Maligned mathematics

Statistics is for me the archetype of science, to work with incomplete data and decide what conclusions we are justified to draw from them. Doing statistics properly is non-trivial, requiring both knowledge and skill, but misused statistics are all too common. Accordingly many tend to treat statistics as if they were just an issue of making up arguments for pre-determined conclusions.

Red Top once quipped:

Statistics is the science that says that if a person has one foot in the freezer and the other on a hob, he will on average be fairly comfortable.

Now this is an example of misusing statistics. Consider: If the example refers to temperature, a freezer would have a temperature of approx 250 K, a hob plate up to approx 600 K. Averaging the two temperatures would give 425 K, tissue-damagingly hot, so the conclusion is false.
(We do not know the heat content of the freezer and hob, respectively, but we can assume that if they are plugged in, the heat-conduction of the feet can be ignored.)

So, is the example to be taken as averaging “too cold” and “too hot”? Since these are (fuzzy) categories, they can't be averaged, so the conclusion is meaningless.

More meaningful for our wide-legged test person would perhaps be measurements of comfort level. The validity and repeatability of these measures can be questioned, but in principle we can get numeric values to work with, so-and-so much for one foot and such-and-such for the other. However, as both are on the “discomfort” side of the scale (per the problem statement), thus averaging out to discomfort, the conclusion is false again.

Remember kids: Always do your stats carefully and do not assume that you can use tests for normal distributed data on any data.