Main Effects and Interactions

1		The following design matrix (table) shows cell means for a 2 X 3 complex design. Use the cell means to describe the main effects of Factor A, Factor B, and the interaction between Factors A and B. (Assume that any difference between means is statistically significant. However, keep in mind that main effects and interactions can be confirmed only through the appropriate inferential statistical tests.)   Factor A   a1 a2 a3 Factor B b1 10 15 40 b2 20 25 30 Based on an examination of the cell means, would you suggest that a main effect is present for factor A? What are the means for the main effect of Factor A? Based on an examination of the cell means, would you suggest that a main effect is present for factor B? What are the means for the main effect of Factor B? Is there an interaction between Factors A and B?
2		The following design matrix (table) shows three cell means for a 2 X 2 complex design. Assume that the analysis of the experiment showed a main effect of factor A, no main effect of factor B, and an interaction between A and B. What value should be placed in the missing cell for this pattern of results to be obtained? (Again, assume that any difference between means is significant.)   Factor A   a1 a2 Factor B b1 20 30 b2 40  ?
3		Assume that the analysis of the means in the table had revealed two main effects but no interaction. What value should be placed in the missing cell for this pattern of results to be obtained?   Factor A   a1 a2 Factor B b1 20 30 b2 40  ?
4		The following graphs show results of two different complex designs involving two variables. For each graph, decide if there is a main effect of variable A, a main effect of variable B, and whether or not an interaction between variables A and B is present. a.  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0072494468/44605/pe_ch9_imga.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> b.  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0072494468/44605/pe_ch9_imgb.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>