Hi everyone I'm currently writing my dissertation and could really use some advice as my tutor is on leave :(
I conducted an experiment and every statistical test selector is pointing me to a 3 way mixed ANOVA but one of my IVs only relates to one level of another IV. I'm not sure if that makes sense so I'll illustrate:
The experiment was designed to find out if gender (IV 1) and question type (IV 2) (moral dilemmas vs factual questions) had an effect on conformity (measured as the % of answers given in line with the perceived majority). For the moral dilemma items, participants were shown two different majority types (IV3)- deontology or consequentialist, and I also want to look at the interaction between each majority type and gender.
However as this third IV only applies to one condition of another IV (Question type - moral dilemma) I'm not sure if a 3 way ANOVA is appropriate or whether I need to run two different 2-way mixed ANOVAs?
Any advice would be a huge help!
First, interesting topic, conformity. I like to think about the lowest level unit, here what the subject said. Is the response only classified as it being conforming or non-conforming, or can it be coded also right v wrong (or some other thing?). So gender is between subject and there are three question types: moral deontological, moral consequential, and factual). So I would predict conformity from this 2x3 taking into account subject variability. This is a multilevel logistic regression. It is what I have used in conformity research (see e.g., appendix of Article Memory conformity affects inaccurate memories more than accu...
).WIth lmer, this would be
glmer(conf ~ gender * as.factor(3groupvar) + (1|subject),family="binomial")
and you can add various things to this model.
This is easy. You never run separate ANOVAS ever. All of your data must be in one big table for analysis to test all interactions. But you need to decide how to structure the data and model, whether there is nesting, crossing, etc., or if you actually need a non parametric model (such as Kruskal-Wallis H test). Parametric tests like t-test and ANOVA shouldn't be used when the dependent variable is proportion or % data
Using three way ANOVA will be a complicated in interpretation of the results. You can do two way analysis and if the response results as 0 and 1 you can use logistic regression to analyze all the data.
Holly Robertson, as you know any research is guided by its objective. The objective of your dissertation is to determine the effect of your independent variables on your dependent variable.
So I will go with Daniel Wright in having a research design that will directly achieve your objective. Logistic regression is most appropriate to deal with a mix of parametric and non paramrtric variables.
In effect, it is the objective from your research problem that dictates the appropriate statistical analysis to use.
I appreciate your interest in ANOVA.
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