B: Though statistics are often associated with math, a true mathematician knows that there’s a big difference between the two disciplines. Mathematicians are more concerned with proving statements with carefully chosen axioms, definitions, and prior results, whereas statistics cannot be used to actually prove anything.
A: But how often does something really need to be proven, in practice? Statisticians use their work to show trends, and based on prior genuinely mathematical research, they can establish their theories beyond the point of “reasonable doubt,” having potential errors of only negligible probability.
B: This is true, although I wonder how often those points beyond reasonable doubt are actually reached. Unfortunately, a bunch of people might skip the heavier statistical analysis and refer to charts and graphs, which are easier to read and may be presented in a way that favors their opinions. This is a notorious misuse of statistics. In any case, statistics will never be a satisfactory substitute for logic. A statement like “and thus Statement A implies Statement B, which, by examination of the accompanying graph – clearly showing the positively correlating trend between Statement B and Statement C – further implies Statement C” would never fly in a logical argument, which demands absolute correlation, and can be measured only on a case-by-case basis – that is, with every possible situation being accounted for: there’s simply no way to accomplish that using methods of data collection and statistical analysis.
In conclusion, we’ve got to remember that there are certain principles at work in statistics. Correlations don’t just “magically” happen; there has to be a reason why, and it’s a lot more useful if we know what that reason is, instead of just saying, “I don’t know what you’re doing, but it’s working, so keep at it!”
A: Well, heck…why not?
B: If you don’t know why it’s working, you’ll not know why it stops working if and when it does, for one. Furthermore, you wouldn’t know how to tweak things to make things even more successful, if you wanted to be, which tends to be the case with most situations.
Statistics often help us see correlations, which give us an idea of what the underlying principle is, which is really the issue at hand. But just because there is a correlation, it doesn’t mean that the principle is apparent from the statistics. Conversely, if there appear to be no statistics to support a given principle, it doesn’t necessarily mean that the principle itself is false.
B: It’s not necessarily that there are no statistics supporting it. It may be that there are no statistics that analysts have invented that show the statistical correlation. Or it could be that the usual guidelines statisticians use for identifying correlations are not satisfied, even though there is a correlation. It could also be that the statistics are measured over too short a time: eternal principles may sometimes take decades or even centuries to show their effect. Most statisticians don’t seem to have that kind of patience. There may not be sufficient data for anyone to make such statistical analyses at the present time, anyway.
Therefore, if we’re interested in logical arguments only – that is, in seeing how someone, given some initial hypothesis, arrives at a certain conclusion, by way of reasoning how and why each step leads to the next; i.e., in understanding precisely why life, the world, and the universe are the way they are, or what truth is – those arguments that are based wholly on statistics must be thrown out the window. They are not enough by themselves; they cannot be the final word on any controversy. This is not to say that statistics are useless; on the contrary, they’re often very helpful in revealing the underlying principle in something. What I’m saying is that for the sake of logical argument, that (the underlying principle) is exactly what we’re looking for. You might think of statistics as the answer in the back of a math textbook: it gives a clue in solving the problem it refers to, but it doesn’t necessarily tell us how or why we got there, or why two things correlate – and it certainly doesn’t tell us what the whole truth is.