Main effect of the first independent variable in two-way ANOVa lost depending on the second independent variable 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?!
 A: 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.
A: 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. 
