pystatpower.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_diff`	Estimate the required mean difference between the alternative hypothesis and 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_null_mean`	Estimate the required mean under the null hypothesis for an inequality test of one mean.
`solve_std`	Estimate the required standard deviation for an inequality test of one mean.

solve_power ¶

solve_power(
    *,
    mean: float | None = None,
    null_mean: float | None = None,
    diff: float | None = None,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"],
    alpha: float,
    dist: Literal["z", "t"] = "t",
) -> float

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

Parameters:

Name	Type	Description	Default
`mean`	`float \| None`	Mean under the alternative hypothesis. If `diff` is not specified, this parameter and `null_mean` are required.	`None`
`null_mean`	`float \| None`	Mean under the null hypothesis. If `diff` is not specified, this parameter and `mean` are required.	`None`
`diff`	`float \| None`	Mean difference between the alternative hypothesis and the null hypothesis. If both `mean` and `null_mean` are not specified, this parameter is required.	`None`
`std`	`float`	Standard deviation.	required
`size`	`int`	Sample size.	required
`alternative`	`Literal['two-sided', 'greater', 'less']`	Type of the alternative hypothesis. If `alternative` is `'two-sided'`, the alternative hypothesis is \(\mu \neq \mu_0\) If `alternative` is `'greater'`, the alternative hypothesis is \(\mu > \mu_0\) If `alternative` is `'less'`, the alternative hypothesis is \(\mu < \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, `alpha` represents the two-sided significance level. If `alternative` is `'greater'` or `'less'`, `alpha` represents the one-sided significance level.	required
`dist`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution.	`'t'`

Returns:

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

Raises:

Type	Description
`ValueError`	If `diff` is not specified, and either `mean` or `null_mean` is not specified.

solve_size ¶

solve_size(
    *,
    mean: float | None = None,
    null_mean: float | None = None,
    diff: float | None = None,
    std: float,
    alternative: Literal["two-sided", "greater", "less"],
    alpha: float,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
) -> int

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

Parameters:

Name	Type	Description	Default
`mean`	`float \| None`	Mean under the alternative hypothesis. If `diff` is not specified, this parameter and `null_mean` are required.	`None`
`null_mean`	`float \| None`	Mean under the null hypothesis. If `diff` is not specified, this parameter and `mean` are required.	`None`
`diff`	`float \| None`	Mean difference between the alternative hypothesis and the null hypothesis. If both `mean` and `null_mean` are not specified, this parameter is required.	`None`
`std`	`float`	Standard deviation.	required
`alternative`	`Literal['two-sided', 'greater', 'less']`	Type of the alternative hypothesis. If `alternative` is `'two-sided'`, the alternative hypothesis is \(\mu \neq \mu_0\) If `alternative` is `'greater'`, the alternative hypothesis is \(\mu > \mu_0\) If `alternative` is `'less'`, the alternative hypothesis is \(\mu < \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, `alpha` represents the two-sided significance level. If `alternative` is `'greater'` or `'less'`, `alpha` represents the one-sided significance level.	required
`power`	`float`	Expected statistical power. 0.8 is a commonly used statistical power.	`0.8`
`dist`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution.	`'t'`

Returns:

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

Raises:

Type	Description
`ValueError`	If `diff` is not specified, and either `mean` or `null_mean` is not specified.

solve_diff ¶

solve_diff(
    *,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"],
    alpha: float,
    power: float,
    dist: Literal["z", "t"],
    direction: Literal["greater", "less"] | None = None,
) -> float

Estimate the required mean difference between the alternative hypothesis and the null hypothesis for an inequality test of one mean.

Parameters:

