Faulty generalisation

 by Tim Harding

The tabloid media often commits a common fallacy known as Faulty Generalisation.  Other terms for this fallacy include false generalisation, hasty generalisation, over-generalisation, unscientific conclusion and even superstition. A fallacy occurs when a general rule is derived from a particular case or anecdote.

For simplicity, this fallacy may be divided into two sub-fallacies – false generalisation and over-generalisation.

In a false generalisation, the premises of an argument are weakly related to its conclusion; but do not sufficiently justify the conclusion.  For example, a person might argue: “I don’t believe that smoking causes cancer, because my uncle Bert smoked like a chimney and yet he lived until aged 93”.  Conclusions are drawn about an entire population from too small a sample of the population – in this case a sample size of one. Contrast this with the enormous sample size of tens of thousands of smokers (plus control samples) that were used in the scientific epidemiological studies that conclusively established the causal link between smoking and cancer.  So in this case, the person committing this fallacy is giving more weight to a personal anecdote than the findings of science.

The extreme feminist slogan ‘All men are rapists’ is clearly a false generalisation.  Other claims such as ‘All men are responsible for the attitudes that lead to rape’ are a little more subtle, but are still false generalisations. Rape is a crime, like murder and bank robbing, and statistics show that only a small percentage of the population are criminals. Just because a person happens to be born of one gender, it does not make that person responsible for criminal attitudes, let alone crimes committed by other persons of the same gender.

In an over-generalisation, conclusions are drawn from an apparent trend to the entire population.  For example, if there are a couple of tragic road crashes on a weekend in which several people are killed, a senior police officer might say at a press conference something along the lines that drivers are becoming more careless.  A sample of one weekend’s road crashes is no evidence of any such trend – in fact, the long term trend is that the annual road toll is decreasing.

In technical logic terms, these are fallacies of defective induction, where the argument typically takes the following form:

   Premise: The proportion Q of the sample has attribute A.

   Conclusion: Therefore, the proportion Q of the population has attribute A.

Statistical methods are used to calculate the necessary sample size before conclusions can validly be drawn about a population.  For example, a random sample in excess of 1000 people is used in opinion polling; and even then there is a stated error margin in the order of plus or minus two per cent.

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