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

In summary, the (n-1) term in standard deviation calculations is necessary for an unbiased point estimator of the variance.
  • #1
The Bug
1
0
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!
 
Mathematics news on Phys.org
  • #2
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.
 

1. What is the definition of degree of freedom in statistics?

The degree of freedom in statistics refers to the number of independent pieces of information that are available to estimate a statistical parameter. It is often denoted by the symbol "df" and is an important concept in statistical analysis.

2. How is the degree of freedom calculated?

The degree of freedom is typically calculated as the difference between the sample size and the number of parameters being estimated in a statistical model. For example, in a simple linear regression with one independent variable, the degree of freedom would be n-2, where n is the sample size.

3. Why is the degree of freedom important in statistics?

The degree of freedom plays a crucial role in determining the accuracy and reliability of statistical tests and confidence intervals. It helps to determine the appropriate critical values and degrees of significance for a given sample size and statistical model.

4. Can the degree of freedom be negative?

No, the degree of freedom cannot be negative. It is always a non-negative integer, as it represents the number of independent pieces of information available for estimation. If the calculated degree of freedom is negative, it is typically a sign of an error in the statistical analysis.

5. How does the degree of freedom change with sample size?

The degree of freedom increases as the sample size increases. This is because with a larger sample size, there are more independent pieces of information available for estimation, leading to a higher degree of freedom. However, the exact relationship between sample size and degree of freedom may vary depending on the specific statistical model being used.

Similar threads

Replies
1
Views
610
  • Mechanics
Replies
5
Views
976
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
951
Replies
5
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
9
Views
2K
Replies
24
Views
2K
Replies
17
Views
2K
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top