Select the method or formula of your choice.
Let tα,v be the upper α (one-sided) critical value for a t-distribution with v degrees of freedom. The power for the two-sided alternative hypothesis Lower limit < test mean - target < upper limit is given by:
For alternative hypotheses of Test mean > target or Test mean - target > lower limit, the power is given by:
For alternative hypotheses of Test mean < target or Test mean - target < upper limit, the power is given by:
where CDF( x ; v , λ ) is the cumulative distribution function, evaluated at x, for a noncentral t-distribution with noncentrality parameter, λ , and v degrees of freedom.
The degrees of freedom, v, is given by:
The noncentrality parameter that corresponds to the lower equivalence limit is denoted as λ1, and is given by:
For the alternative hypothesis Test mean > target, δ1 = 0.
The noncentrality parameter that corresponds to the upper equivalence limit is denoted as λ2, and is given by:
For the alternative hypothesis Test mean < target, δ2 = 0.
Term | Description |
---|---|
α | significance level for the test |
D | mean of the test population minus the target value |
δ1 | lower equivalence limit |
δ2 | upper equivalence limit |
n | sample size |
σ | standard deviation of the population |