  questions about differences, but also about how
  much difference
• Have a both a level of confidence and a degree of
  accuracy

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Calculating Confidence Intervals

• Point estimates
• Interval estimates

Point Estimate Sample mean Difference between
sample means Mean of differences
Interval Estimate Point Estimate Fudge factor
Fudge Factor t value estimated standard error