Question

Gender Treatment Condition
                  Control       MBSR
            F     28, 24        12,   8
           M   14, 10        14, 18      

1. Compute SS(total), SS(within), SS(between-overall) using a 2-way ANOVA.

2. Suppose you treated the data from this experiment as a one-way ANOVA with four groups (i.e., disregarding the factorial arrangement). How would the three sums of squares terms you computed in b, c, and d compare to their counterparts in the one-way approach? Be precise.       

Answer 1

(1)

	Control	MBSR		Squares Table
F	28	12		784	144
	24	8		576	64
M	14	14		196	196
	10	18		100	324
Totals Table
	Control	MBSR	Total
F	52	20	72
M	24	32	56
Total	76	52
Grand Total			128

Correction Factor, CF = Grand Total^2 /N = 128^2 /8 = 2048            

SS Total = Sum of the squares of all the scores - CF = 2384 - 2048 = 336           

SS Factor A = (Sum of the squares for the totals of the two levels for factor A / Number of scores in each level) - CF = [(72^2 + 56^2)/4] - 2048 = 32    

SS Factor B = (Sum of the squares for the totals of the two levels for factor B / Number of scores in each level) - CF = [(76^2 + 52^2)/4] - 20485 = 72    

SS Interaction = (Sum of the squares of the totals of the four levels / Number of scores in each level) - CF - SS Factor A - SS Factor B = [(52^2 + 20^2 + 24^2 + 32^2)/2] - 2048 - 32 - 72 = 200

SS Between = SS Factor A + SS Factor B + SS Interaction = 32 + 72 + 200 = 304           

SS Within = SS Total - SS Between = 336 - 304 = 32             

(2)

	F-C	F-MBSR	M-C	M-MBSR		Squares Table
	28	12	14	14		784	144	196	196
	24	8	10	18		576	64	100	324
Counts	2	2	2	2		Total Count (N)	8
Totals	52	20	24	32		Sum of squares =	2384.00
Grand Total	128

Correction Factor, CF = Grand Total^2 /N = 2048.00      

SS Total = Sum of the squares of all the scores - CF = 336.00     

SS Between = Sum of the (squares of the totals for the treatments/Number of scores in treatment) - CF = 304.00

SS Within = SS Total - SS Between = 32.00      

We observe that the SS values are same for both the ANOVAs.

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