Finite-population correction factor
Message posted by Denice (via 208.147.67.129) on November 5, 2001 at 3:29 PM (ET)

does anyone have a simple explaination on how or why we use the number 1 in n-1?

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Re: Finite-population correction factor
Message posted by Tomi (via 154.32.143.252) on November 5, 2001 at 6:26 PM (ET)

Now it is impractical to catch and measure every fish, so we catch a sample. It is however possible to calculate the mean (x bar) and standard deviation (s) of the sample.

Based on these we are going to try and guess the mean and standard deviation of the population. The obvious guesses (statisticians use the expression "estimators") are:

Population mean = sample mean
Population standard deviation = sample standard deviation.

By a very complicated process it is possible to check how good these guesses are likely to be. For the mean, this guess is quite accurate. The guess may vary above or below the true value but on average it is spot on.

It's a different story with the standard deviation. Your guess would be an underestimate more often than an overestimate. To correct for this it just happens to work if you use the divisor n-1 instead of n.