DENNIS O. CHANTER
The teaching of any subject is enlivened and enriched by the use of suitable anecdotes and analogies. Such material, however, is often passed on from teacher to student without appearing in print, although one useful source is the book by Campbell (1974). The purpose of the present article is firstly to pass on a few ideas, in the hope that some of them will be new to some readers, and secondly to encourage readers to put some of their own pet anecdotes into print. (Please send in all contributions, however short, to the Editorial offices—Editor.)
It is not always easy to remember where one first hears a particular anecdote; in some cases I can make an appropriate acknowledgement, but for most I cannot, although very little of this article is original.
The Importance of Variability
Stories illustrating the weakness of just quoting an average without giving any indication of variability are not hard to find. An old favourite is the person with his head in a fridge and feet in an oven who is said to feel ‘quite comfortable’ on the grounds that his average temperature is normal. Campbell cites the story of the soldiers who drowned in a river with an average depth of two feet, while I rather like the story of two soldiers who both fired on an enemy soldier: one missed by one foot to the left, and the other by one foot to the right, but they nonetheless congratulated each other on the grounds that their enemy was, on average, dead.
For a more mature audience, though, I prefer the following story, which I first heard from D. J. Newell of the University of Newcastle. A statistician went to a conference in Paris. While he was there, he enquired of one of his French colleagues for directions to the red light district. He was told that if he went to a certain address he would find a number of females with an average age of twenty-three. He did; three babes-in-arms and their 87 year old grandmother!
Variability and Precision
The relationship between variability, precision and the number of replicates required in an experiment is nicely illuminated in the story about the Englishman who went on a business trip to Dublin. When he set out for his first meeting, he realised that he had left his watch in the hotel. He wasn’t sure how much time he had to spare, so he looked around for a clock in the street. There were two, but unfortunately they did not agree with one another. So then he asked a passer-by for the right time, but the passer-by merely indicated the street clocks and said (it helps if you can do the right accent), "Sure, but can’t you see the clocks?"
"Yes, but they both tell different times
"Well of course they do, if they both told the same time we’d only need the one
Correlation and Regression
It is difficult to find an amusing story which relates to the use of the linear regression equation, y a + bx. One’s quarterly gas or electricity bill can be used as an analogy though, with a representing the standing charge and b the rate per unit
Moving on to the cause and effect fallacy in regression, there are several examples which illustrate the dangers involved in inferring a cause and effect relationship from a significant linear regression. When my son was two or three years old, he went through a phase of not wanting to eat his lunch, and my wife noticed that refusal to eat at lunchtime was correlated with unsettled and difficult behaviour during the afternoon. Conversely, a good lunch tended to be followed by a contented and ‘easy to live with’ behaviour for a while. This realization led to some quite traumatic lunchtimes, during which my poor son was almost force fed in an attempt to avoid an unpleasant afternoon. I don’t think I ever did succeed in getting across the message that perhaps this was not cause and effect; maybe there was some third factor (e.g. a queasy stomach) which would explain the observed correlation and also imply that the attempted corrective action would probably make matters worse rather than better.
Finally under this heading, consider that often quoted measure of goodness of fit, the percentage variance ‘accounted for’. This is sometimes, quite inappropriately, used to compare goodness of fit across two different sets of data. In his discussion of percentages, Campbell gives a useful (and documented) illustration. It seems that a certain baker once claimed that his bread contained fewer calories per slice than other brands. What he didn’t say was that his slices were thinner.
Hypothesis Testing
A useful analogy when introducing the classical hypotheses testing framework is the British judicial system. The null hypothesis corresponds with the assumption of ‘innocent until proven guilty’, and the different consequences of type I and type II errors are well illustrated by the different implications of the conviction of an innocent person and the acquittal of a guilty one.
For a slightly more light-hearted approach, though, consider the problem of deciding whether to purchase a particular second-hand car at its asking price. The null hypothesis is that the value of the car is equal to (or more than) the asking price. If this is true, you should buy it. If you don’t you’ve committed a type I error, or, more graphically, looked a gift horse in the mouth. The alternative hypothesis is that the vehicle is worth less than its asking price. The type II error is equivalent to being taken for a sucker.
Biased Sampling
A manufacturer of breakfast cereals wanted to carry out a survey on what people ate for breakfast. He opened his telephone directory ‘at random’ and called up the first number of the page. "Excuse me, but would you mind telling me what you had for breakfast today?" Back came the answer, "Porridge". He ‘phoned the next number, and again, "Porridge". The third number produced "Cornflakes", while the next three were all "Porridge". He then realised what had happened. The directory was opened at the Mac’s, and the cornflakes eater was Machinery Installations Ltd.’! (That’s another story I first heard from D. J. Newell.)
Huntingdon Research Centre
References
Campbell, S. K. (1974), Flaws and fallacies in statistical thinking. Prentice-Hall, New Jersey.
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