this post was submitted on 16 Jan 2024
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For basic stats you can ignore a bunch of the underlying theory and just memorize a couple of formulas (or how to apply those formulas if you get a notes sheet on the test) and get good at finding numbers in tables.
The normal distribution represents the idea that most sets of data tend to cluster around the mean (if you grab someone at random, you are more likely to find someone who's 5'8" than 6'7").
Degrees of freedom is the number of observations in your sample minus 1 and is used to look up a value in a table.
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).
Glad you found it useful! Feel free to ping me if there's anything else I can help with.
doesn't this lead to a lot of extraneous variables that are actually linearly dependent on a smaller set? or worse -- overconstraining?
This isn't a universal definition of degrees of freedom, it's just "degrees of freedom as it applies in an undergraduate level stats course," which is typically for the t distribution. It's n-1 because you assume all your observations are independent of one another. In other contexts (ANOVA, e.g.), the calculation is different.
I get that, just thought it was a strange definition given what degrees of freedom actually refers to