Empirical Musicology: aims, methods, prospects (Eds: Eric Clark & Nicholas Cook).
Dan Levitin's chapter on Experimental Design in Psychoacoustic Research.
Gold-MSI a set of tests to evaluate musical sophistication to map musical ability of participants in studied better.
This website explain common mistakes in statistical analysis (useful to understand the pitfalls before you fall into one of them). And a good illustration of the problem of overfitting.
And a good reminder that correlation and causation are not the same thing.
Design a study to investigate one of the following topics:
People who listen to Indian music will be more sensitive to microtonal intervals.
Which activities are the most effective at fostering musical creativity (in primary schools, or at university, or choose your favourite setting).
How quickly do we gain a robust sense of tempo from pulsed music.
You will first need to define the exact nature of the question in more detail. Then you will need to consider the factors at hand and how you may go about investigating the question.
When designing any research, and particularly one dealing with human participants, you need to consider the ethical dimension.