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My problem is this: I have one dependent variable and 4 independent ones: one is age and the other three are temperament dimensions. I did 3 sets of two-way ANOVAs. The first independent variable is always the same (age) and the second is always different - one of the tempeament dimensions. In one case I get that age has significant effecet, the temeprament1 does not, and no interaction. in other case I get that age doesn't have the significant effecet, but still no influence of temperament2, and no significant effect of interaction.

one-way ANOVA for age shows there is significant effect.

My question is how do I interpret the data? My plan was to say if there is effect of age and temperament and interaction of age and temeprament dimensions, but now - the effect of age is sometimes there, and sometimes not?!

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Though not entirely uncommon for this type of thing to occur some people might like to see this as a teaching or learning case. If you could share the data it would be great. You also might get good feedback on your specific problem. – John Feb 25 '11 at 16:23

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Unfortunately there is no good short answer to your question--not one that is likely to help you understand these findings on more than a superficial level. What is required is for you to begin exploring the literature on statistical control and on partialling out (adjusting for, controlling for, or holding constant) extraneous variables. One might spend the better part of a semester on this topic, and there are sources at all levels of sophistication that you might read. James Davis' The Logic of Causal Order and Dana Keller's The Tao of Statistics are two very short, user-friendly, introductory books that come to mind. My short, very basic piece at http://www.integrativestatistics.com/partial.htm might also be of some use as a way of orienting you before you delve into more detailed treatments.

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Sounds like age is correlated with one or more of your temperament measures, which means you're violating the assumptions of ANOVA/regression. You might want to instead look at path analysis to ascertain the relationships amongst your variables.

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Path analysis is an interesting idea, but I don't see your point about violation. Usually in nonexperimental studies predictors are correlated to some degree. Without that there's little point in using statistical control: zero-order correlations of each X with Y will be the same as partial correlations. – rolando2 Feb 25 '11 at 18:26
@rolando not sure if this is appropriate, but PCA would provide orthogonal predictors – David Feb 25 '11 at 19:56
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Hi David - it would, but I don't see any great need for orthogonality in this case, and with just 4 predictors, not much need for the data reduction that PCA provides. There's also the risk that Y's relationship with the derived components would be less interpretable than relationships with the 4 original predictors would be. – rolando2 Feb 26 '11 at 3:35

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