Question

Within and Mixed Subjects Design

• What does it mean to say that “the independence assumption has been violated?” How do we address this violation in a within-subjects design? How does this approach to addressing the violation change the analysis?

Answer 1

The two-way ANOVA layout with equal no. of observations in the cells in a Зік - ц* *; "Pi + 7 + елік малци и таксо, с*), і м2 Р. д-(1) А к - (1) m А м >. Yijk = kth Observation in the cell ) to fixed effect of the ith level of factor A. Bj a fixed effect of the gth level of factor B. Bij = interaction effect of the two factors, which тмач ані з чашмощ оегися w. f. Dru 4 омад і uwd 4 Bad is in addition to the effects Xi and Bj. The hypothues that we usually wish to test are : HA all vi.co He : a Pa -0 . НА 0 : а "The independence assumption has been violated" means that HAR is rejected, that is, did the best interaction is present in the model, then testing Ha all x 20 and to: all pj to have no meaning. To fix our ideas let us assume that the factor & a represents machines and the factor B represents operators, If the interaction is present it means that the performance of a machine depends not on irault but al. Сал и архе kо шо н. ериралари tоо малц In #m jert шелуш иш юм х

w uticular lived the operator wing them or if we need a e consider the performance of a machine averaged over all the operators and compare this "average" performance from for two machines. In the case of presence of interaction, it is самотеш ю ta uslah илoud uu arex significantly when a particular operator is wing them. This is done by making an ANONA for the one-way classified dara obtained by taking the operator but all the machines. 16 koepң оціомаll How 44 opetia 4 ию Eufreactions will be rejected by a statistical test bet but the hypotheses of zero main effects for both factors will be accepted. The correct conclusion is then not that no differences in the main effects has been demonstrated if there are interactions there must must be differences among the cell means. The conclusion should be that there are differences but that when the effects of the levels of one factor are averaged over the other , no auf difference of these averaged effects has been demonstrated.