# Unequal sample sizes in 2x2 between-subjects ANOVA

I have a 2x2 between-subjects design consisting of Gender (Male, Female), and Relationship status (Married, Single). The DV is completion of a certain behaviour (Yes, No). I plan to use SPSS. I plan to do a factorial ANOVA on this design and then I also have one scale (which I will use to complete separate mediation analyses).

I have 4 different sample sizes in my 4 cells (24, 28, 24, 27). I would like to ask whether I need to do something differently when conducting my factorial ANOVA? I have checked google (and this site), some say ANOVA can deal with unequal sample sizes and nothing needs to be done and then there are some youtube videos showing otherwise (it's not always clear and it mostly considers one-way ANOVAs). Thank you so much to whoever answers my query.

The DV is completion of a certain behaviour (Yes, No).

Then you should not be doing ANOVA. That's appropriate for continuous outcomes, not binary outcomes like yours. See this web page for guidance on how to choose a statistical test based on the nature of the outcome and predictor variables.

You should do a binary regression, with logistic regression being the typical version. You would model the log-odds of a Yes response as a function of your Gender and Relationship predictors, and include an interaction term between them. You don't need to worry about the different numbers in each group, as the errors around the group estimates are assumed to be based on binomial statistics rather than a Gaussian distribution.*

This UCLA web page shows how to implement logistic regression in SPSS.

*Even if you were doing ANOVA with a continuous outcome, the sample sizes are so close that you wouldn't have to worry. ANOVA is now typically implemented via regression models with interaction terms, analogously to how you will do your logistic regression. The main issue even in classic ANOVA isn't the equality of sample size per se. It's that without (approximately) equal sample sizes you might get into trouble if the variances within each group aren't the same. Quality control of a regression model includes evaluating how well the equal-variance assumption holds.

• You seem to be absolutely right. It's just that the design seemed so ANOVAy minus the yes/no DV (outcome). We learned that regression is done when we want to know whether independent variables predict an outcome variable. I want to know the differences between different groups and conditions (male vs female and married vs single) in affecting a DV (helping behaviour). We hypothesise that those in the married condition and who are women are more likely to help than those who are men and are in the single condition. Thank you so much for the resources and taking the time to respond.
– user69228
Apr 13, 2022 at 21:52