## The Nature of Statistical EvidenceOur motivation for writing this book was a dissatisfaction with the many books with titles hke Foundations of Statistics. These books provide a needed description of the subject with examples of various statistical methods; but they do not satisfy the discerning reader because they do not explain why certain conclusions may be drawn from certain data and they do not discuss how statistics, the subject, meshes with the scientific process. We naively set out to fill in these gaps, but the situation is not so simple. What is desired is a tool—the one true statistics—which can be applied to data with certainty to justify conclusions, but what is available, in fact, are various competing theories of statistics. The careful reader may correctly point out the relation of this manuscript to po- modem epistemology, a philosophy which emphasizes that all human knowing—in fields as diverse as religion and science—is culture dependent and that therefore "truth" is not absolute. Take, for example, the "truths" of Christianity and Islam— wars have been fought over their differences. In the field of statistics there are, for example, Bayesians and sampling theorists. Carson (2003) states, "Surely it is better, postmodems tell us, to encourage insights that flow from many different perspectives. . . " In statistics, postmodernism is manifest at two levels. First, the findings of statistical applications are not about the true state of nature but about models of experiments on nature. |

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### Contents

1 | |

7 | |

The Evolution of Natural Scientists and Their Theories | 18 |

Law and Learning | 33 |

Introduction to Probability | 41 |

Attitudes Toward Chance | 61 |

A Framework for Statistical Evidence | 75 |

A Critique of Bayesian Inference | 84 |

The LongRun Consequence of Behavior | 97 |

The Nature of Statistical Evidence | 116 |

The Science of Statistics | 122 |

Deductive Logic | 133 |

References | 143 |

Subject Index | 151 |

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### Common terms and phrases

accepted according alternative applied approach argument assumes assumption axioms Bayesian behavior belief calculated called chance Chapter checked common concept concerned conclusion consequence consider consistent continuous deduction defined density depends developed difficult discussion distribution economic equally evidence example exist expected experiment experimental explain fact fair follows formulated frequency function geometry given hence hypothesis ideas important independent individual inference interpretation knowledge likelihood logic mathematics meaning measure method nature objective observed obtain occur outcome p-value parameter particular performed possible practice prediction present principle prior probability problem proposition prove question random variables ratio reason relative rule sample scientific scientists sense significance simple single situation statements statistical success suggests summarize Table Theorem theory true truth write

### Popular passages

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Page 13 - The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order...

Page 143 - ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.

Page 26 - Conclusions are withheld until adequate evidence has accumulated. A conclusion is a statement which is to be accepted as applicable to the conditions of an experiment or observation unless and until unusually strong evidence to the...

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Page 24 - Let me now say only this, that truth is one species of good, and not, as is usually supposed, a category distinct from good, and coordinate with it. The true is the name of whatever proves itself to be good in the way of belief, and good, too, for definite, assignable reasons.

Page 20 - To see what is general in what is particular and what is permanent in what is transitory is the aim of scientific thought.

Page 61 - In applying statistical theory, the main consideration is not what the shape of the universe is, but whether there is any universe at all. No universe can be assumed, nor . . . statistical theory . . . applied unless the observations show statistical control. In this state the samples when cumulated over a suitable interval of time give a distribution of a particular shape, and this shape is reproduced hour after hour, day after day, so long as the process remains in statistical control — ie, exhibits...

Page 10 - If p and q are points, then there exists one and only one line containing p and q. Axiom 4. If L is a line, then there exists a point not on L. Axiom 5. If L is a line, and p is a point not on L, then there exists one and only one line containing p that is parallel to L. These axioms would not...