I have two independent variables (age and gender) and one dependent variable (the results of a questionnaire using a Likert scale). I'm trying to see whether age and/or gender have an effect on the results of the questionnaire. All participants answered the same questionnaire. Is this a mixed factorial design or a within groups design?
Let us see first what it is not:
Not a within subjects design. To be an within subjects experiment, you need a repeated measure, something that you would test for each individual multiple times. E.g.:
In this experiment, subjects diagnosed as having attention deficit disorder were each tested on a delay of gratification task after receiving methylphenidate (MPH). All subjects were tested four times, once after receiving one of the four doses. Since each subject was tested under each of the four levels of the independent variable "dose," the design is a within-subjects design and dose is a within-subjects variable
Not a factorial design. For factorial designs, you need an interaction between different levels of your independent variables, which is not the case with age and gender. One might argue that your third variable might have levels that interact with the independent variables, but that is not an independent variable.
At the end of the day, you will have to look at your design this way: each combination of gender and age variables is a separate group of people, and you are testing the same variable on 3(male)+3(female)=6 or 4(male)+4(female)=8 groups of people, depending on how many age groups you are taking in consideration.
That is a between subjects design. For a study, not an experiment.
Note: I looked up the best explanation for it on several websites, here is the clearest I could find, which ended up being my source: