By D. R. Cox
Publisher: Cambridge University Press
Print Publication Year: 2006
Online Publication Date:March 2011
Online ISBN:9780511813559
Hardback ISBN:9780521866736
Paperback ISBN:9780521685672
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511813559.004
Subjects: Statistical Theory and Methods, Quantitative Biology, Biostatistics and Mathematical Modeling
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Summary. First a number of distinct situations are given in which significance tests may be relevant. The nature of a simple significance test is set out and its implications explored. The relation with interval estimation is emphasized. While most of the discussion is from a frequentist perspective, relations with Bayesian theory are outlined in the final section.
General remarks
So far, in our frequentist discussion we have summarized information about the unknown parameter ψ by finding procedures that would give in hypothetical repeated applications upper (or lower) bounds for ψ a specified proportion of times in a long run of repeated applications. This is close to but not the same as specifying a probability distribution for ψ; it avoids having to treat ψ as a random variable, and moreover as one with a known distribution in the absence of the data.
Suppose now there is specified a particular value ψ0 of the parameter of interest and we wish to assess the relation of the data to that value. Often the hypothesis that ψ = ψ0 is called the null hypothesis and conventionally denoted by H0. It may, for example, assert that some effect is zero or takes on a value given by a theory or by previous studies, although ψ0 does not have to be restricted in that way.
pp. i-iv
pp. v-viii
pp. ix-xii
pp. xiii-xvi
pp. 1-16
2 - Some concepts and simple applications : Read PDF
pp. 17-29
3 - Significance tests : Read PDF
pp. 30-44
4 - More complicated situations : Read PDF
pp. 45-63
5 - Interpretations of uncertainty : Read PDF
pp. 64-95
6 - Asymptotic theory : Read PDF
pp. 96-132
7 - Further aspects of maximum likelihood : Read PDF
pp. 133-160
8 - Additional objectives : Read PDF
pp. 161-177
9 - Randomization-based analysis : Read PDF
pp. 178-193
Appendix A - A brief history : Read PDF
pp. 194-196
Appendix B - A personal view : Read PDF
pp. 197-200
pp. 201-208
pp. 209-212
pp. 213-219