Chapter Six: Statistical Inference Significance Tests

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Chapter Six Statistical Inference
Significance Tests

• DBA 902
• Research Methods II
• J. Schreiber

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Elements of a Significance Test

• Assumptions
• Hypotheses
• Test Statistic
• P-value
• Conclusions

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Assumptions

• Type of Data
• Population Distribution
• Method of Sampling
• Sample Size

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Hypotheses Test Statistic

• Hypotheses
• Ho Null Hypothesis (no effect)
• Ha Alternative Hypothesis (research
  hypothesis)
• Test Statistic
• Usually a point estimate of the parameter in the
  hypotheses
• Calculated using the sample data

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P-value

• Is a probability (between 0 and 1)
• Summarizes the evidence in the data about the
  null hypothesis
• Pr(we would get this sample or more extreme,
  given Ho is true)
• The smaller the value, the more evidence AGAINST
  Ho

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Conclusions

• Start by assuming Ho is true until evidence
  suggests otherwise
• Collect data, compute test statistic and p-value
• Report p-value
• Usually .05 or .01 is enough to cast strong doubt
  on the assumption that Ho is true.
• When too small, we conclude that Ha is more
  plausible.
• Otherwise, we continue to assume Ho is true (NOT
  accept Ho)

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Significance Test for a Mean
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Significance Test for a Proportion
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Other issues

• Alpha level
• Type I and II errors
• Statistical versus practical significance
• Robustness

10
Significance Test for a Mean Small Sample
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Significance Test for a Proportion Small Sample