# Degrees of freedom

degrees of freedom
(df)
tcrit
(for p-value = 0.05)
1 12.7
2 4.3
3 3.2
4 2.8
5 2.6
6 2.5
7 2.4
8 2.3
9 2.2
10 2.1
20+ 2.0

So our tcalc was about 5.1 -- is this good? We still need someone to tell us just how big the number has to be to mean "statistically significant". And finally, we're gonna get a break. Because someone is going to tell us: the magic lookup table, over there on the right.

Why is it magic? Because (at least unless you decide to pursue theoretical statistics) it's pretty hard to explain where it comes from. Just take it on faith -- the numbers in the table work.

But how do they work? Well, first we have to find the correct line in the table. The lines are again related to sample size, although they are not exactly the same. They are labelled "degrees of freedom", which is a common concept throughout all of statistics.

Degrees of freedom tell you how many pieces of information are “free” to vary in an experiment. We measured 8 fish per tank, so n=8. For each tank, if you gave me a list of all the fish measurements but one was crossed out or unreadable, I could figure it out using the average for the tank. But if 2 were crossed out, I wouldn't be able to figure them out using only the average. That means that 7 of the fish are "free" to vary, but the last one is not. Or, degrees of freedom = df = 7.

If degrees of freedom seems a little abstruse at this point, don't worry about it too much -- just remember that df for the t-test is the same as sample size minus one.

Oh, yeah, and tcrit stands for "the critical value of t" -- the value that we can, finally, call "big enough" to be significant.