askchapo

No prob!

The i denotes a category that's determined by the researcher. You can think of Chi squared tests as testing the deviation from an assumption (typically that whatever you're looking at is randomly distributed). So it can be something as simple as heads or tails in a bunch of coin flips - you could calculate your _E_xpected rate of heads - _O_bserved rate of heads / the _E_xpected rate of heads

Here's a really detailed explanation. In evolutionary bio you can use it to see if traits are undergoing selection. Suppose in tribbles allele P causes black fur, p causes white fur, and the heterozygous condition is gray. You know from previous sampling that the rate of appearance for P is 0.80 and p is 0.20. You could then estimate that you would expect to see 64% black Tribbles, 32% gray Tribbles, and 4% white Tribbles. If you go out and your sample only has, say 20% gray tribbles, the chi square can tell you (O_gray - E_gray, etc) if it's reasonable to think that was random sampling error or there's something else going on (possibly sexual selection or predation).