- 100 students, taught by 5 different teachers, take the same exam. The null hypothesis is that when taking the test, there was no significant difference between the the knowledge of the 5 different populations.
Nonsense.
Why would you claim this when the results of every exam taken in the history of education have shown that there will always be a range of results?
- It turns out, however, that the top 7 scores were received by students of Ms Smith. These scores set Ms Smith's class apart from the other classes -- they suggest at least one of two alternative hypotheses: Ms Smith was the best teacher in this case and/or she had (for some reason) been assigned the best students.
Notwithstanding that "at least one of two alternative hypotheses" is virtually meaningless, you've left out 10
80! other possibilities.
- What if Ms Smith was the teacher who set the exam and, whether consciously or unconsciously, taught her students nothing more than what she knew they would need to achieve a good score? Those students might in fact have less knowledge than those in the other four classes.
- How do we know that the teachers and students were the only variables? What if Ms Smith's class was the only one conducted in a modern, well-equipped school, the others being taught in dirt-floored shacks without access to text books and other learning materials?
- What if a clerical error resulted in four of the classes only receiving notification of the exam the day before it was scheduled, while Ms Smith's class was advised two weeks prior to the event.
- What if four of the classes were suffering from the effects of influenza which they'd all caught from each other, while Ms Smith's class were all in good health?
- What if one of Ms Smith's students had obtained a copy of the exam in advance and shared it with his/her friends?
There are 10
80! - 5 other possibilities. I'll be back.
- I suspect that I should hereby slow down...
That's unpossible.
- My example involves something like prediction...
It involves something more like making up a conclusion and attempting (poorly) to form premises which will lead to it.
Where have we seen that before?
- For me, this is the key question -- what is the principle that sets me apart from the rest of you schmucks, for our purposes here? (Or really, what's the principle that sets us scmucks apart from the blank wall?)
The principle of not having thought things through properly, heavily influenced by the Dunning-Kruger effect with
non-sequitur tendencies and a strong leaning towards hubris.
- What's the principle that sets apart one event from a multitude of other similar events -- and, in our formula, allows the entered likelihood of the particular event to be the likelihood specific to it rather than the likelihood general to any example of those similar events?
The principle of different things being different.
And it's not
our formula.
- So far, I can't even express this question with any confidence of it being understood...
Doesn't bode well for Truly Effective Debate™, does it?
If you think you know what I'm trying to ask, see if you can ask it better.
You want other people to present your argument for you?
As it happens, Loss Leader and Giordano have already been doing just that. They'll be back.
- Anyway, I think that I am justified in using 1/1080! as P(me|A) instead of 1.00 --
Of course you do, but only because you were finally convinced that 10
80! at least has the advantage of being a real number as opposed to your previous attempts to use ∞.
In any case, it's irrelevant.
The real problem is that it's your value of "me" that's borked.
. . . and, the specific question is, "What sort of characteristic of "me" would it take to separate me from the masses, and to logically use 1080! as P(me|A) in the Bayes formula?
The only way your claim can succeed is if "me" includes the as-yet-to-be demonstrated "immortal soul" component.
If you were to do that then the whole Bayes thing would become irrelevant.
Not that it isn't already.
You keep saying that like it's a good thing.