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Understanding statistics -- or not!

Not everything in this book is bad: the historical information is very interesting. (The author has a PhD in the history of science.)

Unfortunately, however, the book is riddled with blunders and misconceptions, obfuscations and inaccuracies.

Consider just one topic: the standard deviation -- pretty important when it comes to understanding statistics.

We are told that the standard deviation 'indicates how widely or closely spread the values are in a set of a data' (fine so far, apart from the typo of an extra 'a'), and then that it 'shows how far each of these individual values deviate from the average'. No: as a single summary figure, the standard deviation cannot possibly give information on 'each of these individual values'. (That is not its purpose, of course; indeed it almost the exact opposite of its purpose.)

The accompanying graphic carries the information that the 'standard deviation ... corresponds to the moment of inertia ... of dynamics'. No: it corresponds to the radius of gyration. And we are told that the moment of inertia is 'a geometrical property of a beam, and a measure of the beam's ability to resist buckling or bending'. Oh dear! Clearly the author's grasp of mechanics is no better than her grasp of statistics.

The formula for the standard deviation is then given -- but it is typeset incorrectly!

Next, the standard deviation for a set of data (with mean 8) is calculated (correctly!) as 2.82. The accompanying comment is 'This means that the average amount of deviation in this set of data is 2.82 units away from the mean value of 8 and that, therefore, there is a small amount of variation in this sample'. There appears to be no explanation of the criterion by which the variation is deemed large or small. Certainly it is not a criterion known to this statistician.

Finally, we have 'Although the standard deviation indicates to what extent the whole group deviates from the mean, it does not show how variable a particular group is.' I have read that over and over again and I am at a loss to know what it is trying to say.

I wish I could say that the other statistical concepts in the book fared better than the standard deviation -- but they don't. I can't resist mentioning the coefficient of variation which is said to be useful in comparing the variability of temperatures in two cities, one set of measurements being in in degrees Celsius and the other in Fahrenheit. This, of course, is a perfect example of when it would *not* be appropriate to use the coefficient of variation -- because the mean could be zero and the coefficient of variation would then be infinite.

If you understand anything about statistics this book will infuriate you; if you don't understand much about statistics the book will hinder not help.



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