The main reasoning behind graphology is that as we write, our mood unconsciously influences how we hold the pen, how hard we press down and how quickly we write. Graphologists believe that the part of the brain we use when we write is connected to our central nervous system. Therefore, when our body is in a different state, such as afraid or anxious, our central nervous system will reflect that. Our handwriting will reflect the state of our central nervous system without our control. Experiments in the basics of handwriting analysis would involve studying the samples after having the writers fill out a survey about their mood at the time of writing.
There are three main schools or types of handwriting analysis. Integrative graphology involves studying the strokes or lines present in each letter, such as q's, t's and x's. How these letters are formed will indicate hard character traits that are pretty universal among writers of that style. Holistic graphology studies everything, including margins and pressure. Symbolic graphology evaluates handwriting for things that may mean something significant, such as illness or grief. An experiment in the different types of graphology would involve researching known personality types (such as of celebrities) and comparing their writing samples to determine if their writing reflects the traits as described by the types' bases.
Handwriting analysis is not just used in criminal court cases anymore. Now it is being used by employers to determine whether employees can accurately perform their jobs. It is also being used by professional matchmakers to determine who may be compatible as mates. A few ways it is being used that hold huge controversy include handwriting as divination (predicting the future) and handwriting as indicating illnesses such as cancer before medical doctors can diagnose them. A fun experiment would be to take writing samples and attempt to predict the future based on the idea of divination from handwriting, or to try to determine who in the group would be the most compatible mates.
The main argument against handwriting analysis is that the interpretations are basically left up to the tester. A curve to one school of handwriting analysis may mean happiness; to another it may mean illness. There is also no real correlating evidence to back up the graphologists' claims --especially as a predictor of job performance or a predictor of the future. An experiment for the arguments against handwriting analysis would be to find samples of writing that disprove the different beliefs of graphologists in each school of graphological thought.