Let's say I have two independent variables (Diet-normal,low or high and Treatment-placebo, drug1 or drug2) and dependent variable that I monthly measured for 4 months, which one is appropriate for my case?
You have a two-way anova design with repeated measurements of the dependent variable (in case the monthly samples were obtained from the same subjects).
As mentioned earlier by Mehmet and Enrique, the MANOVA is used when there are two or more dependent variables. It helps to answer the following questions:
1) Do changes in the independent variable(s) have significant effects on the dependent variables?
2) What are the relationships among the dependent variables?
3)What are the relationships among the independent variables?
According to your explanation, you have a longitudinal study in which change over time is assessed. In this case, your study design is a two-way repeated measures ANOVA.