Deriving the Formula for Variance of Variance in Sample Data

  • Thread starter Beamer
  • Start date
  • Tags
    Variance
In summary, the conversation is about someone seeking help to derive the formula for variance of variance for a sample. They know the formula for variance of a sample mean, but are unable to prove it. They reference a book for the derivation and ask if their answer is correct. The person helping confirms their answer and the conversation ends with gratitude.
  • #1
Beamer
3
0
Hopefully someone will be able to help me.

I am trying to derive the formula for variance of variance for a sample. This would be similar to variance of a sample mean which is sigma/sqrt(N).


I know the variance of sample variance is sigma^2 * sqrt (2) / N, but I can't prove it.

Please help!
 
Physics news on Phys.org
  • #2
book: Estimation with Applications to Tracking and Navigation (Hardcover)
by Yaakov Bar-Shalom, X. Rong Li, Thiagalingam Kirubarajan, chapter 2.6.3 The variance of the sample mean and sample varinace, page 106. I assume I cannot put the copy of that page because of the copyright. The derivation is there.
 
Last edited:
  • #3
Thanks

And is the answer the same as I posted?

Thanks
Beamer
 
  • #4
nope :) probably you've made a mistake.
The answer is [tex]\sigma^2\sqrt{\frac{2}{N}[/tex]
 
  • #5
Thanks istealth

Thanks - appreciate your help
 

1. What is variance of variance?

Variance of variance is a statistical measure that quantifies the amount of variability or spread in the values of variances calculated from a set of data. It is used to evaluate the consistency or stability of a data set.

2. How is variance of variance calculated?

Variance of variance is calculated by taking the variance of the variances, which involves calculating the mean of the squared differences between each individual variance and the overall mean variance.

3. What does a high variance of variance indicate?

A high variance of variance indicates that the variances calculated from the data set vary significantly from each other, suggesting that the underlying data may be unstable or inconsistent.

4. How is variance of variance used in research?

Variance of variance is commonly used in research to assess the reliability and consistency of data. It can help researchers identify potential issues with data collection or measurement, and determine if further investigation or adjustments are necessary.

5. Can variance of variance be negative?

No, variance of variance cannot be negative. It is always a positive value, as it is calculated using squared differences and represents a measure of variability.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
11
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
335
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
4K
  • Set Theory, Logic, Probability, Statistics
Replies
28
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
793
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
815
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
995
Back
Top