17.9.7.2 Algorithms (PSS: One-Variance Test)

power

One-sided power: $H_0:\sigma \ge \sigma_0$

$Power=F_{k}[V_{k,\alpha }/r]\!$

One-sided power: $H_0:\sigma \le \sigma_0\!$

$Power=1-F_{k}[V_{k,1-\alpha }/r]\!$

Two-sided power $H_0:\sigma = \sigma_0\!$

$Power=1-F_{k}[V_{k,1-\alpha/2}/r]+F_{k}[V_{k,\alpha/2}/r]\!$

$F_{k}\!$ :distribution function of the chi-square distribution with k degrees of freedom, where k = n -1

$V_{k,C}\!$ :inverse CDF evaluated at C for a chi-square distribution with k degrees of freedom

$\alpha\!$ :significance level

$r=\frac{\sigma^2}{\sigma_0^2}\!$

sample size

Origin uses an iterative algorithm with the power equation. At each iteration,the power for a trial sample size are evaluated and iteration stops when the power evaluated reaches the values which corresponding to an integer sample size, and which is nearest to, yet greater than, the target value.

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(PSS) One-Variance Test

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