degrees of freedom
/ dee-GREEZ uv FREE-dum /
Imagine you must pick four numbers that add up to a fixed total. The first three you can choose freely, but the fourth is then forced — it has to be whatever makes the sum come out right. So although there are four numbers, only three are truly free to vary. That count of freely choosable values is the idea behind degrees of freedom.
In statistics, the degrees of freedom is the number of independent pieces of information left in your data after you have used some of them to estimate a quantity. When you calculate a sample standard deviation, you first need the mean; computing that mean uses up one degree of freedom, which is exactly why the standard deviation divides by n minus one rather than by n.
It matters because the degrees of freedom controls which critical value you read from a t-table, F-table, or Q-table — get it wrong and your test gives the wrong verdict. The honest caveat is that the name is abstract and easy to misremember; a reliable habit is to count your measurements and subtract one for each quantity you had to estimate from the same data along the way.
From five replicate titrations you calculate a standard deviation. Because the mean was estimated from those same five values, the standard deviation carries four degrees of freedom — and it is the t-value for four, not five, that you look up.
Five measurements minus one estimated mean leaves four degrees of freedom.
As the degrees of freedom grow large, the t-distribution edges closer and closer to the Gaussian; this is why tests on many measurements behave almost as if the data were exactly normal.