I have a dataset that contains two features: type of treatment and rate. Some example data would be the following:
trt rate
1 1 100.25
2 1 97.33
3 1 102.46
...
This is a single-factor study. I was asked to get the value for the sample variance $ s^2 $. Usually, I use the following formula to find sample variance: $ \frac{\sum{x - \bar{x}}}{n - 1} $. However, the notes I was given also give me the following formula:
$$ s^2 = \sqrt{MSE} $$
After calculating the variance both ways, I got following:
using $ \frac{\sum{x - \bar{x}}}{n - 1} $ $$ s^2 = 71.323 $$
using $ s^2 = \sqrt{MSE} $ $$ s^2 = 53.0 $$
So I am wondering why there is a difference between the two values? and which one is really $s^2$ of this dataset?