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View Full Version : "i got an idea...how bout n-1!" (nerds rejoice)

erby
08-16-2005, 06:35 PM
why is variance of a sample defined as the sum of the squared deviations of the measurements about their mean divided by (n-1), where n is the number of elements in the sample? My text book stated that "Dividing the sum of squares of deviations by n produces estimates that tend to underestimate sig^2 (for a population). Division by (n-1) eliminates this difficulty."

Is this the only reason...just cuz it works better? Am I missing something?

ERBY /images/graemlins/spade.gif

TomCollins
08-16-2005, 06:41 PM
Degrees of Freedom (http://en.wikipedia.org/wiki/Degrees_of_freedom_%28statistics%29)

BruceZ
08-16-2005, 07:18 PM
[ QUOTE ]
why is variance of a sample defined as the sum of the squared deviations of the measurements about their mean divided by (n-1), where n is the number of elements in the sample? My text book stated that "Dividing the sum of squares of deviations by n produces estimates that tend to underestimate sig^2 (for a population). Division by (n-1) eliminates this difficulty."

Is this the only reason...just cuz it works better? Am I missing something?

ERBY /images/graemlins/spade.gif

[/ QUOTE ]

Dividing by n-1 gives the unbiased estimate of the variance of a normal distribution. This means that the expected value of this estimator is the true variance. Dividing by n gives the maximum likelihood estimate of the variance of a normal distribution. This means it is the value of the variance that maximizes the likelihood of the observed data. Dividing by n+1 gives the estimate which minimizes the mean squared error of the estimate. All 3 estimators give essentially the same value for sufficiently large n.

erby
08-17-2005, 12:17 AM
thanks man. on another note, was this post okay for this forum, or should i have asked it in science, math, and philosophy instead?

ERBY /images/graemlins/spade.gif

BruceZ
08-17-2005, 01:23 AM
[ QUOTE ]
thanks man. on another note, was this post okay for this forum, or should i have asked it in science, math, and philosophy instead?

ERBY /images/graemlins/spade.gif

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This is the right forum.

mosdef
08-17-2005, 08:47 AM
[ QUOTE ]
[ QUOTE ]
thanks man. on another note, was this post okay for this forum, or should i have asked it in science, math, and philosophy instead?

ERBY /images/graemlins/spade.gif

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indeed. from what i've seen, the "science, math, and philosophy" forum would be more accurately described as the "no science, no math, and juvenile philosophies that fit on a bumper sticker" forum.

This is the right forum.

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