16 of 18 people found the following review helpful:
4.0 out of 5 stars
My goto stats book, May 10, 2006
This has been my goto stats book since I bought it for a class in 2002. It's a clear introduction to mathematical statistics. I use it to try to understand some of the more advanced concepts that I'm learning now, but, unfortunately, it is just an introductory book. It does have a lot of information in it, so I still rely on it pretty heavily.
On the flip side, I'm using this book less and less because I bought Wasserman's 'All of Statistics', which is much more compact and has far more concepts in it. 'All of Statistics' is more of a reference tool, instead of a learning tool, though.
If you want to learn statistics, pick up this book and Ross's First Course in Probability. For most non-specialists these books will contain all the probability and statistics you will ever need.
Sorry I can't recommend anything cheaper.
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22 of 26 people found the following review helpful:
4.0 out of 5 stars
Good reference book overall, January 15, 2006
Overall, a good book. Could be a better even after excluding minor details- the ones noticed mentioned below.
Background necessary: Calculus- especially Taylor series, Integration by parts, solving for areas by integration and figuring out their limits; Even with a sufficient background, some proofs are quite rigorous or not well written enough, not sure which sometimes.
Comments based on first 7 Chapters of the book:
Standard deviation- excellently described
Relative frequency- NOT very well described. Makes sense on looking at chart in the book, but readers may forget to look at chart. A good definition for this important term is needed.
p. 43 They mention multinomial expansion before binomial distribution 1 chapter later. Very unnecessary, and doesn't make sense for the general reader to just stick it in there. It's like trying to squeeze information just to try to put something mathematically interesting that is more of a hinderance for learning permutations, combinations, and the multiplication rule. They show it to try to combine the principles together, but to make any sense of the multinomial expansion, besides choosing numbers to do it out, the proof to understand it fully is graduate level mathematics. A big no no for the book!! The least the book could do is expand by showing a specific example of this, and maybe even the proof itself, or just not mention it at all.
Section 2.7, p. 50 intro- too wordy. "relative frequencey of occurrence" in parentheses should probably be taken out for less confusion since a rel. freq. does not have to be based on a conditional probability occurring. Leaving it in leaves the reader at possible ambiguity.
Section 2.9, p. 62 Unnecessarily complicated- 1/5 * 3/4 = answer makes a lot more sense than them breaking it down into an unnecessary 7+ steps = answer.
Binomial Theorem probably could've been presented better. The idea of the binomial expansion and definition 3.7 (binomial distribution theorem) should be explained together right after definition 3.6 (explanation of a binomial experiment) rather than confusing the reader and leaving it off until later on.
p. 102-104 The book does a good job relating some word problems to the real world in good, brief explanations.
p.152 Step function should show hollow points if not the filled end points as well at least- too sloppy.
p. 172 Example 4.9 well done, but makes it sound like = (y- u)/o was intuitively obvious even to the beginner. The book tends to introduce some examples like this to introduce a theory. Just something one needs to get used to. It would be nice if they were able to put a sentence on page 1 about how some conecepts are inrtoduced by example first, but of course not everyone would read it anyway.
p. 188, sec. 4.8- great summary explaining existence for variety of statistical models
Example 5.1, p. 212- not a very good example. The table's correlation to the sample space given is overly ambiguous. Example is confusing, especially since they use the starting point starting from the top right corner instead of the top left corner and show no indication of what stands for what without reader figuring it out. Poorly set up.
p.213 typo- 6/9, not 8/9- tricky to figure out for a beginner
p.225 calculation- just add "= 1" to show solving of one of the integrals. Book sloppily leaves out this simple, but crucial step. A hard read for beginners to notice.
"degrees of freedom (d.f.)" can probably be better and simply defined than the book's "attempts," such as always one less than number of trials or something like that rather than always showing d.f. by notation only.
It's quite arguable if maybe just normal, or normal and t distributions and then central limit theorem should be mentioned in the book first, rather than throwing in all the different kinds of distributions in to learn for Chapter 3 first.
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