The book How to Lie with Statistics written by Darrell Huff shows you how statistics are used to mislead; sometimes unintentionally, other times on purpose. It gives the readers the knowledge necessary to intelligently question and understand the story behind the numbers. In other words, it shows the tricks the crooks use, so that honest men can use this knowledge for self defense.
I think it's particularly useful for a manager or an executive to read and understand this book, because they are usually presented with a lot of numbers, graphs and charts and are expected to make decisions based on these numbers. People collecting and presenting the numbers to management could employ some of the tricks explained in this book and therefore, we should be careful when basing our decisions on those numbers.
It's interesting that although this book was written in 1954, the concepts explained are just as pertinent today. Some salary figures seem to be outdated but the tricks remain pretty much the same.
The book starts with explaining the importance of sample selection and built-in bias. Sampling is critical in statistics because we can't always count or observe every item in a population and therefore have to base our judgments on a selected sample. However, a sample with a built-in bias could dramatically change the results. When examining survey results, you should keep in mind that people who complete the surveys are different than those who didn't respond to the survey and those who respond tend to over or understate the truth. The method of survey and/or the interviewer also impacts the results. Another very important factor is the sample size. If you toss a penny only 4 times, you could get 4 heads. Obviously, from this result you shouldn't decide that you would get a head every time you toss a coin. Small samples could be very misleading and you should try to find out what the sample size is before making your decision based on the results presented.
The book also emphasizes that there are three different numbers one can use when reporting on an "average" value: arithmetic mean, median and mode. Even though they can be similar when describing the heights of men, they are usually far off when describing salaries. One should always be careful when interpreting results with "average" values, and should understand which average is employed. It's also important to understand the ranges or standard deviations along with means. For example, if you pack your clothes according to the average temperature for your vacation to Oklahoma City ignoring the ranges, you could end up in a hospital. Similarly, you should also pay attention to the errors especially when comparing figures with small differences. Ignoring those errors, which are implicit in all sampling studies, you could end up in incorrect results. Percentages could also be another misleading way to present the results as how they are calculated and what the real figures are generally not clear to the reader.
The power of graphs and the tricks on them are well illustrated in the book. It is very easy to tell two different stories by just changing the ranges on graphs or trimming below an artificial baseline– such as a very profitable year vs. a steady one. Sometimes, we prefer to use pictures instead of graphs to better visualize the results. However, they can be exploited even more than graphs to deceive the readers. Honest comparisons should be done in one dimension and pictures should have areas proportional to values. Because executive reports are usually full of graphs, special attention should be paid to see if similar tricks are employed.
Another interesting concept explained in the book is the semi attached figure: if you can't prove what you want to prove, demonstrate something else and pretend they are the same thing. When there is a comparison, you should carefully look at what the comparison product or group is. You should also control for all other potential risk factors when studying effects of factors. The most striking example in the book is the claim used by Navy recruiters: It was safer to be in Navy than out of it just by comparing the death rates of Navy personnel and NY citizens, even though these groups are not comparable.
Maybe one of the most common mistakes about statistics is to think that something is a result of something when they are correlated. However, correlation does not imply causation. A very common instance is where neither of the variables have any effect on each other but there is a real correlation. The book presents a great example for this with rum prices and ministers' salaries. They seem to be correlated and you could decide that one is the cause of the other where in fact the rise in the prices is the real influence for both. Therefore, one should be very careful interpreting results because it is very easy to show a positive correlation between a pair of things.
•Did somebody change the subject? (Is there a switch between the raw figure and conclusion?) •Does it make sense?
In conclusion, I think Darrell Huff wrote a timeless book in 1954, which shows that you shouldn't have blind faith in the numbers that you come across in reports, newspapers, and even in academic research. He explains in a humorous way that statistics is an art of presenting numbers and an area which is widely open to abuse. With the help of this book, we should employ sound statistical reasoning and challenge the results presented, something that people today really need to consider.