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If an analysis of variance produces SSbetween treatments = 20 and MSbetween treatments = 10, then the ANOVA is comparing two treatment conditions.

  1. True or false ? 
I believe it is true. 
  1. An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?  Is the answer 3 and 5 ?


Your next Question confuses me.  How can there be two answers, 3 AND 5, if you want a single value for the SS Between?
BTW, I think both 3 and 5 are wrong.
Dattaprabhakar (Dr.G.)
Each treatment has 5 observations.  Total observations = 15
Means                   1                         2                             3
Totals                   5                        10                           15   Grand total = 30
Squares               25                      100                         225
Divide by 5            5                        20                           45     Total = 70
SS Between = 70 - (30)2 / 15 = 70 - 60 = 10.
Is my arithmetic correct?
Dattaprabhakar (Dr. G.)
Yes you are right again on both questions. Thank you very much for the included chart and the formulas. 
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Dattaprabhakar (Dr. G.)
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Dr. G.
Dr.G ,
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MS between treatments = SS / (t - 1), where t is the number of treatments.
Here, 10 = 20 / (t-1), giving (t - 1) = 2, that is, t = 3, not 2.  The statement is FALSE.
Dattaprabhakar (Dr.G.)