A misuse of statistics occurs when a statistical argument asserts a falsehood. In the period since statistics began to play a significant role in society, they have often been misused. In some cases, the misuse was accidental. In others, it was purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.
The false statistics trap can be quite damaging to the quest for knowledge. For example, in medical science, correcting a falsehood may take decades and cost lives.
Misuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods and even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardisation of their tests.
So just what use are statistics?
Statistics are useful for governments planning for large numbers. Examples would be: deciding how many hospitals or schools an area needs, on average, for the local population; how many surgeons in a speciality were likely to be required in 10 years time and, therefore, how many training places will be needed right now. For the last example, to achieve approximately correct numbers, it would be necessary to assess what percentage were likely to drop out and how many were likely to go abroad for, what they perceived to be, better conditions.
Given average scores in IQ tests, a teacher can have a rather rough idea of how well a pupil is doing relative to a test population and, therefore, how well their reading is advancing compared with their general understanding. Testing could also be used to identify weaknesses in performance, thus indicating what the person had not yet understood clearly (see educating intelligence).
What testing cannot do is tell you why a person got the way they are, nor can it give you a clear indication how much can be done about it at some later stage. Because not enough has yet been clearly analysed or formalised, it often takes a teacher of considerable skill and experience to identify and correct the problems a child has inherited from home and genes. Such pedagogic ability remains in very short supply, and teacher education is usually very weak.
In other words, averages tell you very, very little about individual cases. In order to understand the use and interpretation of statistics, it is essential that this lesson is thoroughly learnt and internalised, to the extent that it becomes instinctual.
Statistics are indicators, not definitive guides, and should never be used as a substitute for individual assessment.
Correlations may give you hints of where to look, they cannot give you anything more. When studies continually pick out cigarettes as dangerous to health, you may do well to throw the filthy things away; but detailed chemical links have to wait for much more investigation. And your particular granny may still smoke until she is 90 and get away with it.