Can we make mediation analysis with ANOVA? I conducted mixed ANCOVA for my research. However, I need to make a mediation analysis as well. I have no idea of converting a mixed ANCOVA with many control variables into a regression. Can't I do three ANCOVA's which shows the relationship between IV and DV, IV and Mediator and Mediator and DV?
Thank you a lot.
 A: No, this is not possible. 
An ANOVA aims to test differences between means of different groups/conditions on one independent variable. E.g. DV: number of strawberries/strawberry plant; IV1: three watering groups (100ml/day, 200ml/day, 300ml/day); IV2: three fertilizer groups (5g/day, 10g/day, 15g/day). Thus, you'd have a 3x3 factorial ANOVA without repeated measures, which you could turn into a 3x3 repeated measures ANOVA by measuring plant height on several points in time (e.g. after 7, 14, and 21 days). An ANCOVA aims to do the same, but in this case you introduce at least one continuous variable, a so-called covariate, for which you do not specify an interaction with the other factors. This reduces error variance in your IV (plant height) due to this covariate and thereby increases statistical power for the effects of your IVs. Yet, you could as well set up AN(C)OVAs as regression models instead (for which you'd have to code your factorial IVs differently), although in some statistics courses ANOVAs are taught differently, i.e. by formulas which actually compare different parts of the total variance in your DV (variance within treatment groups and variance between treatment groups), in order to receive an F-value, which lets you determine a corresponding p-value from the F-distribution. Well I am going into details. The important part is: AN(C)OVAs compare means!
Yet, a mediation analysis has a totally different aim. Here, you test whether your IV (e.g. water/day) predicts your DV (number of strawberries/plant). This, so far, isn's any different from the proceeding layed out above and you might predict mean number of berries/plant from the watering conditions. All of this you could analyse in an ANOVA But now comes the critical part: Here you are also interested in whether the effect of your IV changes the value of your DV mediated by some other value. E.g. you could reason that water/day affects the height of your strawberry plants, thereby leading to variation in sun exposure of the plants, and therefore to variation in berries/plant (For the simplicity of the example let's assume plant height and sun exposure to be one combined variable). This effect (water/day -> plant height|sunexposure -> berries/plant) is called the indirect effect, while the effect water/day -> berries/plant is called the direct effect. Both the direct and indirect effect should be tested for significance with specialized models.
I guess that your intention to test three ANOVAs could be inspired by the model by Baron&Kenny, which examplifies the logic of mediation analyses. Here, you test three mediations (IV->DV, IV->M, and M->DV). Yet, there are more appropriate procedures based on bootstrapping and I would suggest you to use the PROCESS-Macro by Andrew F. Hayes, which is available for both SPSS and SAS and furthermore includes a nice GUI for SPSS (I do not know about SAS). Furthermore, there is a nice template pdf available for many different mediation (and moderation) analyses, which allows you to easily figure out which model is appropriate for you. I hope this helps. Oh, and Andrew Hayes has also published a book on mediation and moderation. Check whether you have access to this book via an institution with which you are associated. It explains quite nicely what happens in mediation and moderation.
