What's the difference between probability and statistics?
These 2 subjects are often intermingled, and confused with each other. To answer the question, "Let's go to the videotape!" as one of my favorite NY sports casters Warner Wolf liked to say ( see https://www.youtube.com/watch?v=gn7VFeRoi7k ) and get answers from both SUNY at Stony Brook and Stanford University.
Why am I writing about this? Good question! Two answers:
- To try to explain the often-confused difference between the two subjects / skills.
- Probability and statistics are 2 of my strongest skills, and I'm hoping that some of my connections will endorse me in those skills. :-)
A view from SUNY at Stony Brook can be seen at
http://www3.cs.stonybrook.edu/~skiena/jaialai/excerpts/node12.html in the section titled Probability versus Statistics.
Probability and statistics are related areas of mathematics which concern themselves with analyzing the relative frequency of events. Still, there are fundamental differences in the way they see the world:
Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.
Probability is primarily a theoretical branch of mathematics, which studies the consequences of mathematical definitions. Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world.
Both subjects are important, relevant, and useful. But they are different, and understanding the distinction is crucial in properly interpreting the relevance of mathematical evidence. Many a gambler has gone to a cold and lonely grave for failing to make the proper distinction between probability and statistics. :-)
A view from Stanford University can be seen at http://stats.stackexchange.com/questions/665/whats-the-difference-between-probability-and-statistics
What's the difference between probability and statistics, and why are they studied together?
The short answer to this I've heard from Persi Diaconis (one of my former Statistics Professors from Stanford) is the following: the problems considered by probability and statistics are inverse to each other. In probability theory we consider some underlying process which has some randomness or uncertainty modeled by random variables, and we figure out what happens. In statistics we observe something that has happened, and try to figure out what underlying process would explain those observations.
answered Jul 26 '10 at 20:47 Mark Meckes
So statistics observes what happens in the physical world, theorizes about the underlying process, and then having found the process, uses it in the sense of probability to predict what will happen next? – hslc Jul 26 '10 at 21:34
I'm not a statistician, but from my understanding I'd say, yes, that part of what statistics does. – Mark Meckes Jul 27 '10 at 0:10
great answer! +1 for Persi and Mark – robin girard Jul 27 '10 at 7:21
Induction vs Deduction? – Paolo Jul 27 '10 at 9:14
Like Paolo said, probability theory is mainly concerned with the deductive part, statistics with the inductive part of modeling processes with uncertainty. Perhaps it's interesting to mention that if one thinks that the plausible inductive reasoning should be consistent, then actually the result is bayesian statistics, and more interesting this can be derived from probability theory. So bayesian statistics is basically applied probability theory so to speak.. – Thies Heidecke May 27 '11 at 2:08
Probability also plays a big role in physics and quantum mechanics, which I find very interesting and will read about whenever I have some down time. :-) See https://en.wikipedia.org/wiki/Probability_amplitude