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. |
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alternative analysis Bayesian statistics better supported binomial Chapter conditional likelihood confidence interval data as evidence data say ECMO estimation evidence for H2 evidence in favor evidence supporting H2 evidential interpretation example experiment fairly strong evidence favor of H2 Figure find strong evidence Fisherian frequentist given H2 is true H2 over H1 hypothesis testing implies law of likelihood likelihood function likelihood interval likelihood principle likelihood ratio marginal likelihood mean misleading evidence Neyman–Pearson tests Neyman–Pearson theory nuisance parameter null hypothesis observations as evidence odds ratio orthogonal likelihood outcome p-value paradigm prior probability distribution probabilities of weak probability density function probability model probability of misleading problem profile likelihood random variable reject H1 rejection trials representing and interpreting sample space shows significance level significance tests specified standard statistical evidence statistical methods strong evidence supporting Suppose tosses Type I error versus H2 weak evidence