In my experiment, each subject is assigned to one of four conditions (2 IVs, 2 levels each). The DVs are measured pre and post intervention.
Is this a 2x2 with repeated measures, or is it a 2x2x2, or something else? Perhaps it is a split plot design?
I would call it a $2\times 2$ pre/post experiment. The number of factors (2) in $2\times 2$ represents the number of independent (regressor) variables, while the value of each factor represents the number of values (experimental conditions) represented by that variable. For various ways to analyze such data see Best practice when analysing pre-post treatment-control designs and Regression model for pre-post single group design.
To say more than this, you would need to tell us some more context: What is the dependent (response) variable, how is it measured, in what consisted the intervention, how long time between the two measurements, ...
This looks to me like what I would call a 'mixed-ANOVA', if you wanted to analyse/understand it using the classic ANOVA format. I'm just going to imagine how your experiment might look given what you've said:
2 IVs, 2 levels each. This could be Sex (Male, Female) and Depression Status (Present vs. Absent). You might then do an experimental intervention where people listen to some sort of mood induction, or they undergo a treatment, and you get their scores on some outcome variable before and after that intervention.
I would call it is 2 (Sex) x 2 (Depression status) x 2 (Timepoint) mixed measures model. It could be analysed that way as an ANOVA where you specify the multiple ratings from pre-post intervention as a repeated measure/within subject, and specify the other two variables as between subjects factors.
An alternative to this ANOVA format would be to run it as a multilevel model/multilevel regression/hierarchical regression, where you 'nest' the repeated observations from pre- post intervention within participants.
Hopefully this is helpful, though it looks like your question is very old - it was bumped up!
