I want to design an experiment with three factors. Factor 1 shall have two levels (say, A and B), factor 2 has two levels (say, C and D) and factor 3 has two levels (say, E and F). By design, factor 2 and factor 3 are nested within the level B of factor 1. Some direction regarding how to appropriately analyze the data for statistical significance would be really appreciated. I want to mainly check for the effect of the factor 1. And consequently whether there is any effect of the factor 2 and factor 3 within level 1 of the factor A. Factor 1 is within-subject factor, factor 2 is a between subject factor and factor 3 is a within subject factor.
Can this be considered under a nested ANOVA? I don't have much clarity on this. I have considered performing a t-test between the two levels of the factor 1 (within subject), and then perform a two way mixed ANOVA (factor 2 - between subject, factor 3 - within subject) inside the level B of the factor 1. I was hoping on finding some alternative way of analyzing the data through a single statistical test(ANOVA?). Kindly help