Misleading Statistics

Most people have more than the average number of legs – or eyes, arms, fingers, or in fact most body parts. This is not because some people have too many body parts, but because some people have lost some or other body part, through accident or disease.

In a strict sense, this means that most of us are better than average. Of course, drawing that strict statistical inference is ridiculous, and illustrates that you must be careful when using statistics, especially since so much discussion statistical discussion tends to get tied up in wordplay.

Probably the best examples of misleading statistics are the definition of the 'average wage'.

By 'average wage', do we mean the median wage, the most common wage, or the average wage?

The median wage is the 'middle wage' so that half earn more and half earn less.

The most common or modal wage is actually the minimum wage – the legal minimum per hour wage that someone can be paid. Obviously most people earn more than this, both per hour and weekly.

Many people imaging that the average wage is the total national income divided by the population, but in fact this is far from the truth, for several reasons:

Many people work part time and are paid per hour.

Many people do not earn a wage, but they are part of the population – children, housewives, unemployed people and pensioners

A lot of income is unearned. Interest and rent is income but does not count as wages.

Self employed people are paid differently from people who work for an employer

If we define the average wage as the total wages paid to all the employed people, we can say – since some people earn very high wages – that modal wage < median wage < average wage.

Another way in which statistics can be misused is when some outcome is unlikely, but a test for that outcome can still indicate that it has happened. These are called 'false positives'. Many people imagine that if they test positive for a disease, then they have it, or that if a person is accused of a crime, that they are guilty. Neither of these are necessarily true, and in fact may be quite unlikely, if the probability of them testing positive for the disease given that they do not have it is not also low, or that the evidence needed for an accusation of guilt to be made is quite low.

Often, one a test has indicated positive for a disease, this only indicates that further investigation is warranted. In criminal trials, a person must be proved guilty beyond all reasonable doubt. Suspicion is not good enough.