How to denote the df (degree of freedom), particularly for $t$, $F$ and $\chi^2$ distributions in hypothesis testing?
Some references state it as the English letter $v$ such as this one, and in Miller and Freund's Probability and Statistics for Engineers, it is denoted as Greek letter $\nu$ (nu). Of course on typesetting, they look almost similar, but for the sake for teaching, I'd like to know. Are they both equally acceptable?
Best Answer
The most common convention in statistics is to use Greek letters for parameters ($\mu, \sigma$ for normal distributions, $\lambda$ for Poisson, $\beta$ when parameterizing the mean in regression and GLMS, etc). I'll assert this without any attempt to offer evidence.
You can define your notation is almost any convenient way as long as it's clear, but $\nu$, the Greek letter is probably the most traditional/widely used for the $t$ and $\chi^2$ distributions at least.
Where feasible, I think conventional notation is better, since it's likely to agree with more sources, and the Greek-letters-for-parameters is pretty well established.
[In no way should this be construed as me saying that any choice is 'right' or 'wrong'. The reason I mostly advocate following convention is because clearer/less ambiguous communication is facilitated. In a situation where there are larger benefits to choosing some other notation, convention be hanged.]
If you're using a text, I'd suggest that unless there's a good reason to do otherwise, you just use what the text uses. It will save some effort.
Presumably the intent in using $\nu$ is for the same reason we often use $\text{n}$ in our notation when dealing with sample size (presumably to stand for number), but transliterated to Greek since it's a parameter.
I expect $\text{v}$ mostly arises because some people are simply unaware that $\nu$ isn't $\text{v}$. In a few cases it could occur because people want to type $\nu$ but either can't or don't-know-how-to get it, and use $\text{v}$ as a visual approximation.