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So, when we calculate the variance within the impersonal group, it is two and when we
calculate the variance within the cute group it is zero. And is it true that zero variance,
zero variability? You can look at numbers within this group and see that indeed they
vary zero. So yes we probably got that right. The way you got this variance within this
group and the variance within that group. Notice that it is exactly the same procedure
you used when you got variance in ANOVA. So this should be very familiar to you and if
it is not, that's a red flag and you need to go back and learn that.
To recap where we are, we're looking to get a "T" obtained and the top of it we're going
to take the difference between the mean of one group and the mean of another, that minus
that. In the bottom we are looking to arrive at a pooled estimate of within groups variance,
error variance, noise, changes that happen only due to chance, not due to the treatment.
And on the way to that we've gotten the variance within this group and the variance within
that group. Now we are going to pool them. But we need to correct for how many are in
each group. It could be that the number from this group might be different from the number
in that group. In this particular example that is not the case but that's the reason
we are going to be putting "N" in the formula for these. And what we are going to do is
we are going to take the pooled estimate of variance within. We are going to take within
groups variance, for group one, and we are going to divide it by the "N" in group one
and then we are going to add that to the following and we are also going to do the same down
here. We are going to take the variance within group two over "N" in group two. So, this
is simply a way to correct in case we had different ends here.
So, in English, this is the formula, conceptual. We are going to also take the square root
of this before we plug it in here and unsquare it and we will talk about that in a second.
Right now I want you to go ahead and see if you can calculate, I'll do the first half
of this with you. Variance within group one was two so I am going to go equals two and
the number in group one, we had one, two scores, two. So do the same for group two put it here
and then you will have the bit of the pooled estimate of variance within.