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Extra Sum of Squares [Statistics]

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data

    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 [Broken]

    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.

    2. Relevant 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

    3. 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!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 10, 2012 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    Through disuse, I have forgotten all content of my statistics subjects :frown:
    and I don't understand the broader issue of what this question is about, nevertheless ....
    This comes no where near what I would expect for the "sum of squares" of anything.

    https://www.physicsforums.com/images/icons/icon2.gif [Broken] I'd be happy to go with: (x1^2)*n1 + (x2^2)*n2 + .....
     
    Last edited by a moderator: May 5, 2017
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