Multivariate analysis (Ancova) I have one continuous dependent, one categorical independent and one continuous covariate. I want to see the relationship between these variable for men and women separately. Now I was wondering do I need to do the ANCOVA analysis for men and women separately? Or do I need to bring sex as a second covariate into ANCOVA model or bring sex as the second independent variables into the ANCOVA model? Which model do I need to choose?   
 A: Forget about ANOVA or AVOCA or ANCOVA, all of them are special case of linear model.
Suppose you fit two models for male and female separately. For each gender the model is:
$Y=\beta_0 + \beta_1X_1 +\beta_2X_2+\epsilon$ and $\epsilon$ ~ $N(0,\sigma^2)$
where Y is response variable, $X_1$ is categorical covariate (assume two level), $X_2$ is continuous covariate and $\epsilon$ is error term. (Of course, you can add the interaction between $X_1$ and $X_2$). In this model, there are 4 parameters need to be estimated. For two models, you have 8 parameters. 
Let $S = 1$ for male and $=0$ for female. we can combine two models into one.
$Y=\beta_0 + \alpha_0S + \beta_1X_1 +\alpha_1SX_1+\beta_2X_2+\alpha_2 SX_2 + S\epsilon_1 +(1-S)\epsilon_2$ and $\epsilon_1$ ~ $N(0,\sigma_1^2)$, $\epsilon_2$ ~ $N(0,\sigma_2^2)$
This single model has 8 parameters and is totally equivalent to two separated models. But by fitting single model, you can check if you can simply the model. For example, you can check if $\sigma_1^2 = \sigma_2^2$. If yes, eliminate one of them, your model will be MORE efficient than two separated models. You can also check if the slops of $X_2$ are equal....
In summary, single model has the possibility of simplification such that the estimate of the parameter will be more reliable. 
A: ANCOVA is a good choice but you should not do separate analyses for males and females. Instead, make gender a second independent variable so you can test its interaction with your other independent variable. Needless to say, be aware of the assumptions of ANCOVA. 
