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发表于 2011-2-15 16:47:52
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这是Purdue中心的专家回答：
The arithmetic mean is the "best" measure of central tendency for true normal (gaussian) distributions, the geometric mean is the same for distributions that are made normal if they are transformed logarithmically (log-normal distribution).
The mean is calculated by summing the values of all measurements and then dividing by the number (n) of measurements, whereas the geometric mean is found by multiplying all measurements and finding the nth root of the product. The geometric mean sounds hard to calculate, but is what you get if you antilog the arithmetic mean of log data, hence its widespread appearance in flow cytometric analysis programs. If a "log" sample is normally distributed (ie Log-normal), then the geometric mean would indicate the centre better than the arithmetic mean.
The median (50th centile) is the value that corresponds to the middle item in a ranked list (ie sorted by magnitude) of all measurements. It's robust in that it doesn't necessarily move in response to small numbers of outliers, or to skewing of the tails of a distribution, whereas the mean is tugged by both. One situation where the median is probably the only valid measure is where data pile up at one extreme of measurement, as long as more than 50% of the cells are clear of the sides you get a valid median, but either type of mean will be way off.
So if you've got normally distributed data, and want to be able to reflect small changes, use the arithmetic mean, if you've got lognormal data use the geometric mean, and if you want a robust indicator use the median (but this will fail to indicate subtle changes). |
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发表于 2011-2-15 15:54:06
回答的很好
