Review of "Statistics" by Freedman, Pisani, and Purves (2017)
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Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#2[deleted]
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#3- David Freedman, Robert Pisani, and Roger Purves, Statistics, 4th ed.
- The article's author also recommends these online materials: https://www.stat.berkeley.edu/~stark/SticiGui/Text/toc.htm.
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#4I read/worked through Freedman's Statistics a couple of years ago and I walked away from it a different person. I always recommend it when someone asks for a good book to learn statistics from. However, it did leave me craving some of the maths that the authors intentionally left out to make the material more accessible. Freedman's more advanced book, Statistical Models, has you derive many of the results from the first book right at the start, then focuses mainly on linear models. It was a great follow-up which provided the mathematical substance that I felt was missing from the first book.
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#5excellent domain name
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#6Most statistics classes are not taught to people who will be professional statisticians. I agree whole-heartedly with this:
> The book by Freedman, Pisani, and Purves is the one I would have liked to teach from, and it was the book I drew upon the most in prepping my own lectures, as an antidote to the overwrought and confused style of my assigned text. The authors maintain the underlying attitude that statistics is a useful tool for understanding certain questions about the world, but in this way it augments human judgement, rather than supplanting it. To quote from the preface:
> > Why does the book include so many exercises that cannot be solved by plugging into a formula? The reason is that few real-life statistical problems can be solved that way. Blindly plugging into statistical formulas has caused a lot of confusion. So this book takes a different approach: thinking.
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#7From the end of TFA:
>The book is not without its weak moments, although they are few. One in particular which I recall is the treatment of A/B testing. Essential to any hypothesis testing is the matter of how to reduce the sampling mechanism to a simple probabilistic model, so that a quantitative test may be derived. The book emphasizes one such model: simple random sampling from a population, which then involves the standard probabilistic ideas of binomial and multinomial distributions, along with the normal approximation to these. Thus, one obtains the z-test.
>In the context of randomized controlled experiments, where a set of subjects is randomly assigned to either a control or treatment group, the simple random sampling model is inapplicable. Nonetheless, when asking whether the treatment has an effect there is a suitable (two-sample) z-test. The mathematical ideas behind it are necessarily different from those of the previously mentioned z-test, because the sampling mechanism here is different, but the end result looks the same. Why this works out as it does is explained rather opaquely in the book, since the authors never developed the probabilistic tools necessary to make sense of it (here one would find at least a mention of hypergeometric distributions). Given the emphasis placed in the beginning of the book on the importance of randomized, controlled experiments in statistics, it feels like this topic is getting short-shrift.
Can anyone recommend good resources to fill this alleged gap?
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#8From the end of TFA: >The book is not without its weak moments, although they are few. One in particular which I recall is the treatment of A/B testing. Essential to any hypothesis testing is the matter of how to reduce the sampling mechanism to a simple probabilistic model, so that a quantitative test may be derived. The book emphasizes one such model: simple random sampling from a population, which then involves th…
I’d ignore the critique completely - it lacks internal consistency. The similar final result is due to central limit theorem, which is a large n result, and actually lets you ignore the hypergeometric construct and use a binomial instead since those are similar for large n.
[edit: grammar]
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#9From the end of TFA: >The book is not without its weak moments, although they are few. One in particular which I recall is the treatment of A/B testing. Essential to any hypothesis testing is the matter of how to reduce the sampling mechanism to a simple probabilistic model, so that a quantitative test may be derived. The book emphasizes one such model: simple random sampling from a population, which then involves th…
In the book, Freedman states that two assumptions of the standard error of the difference are violated by the way subjects are assigned to control and treatment groups in randomized controlled trials (RCTs).
The standard error of the difference assumes that a) samples are drawn independently, i.e., with replacement; and b) that the two groups are independent of each other. By samples being drawn, I mean a subject being assigned to a group in a RCT here.
If you derive the standard error of the difference, there are two covariance terms that are zero when these assumptions are true. When they're violated, like in RCTs, the covariances are non-zero and should in theory be accounted for. However, Freedman implies that it doesn't actually matter because they effectively cancel each other out, as one inflates the standard error and the other deflates it.
Re: Review of "Statistics" by Freedman, Pisani, and Purves (2017)
#10From the end of TFA: >The book is not without its weak moments, although they are few. One in particular which I recall is the treatment of A/B testing. Essential to any hypothesis testing is the matter of how to reduce the sampling mechanism to a simple probabilistic model, so that a quantitative test may be derived. The book emphasizes one such model: simple random sampling from a population, which then involves th…
> gap?
E. L. Lehmann, 'Nonparametrics: Statistical Methods Based on Ranks', ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975.
Sidney Siegel, 'Nonparametric Statistics for the Behavioral Sciences', McGraw-Hill, New York, 1956.
Bradley Efron, 'The Jackknife, the Bootstrap, and Other Resampling Plans', ISBN 0-89871-179-7, SIAM, Philadelphia, 1982.
Hypothesis testing?? Somewhere maybe I still have my little paper I wrote on using the Hahn decomposition and the Radon-Nikodym theorem to give a relatively general proof of the Neyman-Pearson theorem about the most powerful hypothesis test.