Independence of variables and ANOVA I performed a test to study the joint effects of hardness and alkalinity (independent variables, IV) on reproduction (number of offspring, dependent variable, DV) of water fleas, but I’m not sure what statistical test is appropriate to analyze data.
First, I’m not sure whether both IV are independent. They are often correlated in natural waters, thus I kept them autocorrelated in my experiments (they are positively related). However, I manipulated them independently (by adding different salts to water). I may say “they are independent but autocorrelated”?! So are they really independent? 
Second question: how to analyze data? The design is not factorial: I tested 4 levels of hardness, 4 levels of alkalinity (this would give 16 waters, but I tested only 10 waters). Graphically, data suggest an interaction between hardness and alkalinity on reproduction of the organisms, but I cannot test it. Supposing the assumptions for ANOVA are met, can I use ANOVA?  I first thought of performing ANOVA following the GLM procedure and using simultaneously hardness level and alkalinity level as fixed factors (although they vary to a little extent, as a consequence of the measurement technique). But I was told to perform ANOVA (GLM) for hardness level and, separately, for alkalinity level, but I don’t understand why. Anyway, how should I analyze data?
 A: No, don't do them separately, that was incorrect advice (although it might be part of an overall strategy that includes other things).  Their positive correlation when doing them separately would mean that the effect you see of hardness will also include effects of alkalinity, and vice versa.  You should probably be using a regression to look at this.  Alkalinity and hardness are continuous variables, not categorical, and you can put both in your regression and then you can then see the unique contribution of each in their beta coefficients.  You can then do an additional regression to see the interaction by adding an interaction term (the main effects won't mean anything useful to you in the interaction model).
A: It can only be the case that variables are correlated but independent if you mean something different by independence than statistical independence because if two variables are statistically indepedent they must be uncorrelated.  In regression, ANOVA or ANCOVA it is okay for the so-called "independent" variables to have some correlation with each other (and hence not be statistically independent).  Problems arise when the variables are highly correlated because for example in regression the regression coefficients can be unstable due to near multicollinearity.
