I love statistics, and its applications. In particular to things like pattern recognition, classifiaction, computer vision and learning.
Hower, the following technique is a quintessential example of the saying, "There are lies, damn, lies, and statistics".
Factor analysis - Wikipedia, the free encyclopedia
Read the disadvantages sections and you'll see why this technique is hoplessly unsatisfatory for studying something as complex as human beings.
It has been said by many that the fundamental problem with psychological testing is that test makers have to use prejudice in making their questions and assigning interpretations to their answers. No amount of statistical manipulation is going to correct this.
There is no such thing as "being unbiased" in any field of study. Even assuming a Gaussian distribution can be a horrible bias (as physicists know quite well). Weibull, Poisson, and Unform distributions are also quite common. Bimodal distributions (very different from "binomial" distributions) are also quite common. A nuanced understanding of the "Central Limit Theorem" will tell you that the natural place for assuming Gaussians are for sums and averages of independent random variables.
To illustrate the utility of bias, consider a simple situation of measure defect rates of a products from a manfaturing facility. Very good facilities may show no defects for as long as we have time for publication of defect rates. No rational thinking human being with an ounce of common sense will publish a defect rate of "zero" even though "that is what the data shows". The common procedure is to assume (absolutley necessary) a Weibull distribution with a positive defect rate (and other fitting parameters based on prior "bias") and to keep adjusting the the parameters based on our "zero" defect rate for as many products has come up. This is just one example of a "corner case" where a bias is absolutely necessary to make inferrences that are meaningful. The more complex a system, the more corner cases that will come up.
There is something fundamentally wrong about correlatory studies of systems as complex as parts of human beings. Let alone the more mysterious study of "mind" or "health" (let alone "mental health").
First a reminder. Correlation does not imply a cause-effect relationship. I repeat, correlation does not imply a cause-effect relationship.
However, the fundamental problem is that we inherently ignore what is unique about our system in correlatory studies, but it is the uniquness itself that is vital for system function. This is true even for systems much simpler that human beings.