So in that case we might think of not
the relabeling as a process of re-implementing the randomization scheme,
but instead it's a process of, well we think,
if the null hypothesis is true, relative to tumor status,
treatment and control status are a bunch of exchangeable, permutable labels.
And you could do the same procedure to coming up with
the null distribution and that's another way to think of it.
Yet another way to think about it is the development
we going to go through next which is a Mathematical treatment.
But it is interesting that these very
different methods of thinking about the problem
results in the same task and you see this very often in Statistics where you
wind up with procedurally the same approach
but that the interpretation differs quite a bit.
I would argue that explicitly using
the randomization saying well, this treatment and
control was randomized and so we're
going to explicitly work that into our analysis.
It's a very fundamentally different process than what we're about to do.
Which is to assume that the data are binomally distributed, I impose a model,
a super population model for the mice, and to
work with that lined up with the same procedure,
but the interpretation I think is vastly different, and
I hope you think so too after taking this class.