Hume's Problem and Psychological Experimentation (Philosophy)

Can past experiences dictate future results?  No, they can't.  The implications of this are truly terrifying.  How so you ask?  Before we get to that, let's examine how our past can not dictate the future.  To make a really crude example, just because every time I've pressed the power button on my television and it has turned on, does not mean when I press the power button tomorrow it will turn on.  To get back to why the implications of this can be terrifying, apply this to science (or as many consider it, the pseudo-science of Psychology as this will hopefully be my specialty)  First let us examine the process of Psychological Experimentation.  To begin with you need a hypothesis to test.  Let's say that drug 'a' lowers depression scores.  Next we need to set up a null hypothesis.  In this case, drug 'a' has no affect on depression scores.  Now why would we do something so silly as to set up a hypothesis that says the exact opposite of what we want to prove?!  The reason given to me in my Psychological statistics course was this...  There is no way to conclusively prove something is true (short of testing *every* applicable subject which is impossible)  For example, if you met five men with two arms, or ten, or ten thousand, does this prove that all men have two arms?  No, it doesn't.  On the other hand, you only need one man with less (or I suppose more) than two arms to disprove your hypothesis.  So the theory is, you set up a null hypothesis because if you disprove it (especially over repeated tests) there is enough confidence in the research hypothesis to implement whatever treatment your hypothesis indicates.  To use our example, you decide to test the effect of drug 'a' on depression.  After setting up your hypotheses, you choose a sample of depressed people.  You then separate your sample into a control group and a treatment group.  After administering drug 'a' to your treatment group, you retest your sample and decide there was enough statistical significance in the change to warrant releasing this drug to the public.  Now how could this be terrifying?  Because you haven't proved that this drug is helpful!!  All you have proved is that drug 'a' made a "statistically" significant improvement on a limited subset of people.  And what after all is statistical significance?  An arbitrary number decided on by a mathematician.  Enter Hume's problem.  How do we know it was the drug that made the improvement?  We don't.  They could have been having a good day, or maybe the room was painted a cheery color and it brightened them up.  We just don't know what the actual cause of the improvement is, yet because of math we will assume it's the drug.  Does this frighten anyone else?  For that matter because we only tested a limited subset of the population how do we know once this drug is introduced it won't cause suicidal impulses in anyone?  Again we don't.  The implications of Hume's problem on modern science are terrifying because for all of our experimentation, for all our rules and technology, we can never conclusively say whether or not our experiments have proved a thing.  Hmmm....who would have thought an 18th century philosopher would have found such a large flaw in modern science?  For that matter who would have thought an 18th century philosopher could help a 21st century college student understand a statistics course.