Read e-book online Permutation, Parametric and Bootstrap Tests of Hypotheses: A PDF

By Phillip I. Good

ISBN-10: 038720279X

ISBN-13: 9780387202792

Explains the mandatory history in trying out speculation and selection idea to permit innumerable functional functions of facts. This booklet contains many real-world illustrations from biology, company, scientific trials, economics, geology, legislation, medication, social technological know-how and engineering besides two times the variety of routines.

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Additional resources for Permutation, Parametric and Bootstrap Tests of Hypotheses: A Practical Guide to Resampling Methods for Testing Hypotheses

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If it’s just a chance effect—rather than one caused by the new drug—and we opt in favor of the new drug, we’ve made an error. We also make an error if we decide there is no difference, when, in fact, the new drug really is better. 1a below. We distinguish between the two types of error because they have quite different implications. For example, Fears, Tarone, and Chu [1977] use permutation methods to assess several standard screens for carcinogenicity. Their Type I error, a false positive, consists of labeling a relatively innocuous compound as carcinogenic.

The difficulty with reasoning in the opposite direction, from effect to cause, is that more than one set of causes can be responsible for precisely the same set of effects. We can never be completely sure which set of causes is responsible. Consider the relationship between sex (cause) and height (effect). Boys are taller than girls. True? So that makes this new 6 2 person in our lives . . a starter on the women’s volleyball team. In real life, in real populations, there are vast differences from person to person.

One example is H: θ ≤ θ0 K: θ > θ0 . In this example we would probably follow up our decision to accept or reject with a confidence interval for the unknown parameter θ. This would take the form of an interval (θmin , θmax ) and a statement to the effect that the probability that this interval covers the true parameter value is not less than 1 − α. This use of an interval can rescue us from the sometimes undesirable all-or-nothing dichotomy of hypothesis vs. alternative. Our objective is to come up with a decision rule D, such that when we average out over all possible sets of observations, we minimize the associated risk or expected loss, R(θ, D) = EL(θ, D(X)).

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Permutation, Parametric and Bootstrap Tests of Hypotheses: A Practical Guide to Resampling Methods for Testing Hypotheses by Phillip I. Good


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