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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. 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

Comparing Classical and Bayesian Approaches to Hypothesis Testing

James O. Berger

Institute of Statistics and Decision Sciences

Duke University

www.stat.duke.edu


Outline
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

  • Advantages of Bayesian testing

  • Conclusions


I the apparent overuse of hypothesis testing
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



Statistical mistakes in the example
Statistical mistakes in the example Testing

  • 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.)



Statistical mistakes in the example1
Statistical mistakes in the example Testing

  • 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.)



Comparing classical and bayesian approaches to hypothesis testing

II. When is testing of a point null Testing

hypothesis needed?

Answer: When the hypothesis is plausible, to

some degree.


Examples of hypotheses that are not realistically plausible
Examples of hypotheses that are not realistically plausible Testing

  • 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


Examples of hypotheses that may be plausible to at least some degree
Examples of hypotheses that may be plausible, to at least some degree:

  • 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.


Comparing classical and bayesian approaches to hypothesis testing

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

are misleading as measures of evidence




Posterior probability that h 0 is true given the data from bayes theorem
Posterior probability that some degree:H0 is true, given the data (from Bayes theorem):



V advantages of bayesian testing
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:


Comparing classical and bayesian approaches to hypothesis testing


Comparing classical and bayesian approaches to hypothesis testing


An aside integrating science and statistics via the bayesian paradigm
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.


Conclusions
Conclusions Bayesian paradigm

  • Hypothesis testing is overutilized while (Bayesian) statistics is underutilized.

  • Hypothesis testing is needed only when testing a “plausible” hypothesis (and this may be a rare occurrence in wildlife studies).

  • The Bayesian approach to hypothesis testing has considerable advantages in terms of interpretability (actual error rates), general applicability, and flexible experimentation.