Question

a) Show that a constant d can be added to(or subtracted from) each xij without affecting any ofthe ANOVA sums of squares.

 

b) Suppose that eachxij is multiplied by a non zero constant

c. How doesthis affect the ANOVA sums of squares? How does this affect thevalues of F statistics FA and FB ? Whateffect does coding the data by yij = cxij + d have on the conclusionsresulting from the ANOVA procedures?

Answer 1

Solution

The F statistics F and F , remains unchanged since the quantity c² is stand cancelled since it occurs in both numerator and denominator . If each X , is transformed as the variable , Y = cX , + d from the above results it is clear that the conclusions remain unchanged when we analyze the data in the form of Y₁j .