Extra Sum of Squares [Statistics]

[cybernerd]

Homework Statement

I'm trying to study off an old practice midterm for my upcoming statistics midterm. The midterm is attached.

Part One is the following problem:

The effect of a new antidepressant drug on reducing the severity of depression was studied in manic-depressive patients at three mental hospitals. In each hospital all such patients were randomly assigned to either a treatment (new drug) or a control (old drug) group with different doses. The results of this experiment are summarized in the following tables; a high mean score indicates more of a lowering in depression level than does a low mean score.

Summary Statistics for 6 Groups:

http://a8.sphotos.ak.fbcdn.net/hphotos-ak-ash4/429073_10150583998056837_710136836_9423368_1227940643_n.jpg

For the ANOVA, I am given only one value.

Sum of Squares Within Groups: 58.5

I am then asked to calculate the Extra sum of squares to the nearest integer.

Homework Equations

Extra Sum of Squares = Total Sum of Squares - Within Groups Sum of Squares = Between Groups Sum of Squares

Total Sum of Squares = Sum of Squares of All Observations - Correction for Mean

Correction for Mean = (total of all observations) ^2 / N

The Attempt at a Solution

I know from the answer key that the solution is 113.

I know I need to find the Total Sum of Squares, so I started by trying to calculate the correction for mean. I don't have the actual data, just the means, so I tried calculating:

Sum of Squares of All Observations = (n1*x1 + n2*x2 + ... + n6*x6)^2, which gave me 223.6.

223. 6 squared = 49996.96, which, divided by 42, is 1190.4.

Then I tried to add up the sum of squares of all observations by multiplying each mean by its n, then squaring that, for all 6 groups. Then I added all 6 together, such that:

(n1*x1)^2 + (n2*x2)^2 and so forth

= (8*8)^2 + (6*5.5)^2 + (10*5)^2 + (9*3)^2 + (4 * 6.4)^2 + (5*4.8)^2

= 9645.36

So Total would be:

9645.36 - 1190.4 = 8454.96.

... Which is laughably wrong.

Can anybody tell me where I screwed up, and how I can fix it? I feel like I'm calculating this wrong altogether. Can anybody help me at all?

Thank you!

 

[NascentOxygen]

Through disuse, I have forgotten all content of my statistics subjects
and I don't understand the broader issue of what this question is about, nevertheless ...

Sum of Squares of All Observations = (n1*x1 + n2*x2 + ... + n6*x6)^2,

This comes no where near what I would expect for the "sum of squares" of anything.

https://www.physicsforums.com/images/icons/icon2.gif I'd be happy to go with: (x1^2)*n1 + (x2^2)*n2 + ...