I decided to take my own advice in this thread:
https://www.freemathhelp.com/forum/threads/111975-Degrees-of-Freedom
The only way to understand math is to actually do the math. So, before I even posted in that prior thread, I constructed a small numerical example, which took me one step beyond viewing Bessel's Correction as simply an article of faith. My next (unposted) step was to work out the general validity of Bessel's Correction for a sample size of 2, which might be the first step in a proof by induction. So working on that I get this expression:
\(\displaystyle \displaystyle \left ( \sum_{j=1}^p \sum_{k=1}^p v_j + v_k \right ).\)
There are two summation signs because the sample size is 2. But if I want to show the comparable expressions for k and k + 1, is there a notation that indicates k sums with k indices varying independently?
https://www.freemathhelp.com/forum/threads/111975-Degrees-of-Freedom
The only way to understand math is to actually do the math. So, before I even posted in that prior thread, I constructed a small numerical example, which took me one step beyond viewing Bessel's Correction as simply an article of faith. My next (unposted) step was to work out the general validity of Bessel's Correction for a sample size of 2, which might be the first step in a proof by induction. So working on that I get this expression:
\(\displaystyle \displaystyle \left ( \sum_{j=1}^p \sum_{k=1}^p v_j + v_k \right ).\)
There are two summation signs because the sample size is 2. But if I want to show the comparable expressions for k and k + 1, is there a notation that indicates k sums with k indices varying independently?