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Estimation

22 October, 2015 - 14:37

Estimation is one of the basic inferential statistics techniques. The idea is simple; collect data from a sample and process it in some way that yields a good inference of something about the population. There are two types of estimates: point estimates and interval estimates. To make a point estimate, you simply find the single number that you think is your best guess of the characteristic of the population. As you can imagine, you will seldom be exactly correct, but if you make your estimate correctly, you will seldom be very far wrong. How to correctly make these estimates is an important part of statistics.

To make an interval estimate, you define an interval within which you believe the population characteristic lies. Generally, the wider the interval, the more confident you are that it contains the population characteristic. At one extreme, you have complete confidence that the mean of a population lies between -\infty and +\infty but that information has little value. At the other extreme, though you can feel comfortable that the population mean has a value close to that guessed by a correctly conducted point estimate, you have almost no confidence ("zero plus" to statisticians) that the population mean is exactly equal to the estimate. There is a trade-off between width of the interval, and confidence that it contains the population mean. How to find a narrow range with an acceptable level of confidence is another skill learned when learning statistics.