00:01
All right, so we have three groups, and we're going to connect a one -way analysis of variance, and we're going to write the results in apa format.
00:09
So here are the groups, one, two, three, and the null hypothesis is that the means of the three groups are the same, b1 is equal to b2 is equal to b3.
00:17
The alternative hypothesis is that the means are not all equal, and we're going to test this at the alpha of 0 .05 level of significance, which means if our p value goes below this alpha, we're going to reject our null hypothesis.
00:30
This little average function here, this is what i put into my spreadsheet to do the calculations here, to find the average of the data, and so this is just the format for that.
00:42
And let's go ahead and get started here.
00:44
So here's our anova table that we want to fill out with the source, between, within, total, sum of squares, degrees of freedom, mean square, f, and p value.
00:52
To get the p value, we need the f statistic.
00:55
The f statistic is found by taking the mean square of the between groups divided by the mean square of the within groups.
01:02
So now we need the mean squares, and the mean squares are found by the sum of squares divided by their corresponding degrees of freedom.
01:07
So we need our sum of squares.
01:09
And this is where the work comes in, or the calculations come in.
01:15
So let's do our degrees of freedom first.
01:17
The between groups, degrees of freedom is k minus one, where k is the number of groups, and we can see there are k is equal to three groups, so k, three minus one is two.
01:26
The within degrees of freedom is n minus k.
01:28
We already know k is three.
01:31
N is the total number of items in the sample, so n is 15, right, five times three.
01:37
So 15 minus three is 12.
01:40
Then the total degrees of freedom is n minus one, 15 minus one is 14.
01:47
Great, now the sums of squares.
01:48
So these are related, similar to the degrees of freedom.
01:51
You should notice that the total is equal to the within plus the between.
01:55
That's the same thing for the sum of squares.
01:57
The total sum of squares is equal to the sum of squares of the between group plus the sum of the squares of the within groups.
02:05
And so what we'll do is we'll find the total in the between and then take the difference of the total in between and get our within.
02:11
So let's go ahead and get that.
02:12
So the total sum of squares, to do that first, is equal to the sum of each individual x value, 51, 45, 33, et cetera, and you take the difference of each x value and the grand mean, x bar sub g squared.
02:28
And that's where this average function is gonna come into play, because we're gonna get the average of all 15 data values.
02:36
There we go.
02:38
This is what we get.
02:39
This little array here is filled with each x value, like 51 minus the average of all of them together, 51 .133 repeating, and you square that difference to get this.
02:51
And that's small because 51 and the grand mean are close to each other, so that makes sense, that's small.
02:56
Whereas 23 minus 51 .133 repeating, take that difference and square it, you get a large number, it's 791 .484.
03:05
And we add all those up, and that's the sum of the squares of the total.
03:11
And it ends up being, i'm gonna round here, but it ends up being 4 ,887 .73.
03:21
And great, so that's the sum of squares of the total.
03:24
Now we'll do the between...