## Statistical Evidence: A Likelihood ParadigmInterpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics. |

### From inside the book

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**Rejection trials**3.6 A sample of interpretations 65 68 71 76 3.7 The illogic of**rejection trials**3.8 Confidence sets from**rejection trials**3.9 Alternative hypotheses in science 3.10 Summary Exercises 4 Paradigms for statistics 4.1 ...Page 42

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### Common terms and phrases

alternative Bayesian statistics Bernoulli trials better supported binomial Chapter choosing conditional likelihood confidence intervals data as evidence data say ECMO evidence in favor evidential interpretation example Expected value experiment fairly strong evidence favor of H2 females Figure find strong evidence Fisherian frequentist frequentist statistical given H₂ is true H₂ over H₁ hypothesis testing law of likelihood lihood likelihood function likelihood principle likelihood ratio Likelihoods for ratio M₁ M₂ marginal likelihood mean measure the strength misleading evidence Neyman-Pearson tests Neyman-Pearson theory nuisance parameter null hypothesis odds ratio orthogonal likelihood p-value paradigm prior probability distribution prob probabilities of weak probability model probability of misleading problem random variable reject H₁ rejection trials reparameterization shows significance level significance tests specified statistical evidence statistical methods strong evidence supporting success Suppose tion tosses treatment Type I error variance vector versus vis-à-vis W₂ weak evidence white balls

### References to this book

Common Errors in Statistics (and How to Avoid Them) Phillip I. Good,James W. Hardin Limited preview - 2006 |

Early Childhood Educational Research: Issues in Methodology and Ethics Carol Aubrey No preview available - 2000 |