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Function Repository Resource:

VarianceRatioCI

Source Notebook

Estimate the confidence interval of the ratio of the population variances

Contributed by: Wolfram Research

ResourceFunction["VarianceRatioCI"][list1,list2]

gives a confidence interval for the ratio of the population variances estimated from list1 and from list2.

Details and Options

VarianceRatioCI[list1,list2] gives a confidence interval {min,max} for a ratio of the population variances estimated by Variance[list1] and Variance[list2].
For confidence level α, min=ratio/q(1+α)/2 and max=ratio/q(1-α)/2 where ratio=Variance[list1]/Variance[list2] and qi is the ith quantile of an F-ratio distribution with Length[list1]-1 numerator and Length[list2]-1 denominator degrees of freedom.
The following option can be given:
ConfidenceLevel 0.95 probability associated with a confidence interval

Examples

Basic Examples

The 95% confidence interval for the ratio of two population variances:

In[1]:=
ResourceFunction[
 "VarianceRatioCI"][{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}]
Out[1]=

Options

ConfidenceLevel

The 99% confidence interval:

In[2]:=
ResourceFunction[
 "VarianceRatioCI"][{1, 2, 4, 6, 3}, {4, 10, 6, 8, 5, 8}, ConfidenceLevel -> .99]
Out[2]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

License Information