you know that one of the ways to try and combat this problem, issues like this,

is prior to the, conducting the study, to design it in such a way That you

would, will have a high probability of rejecting the

null hypothesis if, in fact, the alternative is true.

And one of the things you have under your control for

doing that is to, to create, to have a large sample size.

so that's one point.

And, so any rate, the, so the tendency is to say fail to reject H naught

rather than, than rejecting H naught. You know, I think a classic

phrase to the people always say is absence of evidence is not evidence

of absence, is another way to put that. so that, that's one point.

The other point I'm making in this

slide is that statistical significance is not the

same thing as scientific significance from, from

in, in, in the context of hypothesis testing.

So the most common argument in favor

of this point, is you know we have these, for most of our hypothesis

test procedures we have that, you know sharply specified nulls.

You know, H naught, H naught is that mu is exactly

5 or something like that, you know, depending on the problem.

and so, it's possible if, let's say, you

have an enormous sample size, to get a sample

mean that's 5.01. With an incredibly small standard error,

because you have an enormous sample size, and still reject the null hypothesis,

even though 5.01 isn't in any scientific sense different from five.

And so, that's the point that's often made, it's that just because you

reject the null hypothesis in the terms of prac, in, in the terms

of of executing statistical test that doesn't mean

the difference that you've detected is in fact meaningful.

now you know I've read an argument by, at one point by a person

saying that in some instanes for example

when you have randomized comparative trials that

[UNKNOWN]

hyphothesis are still meaningful and even small deviations are, are

important but, you know these are kind of subtle issues.

I think the main basic issue that, that sort of at least generally understood is

that it's not always the case that statistical

significance and scientific significance are the same thing.

at least generally understood is that it's not always the case

that, that statistical significance and

scientific significance are the same thing.

So I would like you to at least be aware of that and you can read more about it.

But, and then before, in the previous slide we said, well,

we'll reject if our test statistic is above this value In the

case where we're testing H1, we'll reject if it's either it's, it's

absolute value is above this particular value in the case of H2.

And then we'll reject if it's below this value in the case of H3.

That was our

rules we came up with in the previous slide.

So in H1, the, the upper normal quantile and above.

That's called the rejection region and it, again it's H2 the, the,

the, the upper quantile and above or the negative quantile and below.

In other words the absolute value being above a large value

is the the reject, is the, the rejection region in that case.

And in the third case The normal

[INAUDIBLE]

down below is the rejection region.

So just the collection of values of test statistics for

which you reject the null hypothesis is called a rejection region.

Just a bit of nomenclature there.