MathBench > Statistical Tests

Chi-square Tests

Detour Stop 1: What's a p-value?

shoes are too smallIf your shoes don't fit a little, they might cause a little pain, but not enough to pay attention to. But somewhere there's a threshold. If the shoe is too small, you go out and buy new ones.

model doesn't fit dataSomething similar happens with statistical tests such as the chi-square. If your calculated statistic value (i.e., the chi-square-calc) is a "little bit" big, that's not enough to contradict your hypothesis. But if its a LOT too big, then it does matter -- it is "significant".

I know this is still rather vague, so hang on. Statisticians measure how significant the calculated value is using what they call a "p-value" (p stands for "probability", not "pain"). A big p-value means that the calculated value could "probably" have happened by chance process -- like a little random slop. A small p-value means there's only a small probability that the calculated value arose from a little random slop. A p-value of 0.05 means essentially only 5% similar calculated values come from "sloppy" data, and the rest are "significant". In fact, this is the famous p=0.05 threshold that most scientists use (well, not famous like American Idol, but trust me, famous among statisticians and scientists).