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Sunday, April 24, 2011

Confidence Interval

If you have done statistical analysis, you must have surely heard of this term - confidence interval. In statistics, a confidence interval (CI) is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate.

But quite often, we interpret it incorrectly.

Consider the following confidence interval: We are 90% confident that the population mean is greater than 100 and less than 200.

Some people think this means there is a 90% chance that the population mean falls between 100 and 200. This is incorrect. Like any population parameter, the population mean is a constant, not a random variable. It does not change. The probability that a constant falls within any given range is always 0.00 or 1.00.

The confidence level describes the uncertainty associated with a sampling method. Suppose we used the same sampling method to select different samples and to compute a different interval estimate, say mean for each sample. Some interval estimates would include the true population parameter, in this case the mean, and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; A 95% confidence level means that 95% of the intervals would include the parameter; and so on.

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