#Why do groups need to be compared to its average multiple times?

22 messages · Page 1 of 1 (latest)

naive timber
#

In the following automated translation corresponding to the attached, I'm puzzled why groups need to be compared to its average multiple times, couldn't

(n
Σ
i=1)
be replaced by a leading 'n' and 'i's removed, making
SSE =
n(k
Σ
j=1)
(y˅j - y bar˅j)^2
?
Thank you kindly
3.1 Variance decomposition
3.1.1 Sums of squares
[...]
We calculate the sum of squared errors (SSE):
SSE =
(k
Σ
j=1)
(n
Σ
i=1)
(y˅ij - y bar˅j)^2
where y˅ij corresponds to the i^th observation of group j and y bar˅j is the mean of group j. This sum of squares compares each observation to the mean of its respective group. We obtain the degrees of freedom with df = k(n - 1), where k corresponds to the number of groups and n corresponds to the number of observations in each group.

tmp119.png
spark crownBOT
#
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viral canyon
#

Given that samples yji are drawn from different populations j

naive timber
#

Do you mean that y˅ij isn't all the entries of the factor (j) ?

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For example a group of A-H ⋃ 1-8 and y˅11 would be (B, D, F), y˅12 be (3, 5, 6) ?

viral canyon
#

If y_ji is the height of individual i from group j

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And groups are divided by age range

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You don't really compare the height of a 78 year old dude with the mean of the height of toddlers

naive timber
#

so y˅11 - y bar˅1 would be (174-170)+(166-170)+(172-170)+(168-170) ?

viral canyon
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Wel y11 is a single sample

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For example, group 1 is teenagers

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Sample 1 of group 1 is my 17 year old self, who was 169 cm tall, and the mean in my group is 170cm

naive timber
#

so from my example y˅11 - y bar˅1 is (174-170), y˅21 - y bar˅1 is (166-170) ?

viral canyon
#

So the term is (y11 - ybar_1) = (169 - 170)

viral canyon
#

Well you square the differences as well in the sum

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But if you have a second group of adults, of mean 180cm

naive timber
viral canyon
#

My pops, who is 170cm tall, roughly