The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The sample standard deviation is equal to the square root of the sample variance.
Term  Description 

x_{i}  the i^{th} observation in your sample 
the sample mean  
S  the sample standard deviation 
n  sample size 
The variance measures how spread out the data are about their mean. The variance is equal to the standard deviation squared.
Term  Description 

x_{i}  i^{th} observation 
mean of the observations  
N  number of nonmissing observations 
When you specify a onesided test, Minitab calculates a onesided 100(1–α)% confidence bound, according to the direction of the alternative hypothesis.
A 100(1–α)% lower bound for the population variance is given by:
A 100(1–α)% upper bound for the population variance is given by:
Term  Description 

α  alphalevel for the 100(1 – α)% confidence interval 
n  sample size 
S^{2}  sample variance 
Χ^{2}(p)  the upper 100p^{th} percentile point on a chisquare distribution with (n – 1) degrees of freedom 
σ  true value of the population standard deviation 
σ^{2}  true value of the population variance 
Use this method for any continuous data (normal or nonnormal). ^{1}
When you specify a onesided test, Minitab calculates a onesided 100(1–α)% confidence bound, according to the direction of the alternative hypothesis.
Term  Description 

α  1 – confidence level / 100 
c_{α/2}  n / (n – z_{α/2}) 
c_{α }  n / (n – z_{α }) 
s^{2}  observed value of the sample variance 
z_{α/2}  inverse cumulative probability of the standard normal distribution at 1 – α/2. If n is less than or equal to z_{α/2}, Minitab does not calculate Bonett confidence intervals. 
z_{α}  inverse cumulative probability of the standard normal distribution at 1 – α. If n is less than or equal to z_{α} , Minitab does not calculate Bonett confidence intervals. 
se  
= estimated excess kurtosis  
m  trimmed mean with trim proportion equal to ; m = sample mean when n is less than or equal to 5 
σ  true value of the population standard deviation 
σ^{2}  true value of the population variance 
The hypothesis test uses the following pvalue equations for the respective alternative hypotheses:
H_{1}: σ^{2} > σ_{0}^{2}: pvalue = P(Χ^{2} ≥ x^{2})
H_{1}: σ^{2} < σ_{0}^{2}: pvalue = P(Χ^{2} ≤ x^{2})
H_{1}: σ^{2} ≠ σ_{0}^{2}: pvalue = 2 × min{P(Χ^{2} ≤ x^{2}), P(Χ^{2} ≥ x^{2})}
Term  Description  

σ^{2}  true value of the population variance  
σ_{0}^{2}  hypothesized value of the population variance  
Χ^{2}  follows a chisquare distribution with (n – 1) degrees of freedom when σ^{2} = σ_{0}^{2}  
x^{2} 

The Bonett procedure is not associated with a test statistic. However, Minitab uses the rejection regions defined by the confidence limits to calculate a pvalue.
For a twosided hypothesis, the pvalue is given by:
p = 2 × min(α_{L}, α_{U})
Term  Description  

σ_{0}^{2}  hypothesized variance  
α_{L}  smallest solution, α, of the equation  
α_{U}  smallest solution, α, of the equation  
c_{α/2}  n / (n – z_{α/2})  
α  1 – confidence level / 100  
s^{2}  observed value of the sample variance  
z_{α/2}  inverse cumulative probability of the standard normal distribution at 1 – α/2. If n is less than or equal to z_{α/2}, Minitab does not calculate Bonett confidence intervals.  
se 
