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 required sample size for an inequality test of one mean.
`solve_null_mean`	Estimate the required mean under the null hypothesis for an inequality test of one mean.
`solve_mean`	Estimate the required mean under the alternative hypothesis for an inequality test of one mean.

solve_power ¶

solve_power(
    *,
    null_mean: float,
    mean: float,
    std: float,
    size: int,
    alternative: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ],
    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['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the alternative hypothesis. `'two-sided'`: Two-sided alternative hypothesis: \(\mu_1 \neq \mu_0\) `'lower one-sided'`: Lower one-sided alternative hypothesis: \(\mu_1 < \mu_0\) `'upper one-sided'`: Upper one-sided alternative hypothesis: \(\mu_1 > \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, provide the two-sided significance level. If `alternative` is `'lower one-sided'` or `'upper one-sided'`, provide the one-sided 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[
        "two-sided", "lower one-sided", "upper one-sided"
    ],
    alpha: float,
    power: float,
    method: Literal["z", "t"],
) -> int

Estimate the required sample size 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['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the alternative hypothesis. `'two-sided'`: Two-sided alternative hypothesis: \(\mu_1 \neq \mu_0\) `'lower one-sided'`: Lower one-sided alternative hypothesis: \(\mu_1 < \mu_0\) `'upper one-sided'`: Upper one-sided alternative hypothesis: \(\mu_1 > \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, provide the two-sided significance level. If `alternative` is `'lower one-sided'` or `'upper one-sided'`, provide the one-sided 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:

Type	Description
`int`	The required sample size.

solve_null_mean ¶

solve_null_mean(
    *,
    mean: float,
    std: float,
    size: int,
    alternative: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ],
    alpha: float,
    power: float,
    method: Literal["z", "t"],
    search_direction: Literal["below", "above"] = "below",
) -> float

Estimate the required mean under the null hypothesis 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['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the alternative hypothesis. `'two-sided'`: Two-sided alternative hypothesis: \(\mu_1 \neq \mu_0\) `'lower one-sided'`: Lower one-sided alternative hypothesis: \(\mu_1 < \mu_0\) `'upper one-sided'`: Upper one-sided alternative hypothesis: \(\mu_1 > \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, provide the two-sided significance level. If `alternative` is `'lower one-sided'` or `'upper one-sided'`, provide the one-sided 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:

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

solve_mean ¶

solve_mean(
    *,
    null_mean: float,
    std: float,
    size: int,
    alternative: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ],
    alpha: float,
    power: float,
    method: Literal["z", "t"],
    search_direction: Literal["below", "above"] = "above",
) -> float

Estimate the required mean under the alternative hypothesis 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['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the alternative hypothesis. `'two-sided'`: Two-sided alternative hypothesis: \(\mu_1 \neq \mu_0\) `'lower one-sided'`: Lower one-sided alternative hypothesis: \(\mu_1 < \mu_0\) `'upper one-sided'`: Upper one-sided alternative hypothesis: \(\mu_1 > \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, provide the two-sided significance level. If `alternative` is `'lower one-sided'` or `'upper one-sided'`, provide the one-sided 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:

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