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208 of 212 found the following review helpful:
An excellent reference and self-study guideMay 05, 2000
By Duwayne Anderson
I have six books on statistics in my personal library. All of them are bigger than Bulmer's book, but none have been read as many times, and none are as tattered, marked up, and cross-referenced. Simply put, Bulmer's book is the most useful and complete book on basic statistics that I have. It's a nice package in a reasonably sized book with all the most important stuff for dealing with basic statistical problems that many engineers are likely to encounter in a day's work.
Chapter 1 is a short blurb on the concept of probability. This is very useful because it places the rest of the text on a very specific and concise footing. Essentially there are two concepts of probability. One is the relative frequency with which an event occurs in the long run. An example of this is the tossing of a coin many times and counting the number of times it comes up heads. The author describes this as statistical probability.
The second concept of probability is what the author calls inductive probability. Inductive probability is "the degree of belief which it is reasonable to place on a proposition on given evidence." The essential difference between the two concepts of probability is that statistical probability is an empirical concept, while "inductive probability is a logical concept." Bulmer closes chapter 1 by saying, "It has been reluctantly concluded by most statisticians that inductive probability cannot in general be measured and, therefore, cannot be ............" Read chapter 1 to find some interesting arguments in support of this proposition - a proposition that may be surprising to some people. As a result (and as the book's title suggests) Bulmer keeps his book almost exclusively in the domain of statistical probability.
Chapter 2 introduces two simple law of probability. The first relates to the addition of probabilities of mutually exclusive events. The second relates to the multiplication of probabilities. Simple in concept, Bulmer illustrates these two laws by several examples including tables of measurements made on real experiments, and some from Mendel's laws of heredity.
Chapter 3 is pivotal. It develops the mathematical expressions for random variables and probability distributions. Chapter 3 is relatively short, but lays the groundwork for chapter 4, which describes the properties of distributions. Chapter 4 has many useful equations, including those for the mean, variance, measures of dispersion, moments, etc.
Chapter 5 introduces the notion of expected values for both discrete and continuous variables. These are determined not only for single distributions, but also for distributions that are combined in algebraic ways through multiplication, addition, division, etc., which also leads (naturally enough) to the moment-generating function.
Chapter 6 highlights some important distributions (the Binomial, Poisson, and Exponential) and discusses their statistical properties (mean, variance, skewness, and kurtosis). Bulmer adds additional insight into these distributions by describing how they arise in real-world situations. [As a note here, this chapter is useful and interesting, but it could easily be many pages longer. For example, when I was investigating polarization mode dispersion in optical fibers I wanted to know the statistical properties of the Maxwellian distribution. Bulmer did not have it - and I eventually found what I was looking for in "The Handbook of Mathematical Functions," by Milton Abramowitz and Irene A. Stegun.]
The normal distribution is not covered in chapter 6. Instead, as the granddaddy of all statistical distributions, it gets its own chapter - chapter 7. Here Bulmer derives the moments, variance, and a couple of proofs relating to the Gaussian or normal distribution. He also has a nice discussion on the central-limit theorem - which explains why the normal distribution is found in so many places. Chapter 8 continues the theme of distribution functions by considering the Chi-squared, t, and F functions.
Chapter 9 leaves the subject of distributions and describes tests of significance. This is an extremely important chapter for anyone involved in experimental science where the uncertainty of experimental results must be understood and reported. Chapter 10 deals with a related subject - namely statistical inference. In these two chapters Bulmer develops the tools and techniques needed to properly interpret, understand, and report on statistical data - including non-statistical data with statistical noise.
The book ends with a discussion on regression and correlation. Again, this is a very useful chapter with equations for the slope and intercept for linear regression, as well as variance for the slope and intercept. Bulmer includes the derivations for these equations, making it easy and straightforward to extend the analysis to provide regression and correlation for any polynomial fit. This chapter - along with those on tests of significance and statistical inference - will probably be the most useful to students in the sciences.
The book ends with several tables. Many of these tables were generated before the age of calculators, so they may be less needed today than in days gone by. Still, you don't always have a calculator handy. The tables include the probability and density functions for the standard normal distribution, the cumulative probability function for the normal distribution, percentage points of the t distribution, Chi-squared distribution, and the five-percent and one-percent points of the F distribution.
The book has an adequate index (though I'd like it to be longer) and each chapter has problems - with answers in the back. This makes the book ideal for individual study, and the problems often provide greater insight by helping the student extend ideas found in the book.
Overall, this is one of the most used books in my library. And for the price, it's an absolute steal. If you've been wanting a short, concise, yet relatively complete book on statistics - and one that is well-written and easy to follow, yet mathematically involved - but still practical, I highly suggest Bulmer's book.
