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#1
08-16-2005, 06:35 PM
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\"i got an idea...how bout n-1!\" (nerds rejoice)
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 [img]/images/graemlins/spade.gif[/img] 
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#2
08-16-2005, 06:41 PM
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Re: \"i got an idea...how bout n-1!\" (nerds rejoice)
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#3
08-16-2005, 07:18 PM
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Re: \"i got an idea...how bout n-1!\" (nerds rejoice)
[ 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 [img]/images/graemlins/spade.gif[/img] [/ 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.
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#4
08-17-2005, 12:17 AM
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Re: \"i got an idea...how bout n-1!\" (nerds rejoice)
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 [img]/images/graemlins/spade.gif[/img]
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#5
08-17-2005, 01:23 AM
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Re: \"i got an idea...how bout n-1!\" (nerds rejoice)
[ 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 [img]/images/graemlins/spade.gif[/img] [/ QUOTE ] This is the right forum.
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#6
08-17-2005, 08:47 AM
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Re: \"i got an idea...how bout n-1!\" (nerds rejoice)
[ 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 [img]/images/graemlins/spade.gif[/img] [/ QUOTE ] 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. [/ QUOTE ]
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