On a recent television programme I was learning about populations of wild dolphins around the world. They were mapping graphs and showing different types of charts and data to explain net migration and population growth and (more frequently) decline. It seemed relatively understandable to my non-specialist mind.
However, throughout the programme, some of the statisticians working with the biologists kept on expressing the view that statistics is a very different type of science than mathematics. Well, if they explained that sentiment, it must have gone completely over my head coz I sure as heck didn’t hear one. But the theme was repeated often.
The only thing I can think of to explain it is that in statistics you have more subjective decisions to make when analysing the data than with mathematics (in general). I base this on a complete lack of first-hand knowledge, so it’s probably complete bull. So I figure why not ask the experts?
Why would these (presumably respected) statisticians feel this way about their subject? I’ve always assumed (perhaps wrong-headedly) that statistics was a branch of mathematics (dealing with the manipulation/analysis of data), and therefore the same type of thinking was necessary. However I confess total ignorance and would like those more expert to clue me in.
Another thing. What is statistics used for when dealing in the financial sector? For example I have heard of “Quants” in the stock market and other types of financial data analyst, but I’m not really sure what it is they exactly do. Could someone fill in those details?
And aside from stock market analyses, is there any other way in which statisticians can contribute to the financial sector?
I already know how they can be of help to a biologist, but the market area seems more interesting to me.
Statistics started off as a branch of mathematics, but it really has evolved into something separate. That’s not to say that there’s no interaction between the two disciplines, because that would be false.
It’s kind of a tough question to answer in general. If there was no such thing as the scientific method, there’d be no reason for anyone to do statistics, but math would continue as normal.
Statistics is used in finance much the same way in other disciplines: to quantify uncertainty and to make predictions about the future behavior of systems.
It’s possible that in modelling populations, they were making a distinction in which a “mathematician” might think there is an exact model from which you could tell what the populations will be, whereas a “statistician” would tell you there is randomness inherent in population growth and he can’t model it exactly.
But, that would be a real simplification.
You might say that mathematics is “pure” or “true” in the sense that it is built up proof-by-proof from axioms and statistics is an applied science that was created to study randomness. That’s not to say that statistics (the field of study) isn’t rigorous or subject to interpretation even though a statistic (from data) might be.
Some statistics is very “pure”, just proofs and symbols and mathematical analysis, but statistics can also be very “applied”, used to model populations, experiments, or anything random.
Well, I’m not sure what you’d mean by “financial sector”. Statistics are used in the stock market, and that includes things like “options pricing” and “derivatives”. Businesses use statistics for everything, purchasing, production, whatever. Any transaction relies on someone’s evaluation of the future state of the “market”, which necessarily includes randomness.
Here is another helpful distinction. In regular math, you get an answer - an area, the result of an integration, whatever, which is always true. In statistics your conclusions must come with a disclaimer, that is the probability that the result is not true, but due to rare but possible variance of the data, such as sampling error.
I disagree that statistics would disappear without the scientific method. They are much used in business to forecast demand for products. An article in the NY Times this Sunday says that WalMart has more disk space than the entire Internet (though I’m not sure what they mean by disk space on the Internet). This is used for storing purchase data, which is analyzed statistically looking for trends - such as strawberry pop tarts sell real well after a hurricane.
Is statistics a branch of mathematics, or is it a separate discipline that uses a lot of mathematics (like physics is)? Probably the latter, though you could argue both ways.
Statistics draws heavily on probability theory, which I think is fair to call a branch of mathematics.
I would say that statisticians are a different set of people than mathematicians.
The discipline of statistics involves such issues as how data can be collected reliably, which are outside the scope of mathematics.
At many schools, if you took a statistics class it would be offered by the mathematics department and labeled as a mathematics class (unless it were a specific “Stats for Biologists” or “Stats for Psychologists” or “Stats for Businesspeople” or some such class offered by that specific department). But at some larger univiersities (the University of Illinois at Urbana is one that I know of for sure), there’s a Mathematics Department and a completely separate Statistics Department.
If you read a book on the history of mathematics, you probably wouldn’t see very much about statistics or encounter many of the same names as you’d see in a book on the history of stats.
Also, it’s inaccurate to call statistics and mathematics sciences. They’re heavily used by scientists, and individual statisticians and mathematicians may be scientists, but the disciplines are something else.