Just two (now three, see below), to whet the appetite. Stating the mistakes:
"Correlation implies Causation": it doesn't. The finding of statistical correlation between two variables may strengthen a pre-existing theoretical/logical argument of existing causal links. But it may also reflect the existence of an underlying third variable that affects both and thus creates the correlation. When correlation is unexpectedly found, it indicates the possible existence of hitherto unknown causal links and should initiate a deeper (and not necessarily statistical) investigation -but it does not imply causation from the outset.
"If we take a larger and larger sample from a population, its distribution will tend to become normal (Gaussian) no matter what it is initially": it won't. The Central Limit Theorem, the misreading of which is the cause of this mistake, refers to the distribution of standardized sums of random variables as their number grows, not to the distribution of a collection of random variables. Alternative statement of the mistake: "Everything has a bell-shaped distribution" -let alone the fact that the normal distribution does not always look so bona fide bell-shaped.
The research paper Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education from Ana Elisa Castro Sotos et al., reviewing research papers on the matter can be downloaded from
ADDENDUM April 8 2014
I am adding a third one, which is really dangerous, since it relates in a more general sense to reasoning and inference, not necessarily statistical inference.
3."My sample is representative of the population": it isn't. Ok, it may be, but you need to try hard to achieve that (or to be lucky), so don't take it as a given. It may look an "ordinary" day to you, with nothing special, but this does not mean that it is a representative day. So counting during just this one day, the numbers of red and of blue cars passing outside youyour window, won't give you a reliable estimate of the average number of red and blue cars, or of the average proportion of red and blue cars, or of the probability that the cars will be red or they will be blue per day... This is sometimes called, sarcastically, "the law of small numbers" (but the Poisson distribution is sometimes also called that), and it points out the pitfalls of doing any kind of inference based on too little information, persuading yourself that this information is nevertheless "representative" of the whole picture, and so it suffices to reach valid conclusions. People do it all the time, even when statistics do not appear to be involved. Fundamentally, it has to do with the difficulty we have of understanding and accepting the phenomenon of random variability: it does not need a reason to occur, it just occurs (at least given our current state of knowledge).
