pystatpower.models.mean.single.inequality ¶

Functions:

Name	Description
`solve_power`	Calculate the statistical power for an inequality test of one mean.
`solve_size`	Estimate the sample size required for an inequality test of one mean.
`solve_null_mean`	Estimate the mean under the null hypothesis required for an inequality test of one mean.
`solve_mean`	Estimate the mean under the alternative hypothesis required for an inequality test of one mean.

solve_power ¶

solve_power(*, null_mean: float, mean: float, std: float, size: int, alternative: Literal['lower', 'upper', 'both'], alpha: float, method: Literal['z', 't']) -> float

Calculate the statistical power for an inequality test of one mean.

Parameters:

Name	Type	Description	Default
`null_mean`	`float`	Mean under the null hypothesis (\(\mu_0\)).	required
`mean`	`float`	Mean under the alternative hypothesis (\(\mu_1\)).	required
`std`	`float`	Standard deviation (\(\sigma\)). If `method='t'`, provide the sample standard deviation (\(S\)).	required
`size`	`int`	Sample size (\(n\)).	required
`alternative`	`Literal['lower', 'upper', 'both']`	The direction of the alternative hypothesis. `'lower'`: lower-tailed alternative hypothesis: \(H_1: \mu_1 < \mu_0\) `'upper'`: upper-tailed alternative hypothesis: \(H_1: \mu_1 > \mu_0\) `'both'`: two-tailed alternative hypothesis: \(H_1: \mu_1 \neq \mu_0\)	required
`alpha`	`float`	Significance level.	required
`method`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Standard normal distribution (large sample approximation). `'t'`: Student's t distribution.	required

Returns:

Type	Description
`float`	The calculated statistical power of the test.

solve_size ¶

solve_size(*, null_mean: float, mean: float, std: float, alternative: Literal['lower', 'upper', 'both'], alpha: float, power: float, method: Literal['z', 't']) -> int

Estimate the sample size required for an inequality test of one mean.

Parameters:

Name	Type	Description	Default
`null_mean`	`float`	Mean under the null hypothesis (\(\mu_0\)).	required
`mean`	`float`	Mean under the alternative hypothesis (\(\mu_1\)).	required
`std`	`float`	Standard deviation (\(\sigma\)). If `method='t'`, provide the sample standard deviation (\(S\)).	required
`alternative`	`Literal['lower', 'upper', 'both']`	The direction of the alternative hypothesis. `'lower'`: lower-tailed alternative hypothesis: \(H_1: \mu_1 < \mu_0\) `'upper'`: upper-tailed alternative hypothesis: \(H_1: \mu_1 > \mu_0\) `'both'`: two-tailed alternative hypothesis: \(H_1: \mu_1 \neq \mu_0\)	required
`alpha`	`float`	Significance level.	required
`power`	`float`	Desired statistical power.	required
`method`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Standard normal distribution (large sample approximation). `'t'`: Student's t distribution.	required

Returns:

Name	Type	Description
`int`	`int`	The required sample size.

solve_null_mean ¶

solve_null_mean(*, mean: float, std: float, size: int, alternative: Literal['lower', 'upper', 'both'], alpha: float, power: float, method: Literal['z', 't'], search_direction: Literal['below', 'above'] = 'below') -> float

Estimate the mean under the null hypothesis required for an inequality test of one mean.

Parameters:

Name	Type	Description	Default
`mean`	`float`	Mean under the alternative hypothesis (\(\mu_1\)).	required
`std`	`float`	Standard deviation (\(\sigma\)). If `method='t'`, provide the sample standard deviation (\(S\)).	required
`size`	`int`	Sample size (\(n\)).	required
`alternative`	`Literal['lower', 'upper', 'both']`	The direction of the alternative hypothesis. `'lower'`: lower-tailed alternative hypothesis: \(H_1: \mu_1 < \mu_0\) `'upper'`: upper-tailed alternative hypothesis: \(H_1: \mu_1 > \mu_0\) `'both'`: two-tailed alternative hypothesis: \(H_1: \mu_1 \neq \mu_0\)	required
`alpha`	`float`	Significance level.	required
`power`	`float`	Desired statistical power.	required
`method`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Standard normal distribution (large sample approximation). `'t'`: Student's t distribution.	required
`search_direction`	`Literal['below', 'above']`	Specify whether to search for the null mean below or above the alternative mean. `'below'`: Search the null mean below the alternative mean. `'above'`: Search the null mean above the alternative mean.	`'below'`

Returns:

Name	Type	Description
`float`	`float`	The required mean under the null hypothesis.

solve_mean ¶

solve_mean(*, null_mean: float, std: float, size: int, alternative: Literal['lower', 'upper', 'both'], alpha: float, power: float, method: Literal['z', 't'], search_direction: Literal['below', 'above'] = 'above') -> float

Estimate the mean under the alternative hypothesis required for an inequality test of one mean.

Parameters:

Name	Type	Description	Default
`null_mean`	`float`	Mean under the null hypothesis (\(\mu_0\)).	required
`std`	`float`	Standard deviation (\(\sigma\)). If `method='t'`, provide the sample standard deviation (\(S\)).	required
`size`	`int`	Sample size (\(n\)).	required
`alternative`	`Literal['lower', 'upper', 'both']`	The direction of the alternative hypothesis. `'lower'`: lower-tailed alternative hypothesis: \(H_1: \mu_1 < \mu_0\) `'upper'`: upper-tailed alternative hypothesis: \(H_1: \mu_1 > \mu_0\) `'both'`: two-tailed alternative hypothesis: \(H_1: \mu_1 \neq \mu_0\)	required
`alpha`	`float`	Significance level.	required
`power`	`float`	Desired statistical power.	required
`method`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Standard normal distribution (large sample approximation). `'t'`: Student's t distribution.	required
`search_direction`	`Literal['below', 'above']`	Specify whether to search for the alternative mean below or above the null mean. `'below'`: Search the alternative mean below the null mean. `'above'`: Search the alternative mean above the null mean.	`'above'`

Returns:

Name	Type	Description
`float`	`float`	The required mean under the alternative hypothesis.