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Best Book for Learning/Implementing Statistics and Probability Using Mathematica?
I am a relatively novice Mathematica user having now used the product about 2 years. Presently, I am in critical need to learn how better to apply Mathematica's statistical and probability tools, but find myself having difficulty in working solely from the documentation center and on line resources. In particular, I seek to learn how to perform hypothesis testing using an ANCOVA model for multiple groups and application of the Johnson-Neyman and potentially related procedures for those comparisons in which the slopes for multiple groups are not homogeneous. Designs of most interest to me, fortunately, only involve one covariate, although it would be helpful to underst and how to analyze situations involving multiple covariates. Also, I need to learn how Mathematica can be used to establish confidence limits and critical values for Bonferroni F-tables and Sheffe-like tests to establish experiment-wide error rates for such comparison tests. Ideally, I would like to be able to program simple pure functions that would run such multiple-group comparisons for easy use in routine "production-level" analysis of data. Until now, I have used another system to perform these kinds of analyses and tests, but seek to implement this in the context of functional programming and within the broader framework of tools and functions available in Mathematica. Although I am getting better at understanding both the subject matter and its implementation using Mathematica, I seek one or two good books that discuss hypothesis testing in more detail than the relatively "bare-bones" examples in the Mathematica documentation, yet at a somewhat basic entry level and with more elaboration and examples that would improve both understanding of basic statistical analysis and facility implementing it in Mathematica. Although I am eager to learn more about relatively sophisticated statistical designs and distributions, at this point, I really need a book that will serve as a guide to the basics of hypothesis testing and a bridge to the functional programming required and usable perhaps as a tutorial that could serve as a basis for studying and implementing ideas that may appear in more advanced texts. Ideally, such texts would serve as a bridge for programming procedures discussed in Huitema (1980) and similar texts and hopefully further elaborate on the relation of ANCOVA to various ANOVA designs as implemented in Mathematica. I already have Ruskeepaa's Mathematica Navigator and Mangano's Mathematic Cookbook, but find chapters in these, although helpful, only getting me part of the way there. Does anyone, who has found themselves in this situation or who teaches statistics using Mathematica, have any suggestions as to what would be the best book or books that might be of most help to me? Any suggestions and or discussion would be most appreciated. Thank you.