Course Notes - Department of Mathematics and Statistics

RESIDUAL MEAN SQUARE (s 2 e)Group A Variance: s 2 A = ∑(xAi − ¯x A ) 2(n A − 1)Group B Variance: s 2 B = ∑(xBi − ¯x B ) 2(n B − 1)Group C Variance: s 2 C = ∑(xCi − ¯x C ) 2(n C − 1)Group D Variance: s 2 D = ∑(xDi − ¯x D ) 2(n D − 1)Group E Variance: s 2 E = ∑(xEi − ¯x E ) 2(n E − 1)AND n A = n B = n C = n D = n E (= 4)Pooled Variance = 5[ 1 s2A+ s 2 B + s2 C + s2 D + ]s2 E=51 [∑ ∑ ](xAi −¯x A ) 2(xEi −¯x3+ . . . +E ) 23[ ∑(xAi − ¯x A ) 2 + . . . ∑ (x Ei − ¯x E ) 2]CALCULATING THE POOLED VARIANCE= 1 15=Residual SSResidual df= Residual Mean Square(s 2 e)Residual mean square (MSE)= pooled variance for all 5 group samplesNOTES:• For the F test to be valid, the variances in all samples should beapproximately equal• The square root of (s 2 e) is the standard deviation of the residuals(often called ’pooled standard deviation’).172