I've just finished reading a wonderful book on statistics – How to lie with statistics (Huff, 1954). An absolutely brilliant book – and not an equation in sight!
But it does contain is an excellent series of explanations of various statistical fallacies & downright misuse of statistics, making it quite clear that yes, you can lie with statistics, and it's a good idea to be aware of that when sizing up claims that are apparently supported by the numbers.
Here's an example, to help show why I think this particular book is an excellent read for anyone with an interest in critical thinking. (And don't let the publication date put you off; it's as relevant now as when it was written. Just bear it in mind for this particular example, given that the lifespan data will have changed since then.)
A medical article once pointed with great alarm to an increase in cancer among milk drinkers. Cancer, it seems, was becoming increasingly frequent in New England, Minnesota, Winsconsin, and Switzerland, where a lot of milk is produced and consumed, while remaining rare in Ceylon, where milk is scarce. For further evidence it was pointed out that cancer was less frequent in some Southern states, where less milk was consumed. Also, it was pointed out, milk-drinking English women get some kinds of cancer eighteen times as frequently as Japanese women who seldom drink milk.
A little digging might uncover quite a number of ways to account for these figures, but one factor is enough by itself to show them up. Cancer is predominantly a disease that strikes in middle life or after. Switzerland and the states mentioned first are alike in having populations with relatively long spans of life. English women at the time the study was made were living an average of twelve years longer than Japanese women.
In other words, don't accept every claim you hear at face value. Hmmm, I think I might have to use some of the material in Huff's book at the next Schol Bio preparation day…
Darrell Huff (1954) How to lie with statistics. pub W.W. Norton & Co. NY. (Paperback re-issue, 1993)