Course Notes - Department of Mathematics and Statistics

CALCULATING INTERACTION EFFECTInteraction effect found by subtraction (used to be residual effectthat was found in this way).For the Dose 1/Brand A treatment, the three data values are brokenup as follows:64 = 58.61 + 8.83 + 1.64 + -2.41 + -2.6766 = 58.61 + 8.83 + 1.64 + -2.41 + -0.6770 = 58.61 + 8.83 + 1.64 + -2.41 + 3.33Note that the interaction effect is common amongst the three replicatesfrom the one cell.The interaction effect for the other 11 treatments can be found inthe same way.SYSTEMATIC CALCULATIONS - Table of valuesDose Brand A Brand B Brand C R i Ri21 607 3684492 510 2601003 527 2777294 466 217156C j 723 736 651 2110 1123434Cj 2 522729 541696 423801 1488226SYSTEMATIC CALCULATIONS - Using FormulaeTotal SS = 127448General level SS = 36 × ( )2110 236 = 123669Dose Effect SS = 1 9(1123434) - 123669 = 1157Brand Effect SS =12 1 (1488226) - 123669 = 350SYSTEMATIC CALCULATIONS - Finding Residual SSSquare all the residuals (calculated as the deviation of each datavalue from its treatment/cell mean) and add together.Error SS = (−2.67) 2 + (−0.67) 2 + (3.33) 2 + (3) 2 + (1) 2 + (−4) 2 + . . .= 1501.33Note that the residuals add to zero for each of the twelve treatments,so twelve degrees of freedom are lost.Hence, Residual degrees of freedom = 36 - 12 = 24.189