Name: ANOVA 2: Calculating SSW and SSB (total sum of squares within and between) | Khan Academy
Uploaded: 2016-11-19T19:13:27.000Z
Duration: 13 min 20 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

In the last video, we were able to calculate

the total sum of squares for these nine data points

into three different groups, or if we want to speak generally,

to figure out how much of this total sum of squares

is due to variation within each group versus variation

So first, let's figure out the total variation

So let's call that the sum of squares within.

So let's calculate the sum of squares within.

Actually, I already used yellow, so let me do blue.

So we want to see how much of the variation

is due to how far each of these data points

are from their central tendency, from their respective mean.

So instead of taking the distance between each data

want to square the total sum of squares between each data

So it's 3 minus-- the mean here is 2-- squared, plus 2 minus 2

squared, plus 2 minus 2 squared, plus 1 minus 2 squared.

but for each group, the distance between each data point

So plus 5 minus 4, plus 5 minus 4 squared,

plus 4 minus 4 squared-- sorry, the next point was

3-- plus 3 minus 4 squared, plus 4 minus 4 squared.

And then finally, we have the third group.

But we're finding that all of the sum of squares

from each point to its central tendency within that,

So we have 5 minus-- oh, its mean is 6-- 5 minus 6 squared,

plus 6 minus 6 squared, plus 7 minus 6 squared.

So this is going to be equal to-- up here,

And then this is going to be equal to 1, 1 plus 1 plus 0--

So this is going to be equal to our sum of squares

So one way to think about it-- our total variation was 30.

And based on this calculation, 6 of that 30

comes from a variation within these samples.

Now, the next thing I want to think about

is how many degrees of freedom do we have in this calculation?

How many independent data points do we actually have?

So in this case, for any of these groups,

If you know these two, you can always figure out the third

So in general, let's figure out the degrees of freedom here.

Or let me put it this way-- you have n minus 1

for each of these groups, and there are m groups.

So there's m times n minus 1 degrees of freedom.

And in this case in particular, each group-- n minus 1 is 2.

Or in each case, you had 2 degrees of freedom,

And in the future, we might do a more detailed discussion

But the best-- the simplest way to think about it

to calculate the squared distance in each of them.

If you know them already, the third data point

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ANOVA 2: Calculating SSW and SSB (total sum of squares within and between) | Khan Academy

assume

figure

negative

general