Who can tell me something about degree of freedom in statistic?

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SUMMARY

The discussion focuses on the concept of degrees of freedom in statistics, specifically the distinction between using n and n-1 when calculating standard deviation. It is established that using n-1 provides an unbiased estimator of variance and standard deviation, which is crucial for accurate statistical analysis. The reasoning behind this adjustment is rooted in the properties of unbiased estimators, ensuring that E[σest²] equals E[σ²]. Concrete examples were requested to clarify this concept further.

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The Bug
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being stuck by standard deviation, I just can't understand the difference between n and n-1.
who can give me some concrete examples?
thank you!
 
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The Bug said:
being stuck by standard deviation, I just can't understand the difference between n and n-1.
who can give me some concrete examples?
thank you!

Are you referring to the estimated standard deviation vs the actual standard deviation?

If so the reason is because the (n-1) term has to do with the fact that dividing by (n-1) instead of n will result in an unbiased point estimator of the variance and hence standard deviation.

Basically for unbiased estimators you have to show that E[σest2] = E[σ2] and what this ends up doing is forcing you to use the (n-1) in terms of n.
 

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