IV1: gender

IV2:age

IV3: level of musicianship

DV: mmr38 - result on "music in mood regulation scale" 

N: 297, males/muško (0) n=99, females/žensko n=198 , age A: 18-20 (0) n=41, age A: 30-43 (1) n=44, age B: 18-21 (0) n=70 , age B: 27-43 (1) n=85, musicianship: no(0)/yes(1). 

The numbers in parentheses represent coding. The correlations between IV's and categorical variables for age are attached. I'm working in SPSS.

I want to find out if there is a difference between gender, age and level of musicianship on DV, so I performed three t-tests for each variable and DV. Then my thesis mentor suggested to see if there is interaction between gender and musicianship on DV.  Main effects for 2x2 anova with gender and musicianship are both signifcant, while t-test said there were no differences for either on DV. This was because main effects represent unique contribution to DV, and gender and musicianship are correlated. Mentor didn't say to test for interactions between age and gender, or age and musicianship, although it makes sense to check for those as well. Besides, how to justify not looking into other interactions? My research question is basically revolving around main effects, i.e. is there a difference on DV based solely on gender, age or musicianship.

Natural choice seems to be a three-way ANOVA. However, one group has just three participants if age A is selected, or five participants if age B is selected. Age B approach is barely acceptable from a statistical standpoint, while both approaches of categorizing gender will probably yield small power in ANOVA, due to small group sizes. Also, the correlations between age A and age B and other variables are somewhat different, although the age A approach is more valid from a theoretical view. So, it seems three-way ANOVA is the way to go, but there are not enough ns in each group to make a valid conclusion without comitting type II error, rejecting a difference where there is one.

Research A (without _ in title) showed no connection between age or gender and DV, and this was done with Pearson correlation. Isn't that way too simplistic? Research B (with _ in title) showed interaction between age and gender, but did not examine musical engagement.

It seems to me that there is a "way" to disregard gender*age or age*musicianship correlations and interactions. I am a musician myself, age 26, male. I shared the survey link with my Facebook friends, and some of those shared the link on their FB profiles. I am also told women tend to respond much more often in online surveys. Knowing that age*gender correlation is mostly due to sampling, it is also sort of expected that older participants will have more musicianship experience (yes group) than younger ones, although the musicianship question was phrased: Pick a response that best fits your current musical engagement level. This was on a 1-5 scale, 1 being non-musician and 5 being professional musician. Later on this was simplified to non-musicians and musicians. I tried to find a research that would confirm that men play and sing more than women, but to no avail. In other words, I tried to show that these correlations were more a matter of population differences than due to sampling.

It could be that all of this is more a research problem question than analysis question.

Bottom line: why would my mentor suggest to look for gender*musicianship interactions, and not the others? If other interactions (gender*age and age*musicianship) are also relevant, which statistical analysis would be appropriate if some groups are way too small compared to others, and even below the minimum requirement of 5 per group?

I also thought of ANCOVA with age as covariate, being the only continuous variable among the IV's, but also because age and a) gender or b) musicianship correlations can be explained as age and gender being due to sampling and age and musicianship because older people will have more likely attained more musical experience just because they are older. However, I am not certain my data supports all the assumptions for ANCOVA.

I am just trying to write my graduation thesis and any help is greatly appreciated. Also, I would be happy to send anyone the SPSS data file. Cheers!