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Say I have eaten hamburgers every Tuesday for years. You could say that I eat hamburgers 14% of the time, or that the probability of me eating a hamburger in a given week is 14%.
What are the main differences between probabilities and proportions?
Is a probability an expected proportion?
Are probabilities uncertain and proportions are guaranteed?
I have hesitated to wade into this discussion, but because it seems to have gotten sidetracked over a trivial issue concerning how to express numbers, maybe it's worthwhile refocusing it. A point of departure for your consideration is this:
A probability is a hypothetical property. Proportions summarize observations.
A frequentist might rely on laws of large numbers to justify statements like "the long-run proportion of an event [is] its probability." This supplies meaning to statements like "a probability is an expected proportion," which otherwise might appear merely tautological. Other interpretations of probability also lead to connections between probabilities and proportions but they are less direct than this one.
In our models we usually take probabilities to be definite but unknown. Due to the sharp contrasts among the meanings of "probable," "definite," and "unknown" I am reluctant to apply the term "uncertain" to describe that situation. However, before we conduct a sequence of observations, the [eventual] proportion, like any future event, is indeed "uncertain". After we make those observations, the proportion is both definite and known. (Perhaps this is what is meant by "guaranteed" in the OP.) Much of our knowledge about the [hypothetical] probability is mediated through these uncertain observations and informed by the idea that they might have turned out otherwise. In this sense--that uncertainty about the observations is transmitted back to uncertain knowledge of the underlying probability--it seems justifiable to refer to the probability as "uncertain."
In any event it is apparent that probabilities and proportions function differently in statistics, despite their similarities and intimate relationships. It would be a mistake to take them to be the same thing.
Huber, WA Ignorance is Not Probability. Risk Analysis Volume 30, Issue 3, pages 371–376, March 2010.
If you flip a fair coin 10 times and it comes up heads 3 times, the proportion of heads is .30 but the probability of a head on any one flip is .50.
A proportion implies it is a guaranteed event, whereas a probability is not.
If you eat hamburgers 14% of the time, in a given (4-week) month (or over whatever interval you based your proportion on), you must have eaten 4 hamburgers; whereas with probability there is a possibility of having eaten no hamburgers at all or perhaps eaten a hamburger everyday.
Probability is a measure of uncertainty, whereas proportion is a measure of certainty.
The difference is not in the calculation, but in the purpose to which the metric is put: Probability is a concept of time; proportionality is a concept of space.
If we want to know the probability of a future event, we can use the probability at which the event took place in the past to derive our best estimate for the probability of the event in the future. If we want to know how much space is left in the theater then we use proportionality: the number of unoccupied seats/the number of seats.
This ratio is not the probability of securing a seat; the probability of securing a seat (a future event) is a function of the occupied and unoccupied seats, as well as the reserved seats, the no-show probability, and a myriad of other conditions.
Proportion and probability, both are calculated from the total but the value of proportion is certain while that of probability is no0t certain..
From my point of view the main difference between proportion and probability is the three axioms of probability which proportions don't have. i.e. (i) Probability always lies between 0 and 1. (ii) Probability sure event is one. (iii) P(A or B) = P(A) +P(B), A and B are mutually exclusive events
In the Frequentist Interpretation of Probability, the probability is long-run relative frequency. That means, the proportion in a large number of observations.
If you toss a coin 10 times and you get 4 tails, the proportion of tails is 0.4. However, 10 is not a very large number. This is only a proportion, not a probability.
Well, what is "a large number"? Bernoulli's estimation is 25,000 minimum. If you toss a coin around 50,000 times (for example) you are bound to get something close to 0.5 tails/heads. This means that the probability of getting heads/tails is 0.5. (and if you increase the number of trials, say, to 1 million, the proportion would become closer to 0.5)
The only problem here is: what is probability? Long-run relative frequency is how we MEASURE probability, but what is it? What does it really mean when I say "The probability of getting heads is 0.5"? This is one of the great problems with the Frequentist Interpretation. But this is my opinion only. I am sure many people differ.
I don't know if there is a difference, but probabilities are not % they range from 0 to 1. I mean if you multiply a probability by 100 you get %. If your question is what's the difference between probability and % then this would be my answer, but this is not your question. The definition of probability assumes an infinite number of sampling experiments, so then we can never truly get probability because we can never truly conduct an infinite number of sampling experiments.
