00:01
Item 1 we want to in this case select the right statement so when we have an anova test here in an anova table we should say what happens when the null hypothesis is false so basically in the anova what we are tests is usually are comparing like averages or something like this so you could have like a in the new hypothesis, it's always like equality here, so the means are equal.
00:36
And in the alternative, at least one pair is different.
00:40
So we could have like a mu -1 is different than mu -2 or mu -1 is different than me -3 or mu -2 is different than mu -3.
00:52
So at least one of these pairs is different.
00:56
So if, like, we are saying that the new hypothesis is false, this means basically that in this case we are here, like we are supporting our alternative hypothesis.
01:11
So basically here, we have some options that we can choose.
01:16
So the first one is that the between groups, variance, reflects the variation within samples and the variance between the sample means.
01:27
And in this case, what we are saying is, because in the anova, we have this kind of statistic.
01:35
In the numerator here, we should, like, compare the sample means.
01:40
So we have, like, the sample, each sample mean that we have in relation to, like, a general, like, sample mean, considered all the observations.
01:52
So if in this case we are considered like three sample means, three groups, and we should divide this by what we call a residual.
02:03
So basically for each observation that we have, we are going to like subject its specific like sample mean because this observation is like from a specific group.
02:16
So basically this is what we are doing here.
02:19
So if you have like n observations in each group, or we can have like a different number.
02:27
So basically this is like the formula that we have here.
02:33
So because of this, when the h0 is false, basically, it's saying that this here is large.
02:42
Okay.
02:43
So this could be, this means that this here is large or this here is small.
02:50
Right so this means that if this is large this means that the difference between the means between the groups here or the between group of variance is larger than like the within group so we usually call this as like a within group and this here we call like a between group so like i said if it is zero is false this should be large like this ratio should be large.
03:26
So from the options that we have, basically we have like the first one already mentioned.
03:32
The second one we have the within group variance.
03:35
So the within group, this one, is significantly larger than the between group variance.
03:41
So this is not true because otherwise the f statistic would be small.
03:47
Now, so letter b is not right or the second option is not right.
03:52
So the other option is that the variance within each sample that we have is larger than if the new hypothesis were true.
04:02
If the new hypothesis is true, this means that we have like equality.
04:08
Okay.
04:09
So if you have equality, this means that this here will be the opposite.
04:13
This will be small.
04:15
So this means that this thing here will be small or the variation between groups should be small.
04:23
And because of this, this is saying that because of this, like this option is also not true.
04:30
Because if the variance within each sample is large, in this case, we are saying that it's larger than if the new hypotheses were true.
04:41
And the last one is that the variance between sample means is no greater than the variance within the sample with the largest variance...