Principles of Applied Statistics

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A focus on study designs and types then follows. The next sections cover measurement of variables, including discussions of scale, classification, and censoring. The succeeding chapter deals with the properties of data itself. Discussed are topics such as data auditing, data screening, graphical presentation, and tabular data. The next several chapters are devoted to the formulation and selection of analytic models, again with little discussion of statistical theory and implementation. Cox and Donnelly have successfully walked a tightrope between being too technical for the beginner and including enough sophistication for the advanced reader.

An exceptional feature of their text is the large number of applied and interesting examples, which makes sometimes subtle statistical concepts accessible to a wide audience.

PDF Principles of Applied Statistics

There are many examples more than illustrating in a concrete fashion the important statistical concepts of data analysis. For example, data describing the relation between badgers and bovine tuberculosis illustrate that careful measurement and reanalysis are vital to statistical analysis. The numerous illustrations enrich the presentation, and in addition they reflect the vast range of areas where data analysis plays an essential role. In the same vein, the authors comment that approximations do not usually have important influences on analytic conclusions.

Throughout the text, important but frequently neglected issues are raised that are relevant to most statistical analyses. For example, the text contains a complete description of the role of scale, and the authors note that rather different statistical descriptions depend on the scale chosen to measure the variables under study. This issue is particularly important in the analysis of epidemiologic data, where, for example, often little thought is given to choosing between an odds ratio ratio scale and a difference between two proportions additive scale.

Also important to epidemiologic data, the text contains a well-crafted section on differences in interpretation that arise from the analysis of observational data versus experimental data. This book will be useful to persons with little experience with statistical methods as a guide to analytic strategies. Equally, for those familiar with statistical methods, the material is a clear and concise reminder of the critical importance of considerations beyond the technical assumptions necessary to apply statistical techniques.

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Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account. Bayes wraps many assumptions needed for decision into the prior e.

Applied Statistics - Principles and Examples | Taylor & Francis Group

That prior is supposed to be an analysis-design or protocol function, determined independently of the analysis data unless you do empirical Bayes. The resulting posterior uses all those assumptions plus all the data-generation assumptions used for the P-value. In addition Bayes decisions need a loss function. So a well-informed and rational decision-maker will end up facing the same problem and process: How to quantify in the prior and model the contextual information about what is going on, and how to quantify a loss function.

Both are harder problems than how to crank the math once you have these ingredients specified. If you agree with that, maybe the big split here is whether we need or should even try for a decision.

Principles of Applied Statistics by D. R. Cox and Christl A. Donnelly

Why do we have to force a decision out of an analysis? Bayes does not solve this core uncertainty problem, although if used as in nonidentified-bias analysis it can illustrate it. None of that addresses requirements for FDA submissions and the like, but those issues go far beyond the present scope into politics and the like BTW I have presented hierarchical Bayesian methods for postmarketing surveillance at the FDA. We face some of these same issues across disciplines. Particularly in discussing appropriate standards of proof to apply in different contexts. As the statistician, I would be only too happy to present the relevant probabilities and leave subsequent decisions alone. Is atrial fibrillation a risk factor for readmission in heart failure patients? Are candidates for lung transplant with severe pulmonary hypertension more likely to experience a rejection if they get a transplant?

Is the end user going to be happy presenting the same? I doubt it. This is a bit of an aside, but even we statisticians are not always good at grasping or estimating probabilities, never mind people without any quantitative training. Good points ADA. My end users almost never expected or demanded more because any decisions were reserved for them or the consumers of the report. In fact I have often seen some statisticians try to inappropriately force decisions on such consumers by declaring their statistics proved harm or safety.

Now if your charge really is to offer a discrete decision about a substantive issue - e. A classic academic illustration of that conflict is the Jeffreys-Lindley paradox, where the Neyman-Pearson heuristic of alpha-level testing using the maximum-likelihood ratio will in large enough samples conflict with the Jeffreys Bayesian heuristic of using a prior point mass spike on the tested hypothesis. Though both heuristics have been called brilliant by non-overlapping subsets of statisticians, of course I find both distasteful due to the contextual absurdities they entail in soft-science research, and I think both are unnecessary for decision making in light of modern alternatives that instead lead to convergent decisions using explicit loss functions.

Principles and guidelines for applied statistics interpretation. Sander September 9, , pm 1. Sander September 7, , am 2. Is the distribution normal? Should an interaction term be in the model? SameeraDaniels September 7, , pm 4. Great set of insights Sander. I concur. Thank goodness for that Edit Feature Frank.

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Excellent insights so far. Stephen September 8, , pm 7. Reference Senn SJ.

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  • Mathematics: governess or handmaiden? PaulBrownPhD September 8, , pm 8. I heard a rumour that f2harrell and Stephen wrote a blog post about composites but i have never found it Sander spoke about p-values and Bayes. Sander September 11, , pm Thanks to the experts who have taken the time to post here and start this thread.

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    Cheers, Philip Consider the underlying science. The interesting scientific questions are not always questions statistics can answer. Think about where the data come from and how they happened to become your sample. Think before you calculate. Will the answer mean anything?

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    The data, the formula, and the algorithm all can be right, and the answer still can be wrong: Assumptions matter. Enumerate the assumptions. Which are plausible? Which are plainly false? How much might it matter? Why is what you did the right thing to have done? Beware hypothesis tests and confidence intervals in situations with no real randomness.

    Nevertheless, it is important that this rather negative role does not inhibit general judgement and initiative. This is one reason why estimation of effects is usually desirable as well as significance testing. Significance tests are concerned with questions like 'is such and such an effect reasonably firmly established by these data', and not with the question 'might there be something here well worth further study'.

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    In some cases it will be enough to obtain a good point estimate of without considering explicitly the precision of the estimate. Now, however, we consider what is to be done when explicit calculation of precision is required. We can define lower confidence limits in a similar way. Very often it is convenient to specify the uncertainty in the parameter by giving for a few values of a: a 1-ia: upper limit and a 1-ta: lower limit, thereby forming a so-called 1-a: equi-tailed confidence interval.

    This is an interval of values calculated from the data in sueh a way that only in a proportion to: of hypothetical repetitions will it lie below the calculated lower limit, and similarly for the upper limit. In the special case of the normal distribution mentioned above, the 1- a: confidence interval using the mean of the data is 4. No attempt will be made here to cover the full theory of confidenceinterval estimation.

    The following general points need watching in working with the various special cases which we shall encounter later. We can look on a 1- a: confidence interval as,. Occasionally, other concise descriptions are useful.