It all depends on the research question. Instead of reporting separate t-tests it would be better give results of some 2way ANOVA (with or without interaction term).

I agree with Mehmet Sinan Iyisoy. 

You are better off reporting the results of the ANOVA than reducing the analysis to a t-test.

I believe the "estimated marginal means" in SPSS are like least square means in SAS and R.  Because your design is unbalanced, reporting these statistics may be more useful than  reporting simple means.  There is a simple example at the following, that may help explain why marginal means are more meaningful for unbalanced cases: http://rcompanion.org/handbook/G_05.html .

Thank you both for your input! I already reported LSMs, along with their standard error and confidence interval. My main research question is whether there is difference in DV based on musicianship, with no hypothesis on gender and interaction is something done out of curiosity. If I understand correctly, a 2x2 ANOVA with just main effect significant comes down to analyzing that main effect for post-hoc testing, which isn't needed because there are only two groups. But if there were 3 levels on musicianship, you would do post-hoc tests with one way anova, right? And that anova uses different means from the two-way. So, in my case, one way anova with musicianship as IV would say there is no difference between levels of IV on DV. Significance of musicianship factor in manova varies if there is gender and/or interaction included in the model, and all I'm really interested in is whether there is an effect of musicianship on DV. When i perform separate one way anovas based on gender, with same IV and DV, it shows there is a difference in DV based on musicianship, but only in males,  which sounds like an interaction. Why is ANOVA something preferable in this situation?

I am definitely missing something here.

You aren't missing anything.  Because the design is unbalanced and the IV's are correlated, the p-value for one effect can change based on which other effects are included in the model.  To make it even more complicated, the type of sums-of-squares you use will affect the results.  This is a good summary of the different sums of squares: http://dwoll.de/rexrepos/posts/anovaSStypes.html .

If I correctly understand your link Salvatore, type III controls the other main effect, but still leaves the main effect being studied in the interaction term, resulting in different p values for a type III SS model without interaction term? Different sources say different things about dropping an interaction term and making a new anova without it. It seems to me choosing type II instead of III and keeping the interaction term is the same as redoing the analysis without interaction term with SS III. Isn't the whole point of SS III to correct for unbalanced design, thus collinearity?

I think I agree with what you are saying, but I don't think I have much further insight

The following include the previous link a few others:

http://dwoll.de/rexrepos/posts/anovaSStypes.html

https://mcfromnz.wordpress.com/2011/03/02/anova-type-iiiiii-ss-explained/

http://www.utstat.utoronto.ca/reid/sta442f/2009/typeSS.pdf

https://www.researchgate.net/profile/Oyvind_Langsrud/publication/220286726_ANOVA_for_unbalanced_data_Use_type_II_instead_of_type_III_sums_of_squares/links/556f3ffd08aefcb861dd622f/ANOVA-for-unbalanced-data-Use-type-II-instead-of-type-III-sums-of-squares.pdf

Article ANOVA for unbalanced data: Use type II instead of type III s...

 Thanks, Fausto! The SPSS file is sent.

 I think your confusion is related to post-hoc testing. The answer is No to your question "But if there were 3 levels on musicianship, you would do post-hoc tests with one way anova, right?". I perform lsmeans (or emmeans) comparisons. You can use Type III SS with interaction term and report the results.

Thank you, Mehmet. One more thing, please: when doing a 2x2 anova, with gender and musicianship as IVs, if there are twice as many women than men, and in the men group there are 4 times more musicians than non musicians, while in the women group there are approximately equal number of musicians and nonmusicians, does that represent a problem as described in the last two paragraphs here? http://www.theanalysisfactor.com/when-unequal-sample-sizes-are-and-are-not-a-problem-in-anova/

Oniram, yes.

Mehmet, isn't your answer contradictive with Fausto's? https://www.researchgate.net/publication/319016748_ANOVA_for_a_2x2_UN-balanced_design Although Fausto unintentionally used a subscale of DV, the group sizes are the same.

Meanwhile, I have created a new topic with much more info on the whole thesis at https://www.researchgate.net/post/analysis_research_problem_3_correlated_IVs_unbalanced_groups

Data ANOVA for a 2x2 UN-balanced design

Fausto, could you be more elaborate on G method in your analysis?