Bad Statistics

16 August 2011

A journalist, a psychologist and a statistician are travelling from London to Edinburgh by train. As the train crosses the border, the three travellers look out of the window and notice a black sheep standing alone in a field. The journalist says, “Look! The sheep in Scotland are black.” To which the psychologist replies, "Actually, we can conclude at least one sheep in Scotland is black”. The statistician shakes his head and boldly states, “I think you’ll find we can confidently say that at least one half of one sheep in Scotland is black.”

Statistics is the study of the collection, organisation, and interpretation of data. You may be familiar with Statistics in the form of surveys and experiments, pie charts and bar graphs. Statistics as a branch of Mathematics is a very powerful tool in trying to explain the world around us, and form predictions about future events.

But Mathematicians and Statisticians need to be careful! Statistics is often misused (or selectively used), and poor conclusions may be incorrectly drawn from data. Here are some examples:

  • Children with bigger feet spell better! In a survey of 200 children those with larger feet consistently scored more highly on a spelling test. ... Of course they did! Children with larger feet are likely to be older, and older children are generally better spellers having had more exposure to words at school and at home.
  • Exams are getting easier! Pass rates are rising. The proportion of papers being awarded the top grades has increased. Exams ‘getting easier’ is one explanation. However, could children be getting cleverer? (there is evidence for a gradual improvement in IQ scores (the Flynn effect). Perhaps syllabuses have changed, or is teaching more rigorous or exam-focused. Is there a political motivation to see grades rise?
  • Alcohol use is out of control in the UK! Alcohol sales are soaring because sales increased by 5% between 1999 and 2004. What’s wrong with this statement? For example...Is the rise in alcohol sales at least partly down to the fact that the population grew by 2% in the same period? Are there more over 18s at the end of the study period? Are people buying more wine and beer instead of home brewing?
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