Hi, I am just a little confused of mian effect in the analysis of variance (ANOVA) when you include or do not include an interaction term. Let's assume a simple case of 2-way ANOVA with 2 factors A and B, each with 2 levels. If it shows that main effect for A is significant when the interaction between A and B is NOT included, and the main effect for A is NOT significant when the interaction is included, what simply does this difference mean? I understand that main effect for A generally means averaging over levels of B, is this explanation for the situation when interaction is included or is not included or is irrelavant? And if my interest is in the main effect of A, in the above senario, should I include the interaction (thus lose the significance) or not include the interaction (thus keep my significance)? Thanks!
array chip <arrayprofile at yahoo.com> writes:> Hi, > > I am just a little confused of mian effect in the > analysis of variance (ANOVA) when you include or do > not include an interaction term. Let's assume a simple > case of 2-way ANOVA with 2 factors A and B, each with > 2 levels. If it shows that main effect for A is > significant when the interaction between A and B is > NOT included, and the main effect for A is NOT > significant when the interaction is included, what > simply does this difference mean? I understand that > main effect for A generally means averaging over > levels of B, is this explanation for the situation > when interaction is included or is not included or is > irrelavant? > > And if my interest is in the main effect of A, in the > above senario, should I include the interaction (thus > lose the significance) or not include the interaction > (thus keep my significance)? > > Thanks!(Uh, oh, here we go again...) As a number of people will probably soon point out, you shouldn't even worry about that. Anyways, the results depend competely on parametrization. In the 2x2 layout with contr.treatment, you generally end up with "main effects" of A testing differences within only one level of B. -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
array chip <arrayprofile <at> yahoo.com> writes: : : Hi, : : I am just a little confused of mian effect in the : analysis of variance (ANOVA) when you include or do : not include an interaction term. Let's assume a simple : case of 2-way ANOVA with 2 factors A and B, each with : 2 levels. If it shows that main effect for A is : significant when the interaction between A and B is : NOT included, and the main effect for A is NOT : significant when the interaction is included, what : simply does this difference mean? I understand that : main effect for A generally means averaging over : levels of B, is this explanation for the situation : when interaction is included or is not included or is : irrelavant? : : And if my interest is in the main effect of A, in the : above senario, should I include the interaction (thus : lose the significance) or not include the interaction : (thus keep my significance)? : There are simplified interpretations if you restrict yourself to hierarchical or graphical (graphical are a subset of hierarchical) models. These require that if an effect is set to zero that all higher order effects that include it must be set to zero too. Thus if A is set to zero you would have to set AB to zero too if you wish to follow that philosophy (and also if you want to use any of the R packages that support it).
On Thu, 24 Feb 2005, array chip wrote:> I am just a little confused of mian effect in the > analysis of variance (ANOVA) when you include or do > not include an interaction term. Let's assume a simple > case of 2-way ANOVA with 2 factors A and B, each with > 2 levels. If it shows that main effect for A is > significant when the interaction between A and B is > NOT included, and the main effect for A is NOT > significant when the interaction is included, what > simply does this difference mean? I understand that > main effect for A generally means averaging over > levels of B,Not in the presence of an interaction, with R's default coding. is this explanation for the situation> when interaction is included or is not included or is > irrelavant? > > And if my interest is in the main effect of A, in the > above senario, should I include the interaction (thus > lose the significance) or not include the interaction > (thus keep my significance)?In R's default coding you are being told: 1) That the effect of A in the base level of B is not significant 2) There is a significant difference between the effect of A at the two levels of B. So, probably, A has no effect at the base level of B and an effect at the other level. You may or may not be interested in the effect of A averaged over the two levels of B. Note that R's default coding is unusual, and using Helmert contrasts will give results which are easier to interpret from conventional accounts. -- Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595