I'm trying to figure out which type of factorial ANOVA test to use for this data. The data is from a hypothetical study looking at whether males or females are more likely to ask questions during a seminar where people give various presentations. The dependent variable is "balance" (the proportion of men who ask questions minus the proportion of women who ask questions). There are two independent variables: one is the gender of the person giving the presentation and the other is the gender of the person controlling the event (the host, a teacher, etc.).
I'm thinking it would be a two-way ANOVA, but it's been so long since I've worked with statistics that I'm still a little unsure.
To determine which type of factorial ANOVA test to use for this data, you need to consider the number of independent variables and their levels, as well as the type of data you have.
In your hypothetical study, you have two independent variables: the gender of the presenter and the gender of the event controller. Each independent variable has two levels (male and female).
Given that you have two categorical independent variables, each with two levels, you are correct that a two-way ANOVA would be appropriate for this analysis.
The dependent variable, "balance," represents the difference between the proportion of men who ask questions and the proportion of women who ask questions. From your explanation, it seems like the "balance" variable is continuous or at least can be treated as continuous (quantitative data). This assumption is important because ANOVA is typically used to analyze continuous variables.
Therefore, a two-way factorial ANOVA with two categorical independent variables (gender of the presenter and gender of the event controller) and one continuous dependent variable (balance) would be suitable for your study.