I've had 3 college classes for probability of statistical analysis, decision sciences and I forget the other class. They were in the business college but I think they are pretty much the same thing, just applied a little differently.
This is a good start to the topics needed. I'm glad to hear you have this knowledge, it will serve you well, and maybe even give you a different perspective, that makes you better than others.
What I'm trying to figure out is what equipment is needed to analyse
Sounds good.
a substance/solution for its contents
That's what analytical chemistry is for.
most of which would be organic in nature.
Annnnd ... *swish*, swing and a miss.
Well, I exaggerate a little bit right here. Hopefully you mean that you're not interested in elemental analysis, of the sort done by flame atomic adsorption, or ICP-MS. Its just that, when someone says, "organic in nature", its like saying, "All trees are made of wood, so I should easily know them all." And I feel like l I really have to inject into a long missive like yours -- that it is simply not that simple.
I've watched a number of youtube videos
That can be a good way to learn some tips and tricks, if you have the basics. There's also some complete crap on Youtube of made up science. So please be careful.
on various analytical processes like HPLC, GCMS, LCMS and those seem like they would give the results which I am looking for
I'm glad you found some good stuff.
but in most of the videos they demonstrate making a solutions/mixture of a known substance at a given molarity and then put it through the machine.
This is a good way to learn.
Out of all the videos they never said "if dealing with an unknown substance...".
And there is a good reason for that. I already told you in my first post. You ignored it because you don't want to hear it. I'll be telling you again soon.
Maybe these were just technique videos, but the process seemed easily replicatable by a competent human, .
Well, yeah. All human endeavors are the same. Analytical science, architecture, cooking, automobile repair, sex, warfare ... whatever ... anyone can be competent with a little training, and a little practice. Some people are really good naturally, and some people really love a task they're really competent at. But lots of times, we like to be secure in our choice of practitioner with verified training and certification. Depending. Probably not for sex.
If testing an unknown substance, would the results graph be analysed to see where the spikes are and see what substance matches those (i'm guessing it is weight that is measured..?) by cross referencing a database?
For the instruments you described, almost never. Well, maybe GC for something like a petroleum sample, or a wastewater or food sample for a particular pesticide or other contaminant.
It is more common to use an FTIR on an unknown sample, to analyze its peaks to try to discern functional groups, and then try to predict what an organic molecule is made of and is.
Some time ago some people I know wanted some compounds tested and the issues was that they might not have a known sample to test it against, so if they got results, they might not be able to identify it b/c it was very rare and not commonly in databases (it was an old patent drug). Is this a common issue with rare substances or was this misleading information given to the group?
No, thats how analytical chemistry is. I've told you above, its not appropriate to just drop a sample and say, "Tell me about it." Ignorant people expect that of a chemistry lab, and its not really possible.
Finally, are there more advanced methods of analysis than the three I mentioned - probably newer and more expensive (I would assume) and/or are there methods nearly as accurate that are less expensive and more accessible than the mentioned 3?
You can search ab bit about FTIR as I mentioned, even here on our forum. Also how we use mass spec to help us identify compounds. Again, or forum shows people working with that sort of task.
I know you mentioned the research and I'm not trying to avoid it but I'd like to have an idea of what could be possible in my current situation
And your current situation is ... what, exactly?
related to these technologies so when I read I might be able to apply it in thought, to the correct application/technology.
Annnd ... this means what exactly?
What is it that you want to do? Are you trying to setup a texting lab without knowing what to do? Are you planning on testing random stuff you've ... found? Cool rocks, or natural products? Random pills you've found lying around? Third party pharmaceutical testing? What?