60 of 62 found the following review helpful:
A classic textbook; probably the best introduction aroundMay 09, 2000
I've learned probability and statistics from at least four other authors, and have constantly been browsing other textbooks that appear in the bookstore. I chanced upon Bulmer's 1965 book one fortunate day. It is still useful and relevant more than thirty years after its first printing. This clear and elegant book is also concise and straight-to-the-point, offering beautiful and brief developments of material that usually appears hopelessly muddled in many a reputable current statistics textbook (e.g., different notions of probability, the binomial, Poisson, normal distributions, and the Central Limit Theorem). Aside from the solid mathematics and many worked examples, the book includes a few entertaining digressions into the history of the subject.
In short, learn and review statistics from this classic. Thank you, Mr. Bulmer, and Dover Publications (for making this textbook available in a nice format at such a low price).
34 of 35 found the following review helpful:
Rich in InsightSep 23, 2002
This modest little book is both a masterpiece and a gem! I can't praise it enough! It is different from any other statistics book I have ever read in that it puts you in the place of famous historical figures in statistics and helps you rediscover their findings. His use of original source material is very well done. The book is self-contained and the author proves almost everything of importance(some of the proofs are more intuitive than rigorous at times, but that's the point). Bulmer has a knack of making the most difficult concepts (hyperspace, degrees of freedom) seem natural. He covers a very broad terrain from distributions, tests of significance, inference, Bayesian methods, etc. Written on many levels, this is useful for a novice or intermediate student but I suspect professional statisticians will find much to keep them thinking about. While reading through this book you will often say "aha, so that's why they do that". For the price it is the best value possible; you won't regret picking up a copy of this book and if you enjoy the inner workings of statistical theory you will refer to it again and again.
31 of 33 found the following review helpful:
Unlocks the mystery behind the equationsJan 08, 2010
By L. Mickelson
"PhD in Mat Sci & Engr"
The positive reviews for this book seem to be written by people with a previous background in statistics and/or strong math skills. Furthermore, they want to know the why behind every equation. I mostly fall into this category.
The negative reviews come from people who use this as their introduction to statistics, and who probably don't have a strong grasp of calculus or perhaps higher level math in general.
In my opinion this book offers something that no other statistics book has: clear derivations of all the fundamental and important equations and distributions in statistics; followed by lucid explanations. In other words this book unravels the mystery behind the equations. If you've thought about a statistics equation a lot and wondered, WHY? Then this is the book to read.
Here are 4 questions I had that Bulmer answered:
1) Why is the mean more commonly used than the median (and in which cases is the median better)? p.51-54
2) As a measure of variability why use a root-mean-square procedure (i.e. accepted def. of std deviation ) instead of mean deviation (i.e. take absolute value of deviations)? p.54-59
3) What is the logical error in the gambler's fallacy? p.87-88 (Note: many statistics books treat this, but I've found Bulmer's book to give the most satisfying answer.)
4) Why does the standard deviation of a sample have the n-1 term in the denominator instead of the n term like the stdev of the population? p.129-130
(Note that he answers questions 1, 2, and 4 more than once, but the pages listed are the first time the answer appears.)
Thus, I strongly recommend buying and reading this book if, like me, you have a burning desire to know why the equations are the way they are. I would recommend a different book, say Statistics by Freedman, if you're either new to statistics or you don't have a great handle on math (i.e. proofs, calculus, etc.).
Note that Statistics by Freedman is an excellent introductory text with a plethora of examples and will not take you down the terrible path of memorizing formulas that you don't understand. Rather it seeks to give a conceptual understanding of statistics without delving too deeply into the underlying math.
Finally, I gave Bulmer's book 4 stars rather than 5 because Bulmer often derives equations that I'm not interested in.
19 of 20 found the following review helpful:
Great book, easy to read and complete tooJun 15, 2005
By Mario V
Why I think this is a great book:
1) It is easy to read and understand. Author has a great aproach and examples all around.
2) At the same time nothing is left not proven. Prior to this, I purchased couple of books that just give you this or that for granted as a formula (for example they just "anounce" what the standard deviation is for the binomial distribution without proving it or explaining why). I despised that, as I believe you either understand and learn something completely, or you don't.
3) The book even went further than I expected - not only that everything mentioned in the book is proven, it is even explained why some choices in the statistics are made in such a way that they are. Ever wondered why quadratic mean is used as a measure of deviation instead of arithmetic mean of absolute values? This is just one example of a fine job author did in making audience UNDERSTAND statistics.
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