For instance, in the coin flipping example, we can write down the model like this: (P(mboxheads) 0.5) which you can read as the probability of heads is 0.5.I have studied many languages-French, Spanish and a little Italian, but no one told me that Statistics was a foreign language.Section 4.10 - 4.11 4.13 - Mix of Matthew Crump Danielle Navarro.
To a lot of people, this is all there is to statistics: its about calculating averages, collecting all the numbers, drawing pictures, and putting them all in a report somewhere. In fact, descriptive statistics is one of the smallest parts of statistics, and one of the least powerful. The bigger and more useful part of statistics is that it provides tools that let you make inferences about data. For instance, heres a tiny extract from a newspaper article in the Sydney Morning Herald (30 Oct 2010). A polling company has conducted a survey, usually a pretty big one because they can afford it. Im too lazy to track down the original survey, so lets just imagine that they called 1000 voters at random, and 230 (23) of those claimed that they intended to vote for the party. For the 2010 Federal election, the Australian Electoral Commission reported 4,610,795 enrolled voters in New South Whales; so the opinions of the remaining 4,609,795 voters (about 99.98 of voters) remain unknown to us. Even assuming that no-one lied to the polling company the only thing we can say with 100 confidence is that the true primary vote is somewhere between 2304610795 (about 0.005) and 46100254610795 (about 99.83). So, on what basis is it legitimate for the polling company, the newspaper, and the readership to conclude that the ALP primary vote is only about 23. In other words, we assume that the data collected by the polling company is pretty representative of the population at large. But how representative Would we be surprised to discover that the true ALP primary vote is actually 24 29 37 At this point everyday intuition starts to break down a bit. No-one would be surprised by 24, and everybody would be surprised by 37, but its a bit hard to say whether 29 is plausible. We need some more powerful tools than just looking at the numbers and guessing. ![]() A brief introduction to probability theory, and an introduction to sampling from distributions. The two disciplines are closely related but theyre not identical. Its a branch of mathematics that tells you how often different kinds of events will happen. For example, all of these questions are things you can answer using probability theory. In each case the truth of the world is known, and my question relates to the what kind of events will happen. In the first question I know that the coin is fair, so theres a 50 chance that any individual coin flip will come up heads. In the third question I know that the deck is shuffled properly. And in the fourth question, I know that the lottery follows specific rules. You get the idea. The critical point is that probabilistic questions start with a known model of the world, and we use that model to do some calculations.
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