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# Comparing Classical and Bayesian Approaches to Hypothesis Testing - PowerPoint PPT Presentation

Comparing Classical and Bayesian Approaches to Hypothesis Testing. James O. Berger Institute of Statistics and Decision Sciences Duke University www.stat.duke.edu. Outline. The apparent overuse of hypothesis testing When is point null testing needed? The misleading nature of P-values

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### Comparing Classical and Bayesian Approaches to Hypothesis Testing

James O. Berger

Institute of Statistics and Decision Sciences

Duke University

www.stat.duke.edu

Outline Testing

• The apparent overuse of hypothesis testing

• When is point null testing needed?

• The misleading nature of P-values

• Bayesian and conditional frequentist testing of plausible hypotheses

• Conclusions

I. The apparent overuse of Testinghypothesis testing

• Tests are often performed when they are irrelevant.

• Rejection by an irrelevant test is sometimes viewed as “license” to forget statistics in further analysis

• The hypothesis is not plausible; testing serves no purpose.

• The observed usage levels are given without confidence sets.

• The rankings are based only on observed means, and are given without uncertainties. (For instance, perhaps Pr (A>B)=0.6 only.)

• The hypothesis is not plausible; testing serves no purpose.

• The observed usage levels are given without confidence sets.

• The rankings are based only on observed means, and are given without uncertainties. (For instance, perhaps Pr (A>B)=0.6 only.)

hypothesis needed?

Answer: When the hypothesis is plausible, to

some degree.

• H0: small mammals are as abundant on livestock grazing land as on non-grazing land

• H0: survival rates of brood mates are independent

• H0: bird abundance does not depend on the type of forest habitat they occupy

• H0: cottontail choice of habitat does not depend on the season

• H0: Males and females of a species are the same in terms of characteristic A.

• H0: Proximity to logging roads does not affect ground nest predation.

• H0: Pollutant A does not affect Species B.

III. For plausible hypotheses, P-values some degree:

are misleading as measures of evidence

Posterior probability that some degree:H0 is true, given the data (from Bayes theorem):

V. Advantages of Bayesian testing probability of H

• Pr (H0 | data x) reflects real expected error rates: P-values do not.

• A default formula exists for all situations:

An aside: integrating science and statistics via the Bayesian paradigm

• Any scientific question can be asked (e.g., What is the probability that switching to management plan A will increase species abundance by 20% more than will plan B?)

• Models can be built that simultaneously incorporate known science and statistics.

• If desired, expert opinion can be built into the analysis.