Naked Statistics: Stripping the Dread from the Data

The core principle underlying the central limit theorem is that a large, properly drawn sample will resemble the population from which it is drawn.

This is one of the crucial lessons of probability. Good decisions—as measured by the underlying probabilities—can turn out badly. And bad decisions—like spending $1 on the Illinois lottery—can still turn out well, at least in the short run. But probability triumphs in the end.

Bad polling results do not typically stem from bad math when calculating the standard errors. Bad polling results typically stem from a biased sample, or bad questions, or both. The mantra “garbage in, garbage out” applies in spades when it comes to sampling public opinion.

The population from which the samples are being drawn does not have to have a normal distribution in order for the sample means to be distributed normally.