Name	Type	Description	Default
`std`	`float`	Standard deviation.	required
`size`	`int`	Sample size.	required
`alternative`	`Literal['two-sided', 'greater', 'less']`	Type of the alternative hypothesis. If `alternative` is `'two-sided'`, the alternative hypothesis is \(\mu \neq \mu_0\) If `alternative` is `'greater'`, the alternative hypothesis is \(\mu > \mu_0\) If `alternative` is `'less'`, the alternative hypothesis is \(\mu < \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, `alpha` represents the two-sided significance level. If `alternative` is `'greater'` or `'less'`, `alpha` represents the one-sided significance level.	required
`power`	`float`	Expected statistical power. 0.8 is a commonly used statistical power.	required
`dist`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution.	required
`direction`	`Literal['greater', 'less'] \| None`	The search direction for the mean difference relative to zero. `'greater'`: Search for the mean difference that is greater than zero. `'less'`: Search for the mean difference that is less than zero. Note If `alternative` is `'two-sided'`, the parameter `direction` is required. If `alternative` is `'greater'`, the search direction is automatically inferred to be `'greater'`, and the parameter `direction` is ignored. If `alternative` is `'less'`, the search direction is automatically inferred to be `'less'`, and the parameter `direction` is ignored.	`None`

Returns:

Name	Type	Description
`float`	`float`	The required mean difference between the alternative hypothesis and the null hypothesis.

Raises:

Type	Description
`ValueError`	If `alternative` is `'two-sided'` but `direction` is not specified.

solve_mean ¶

solve_mean(
    *,
    null_mean: float,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"],
    alpha: float,
    power: float,
    dist: Literal["z", "t"],
    direction: Literal["greater", "less"] | None = None,
) -> 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.	required
`std`	`float`	Standard deviation.	required
`size`	`int`	Sample size.	required
`alternative`	`Literal['two-sided', 'greater', 'less']`	Type of the alternative hypothesis. If `alternative` is `'two-sided'`, the alternative hypothesis is \(\mu \neq \mu_0\) If `alternative` is `'greater'`, the alternative hypothesis is \(\mu > \mu_0\) If `alternative` is `'less'`, the alternative hypothesis is \(\mu < \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, `alpha` represents the two-sided significance level. If `alternative` is `'greater'` or `'less'`, `alpha` represents the one-sided significance level.	required
`power`	`float`	Expected statistical power. 0.8 is a commonly used statistical power.	required
`dist`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution.	required
`direction`	`Literal['greater', 'less'] \| None`	The search direction for the mean under the alternative hypothesis relative to the mean under the null hypothesis. `'greater'`: Search for the alternative mean that is greater than the null mean. `'less'`: Search for the alternative mean that is less than the null mean. Note If `alternative` is `'two-sided'`, the parameter `direction` is required. If `alternative` is `'greater'`, the search direction is automatically inferred to be `'greater'`, and the parameter `direction` is ignored. If `alternative` is `'less'`, the search direction is automatically inferred to be `'less'`, and the parameter `direction` is ignored.	`None`

Returns:

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

Raises:

Type	Description
`ValueError`	If `alternative` is `'two-sided'` but `direction` is not specified.

solve_null_mean ¶

solve_null_mean(
    *,
    mean: float,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"],
    alpha: float,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
    direction: Literal["greater", "less"] | None = None,
) -> 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.	required
`std`	`float`	Standard deviation.	required
`size`	`int`	Sample size.	required
`alternative`	`Literal['two-sided', 'greater', 'less']`	Type of the alternative hypothesis. If `alternative` is `'two-sided'`, the alternative hypothesis is \(\mu \neq \mu_0\) If `alternative` is `'greater'`, the alternative hypothesis is \(\mu > \mu_0\) If `alternative` is `'less'`, the alternative hypothesis is \(\mu < \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, `alpha` represents the two-sided significance level. If `alternative` is `'greater'` or `'less'`, `alpha` represents the one-sided significance level.	required
`power`	`float`	Expected statistical power. 0.8 is a commonly used statistical power.	`0.8`
`dist`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution.	`'t'`
`direction`	`Literal['greater', 'less'] \| None`	The search direction for the mean under the null hypothesis relative to the mean under the alternative hypothesis. `'greater'`: Search for the null mean that is greater than the alternative mean. `'less'`: Search for the null mean that is less than the alternative mean. Note If `alternative` is `'two-sided'`, the parameter `direction` is required. If `alternative` is `'greater'`, the search direction is automatically inferred to be `'less'`, and the parameter `direction` is ignored. If `alternative` is `'less'`, the search direction is automatically inferred to be `'greater'`, and the parameter `direction` is ignored.	`None`

Returns:

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

Raises:

Type	Description
`ValueError`	If `alternative` is `'two-sided'` but `direction` is not specified.

solve_std ¶

solve_std(
    *,
    mean: float | None = None,
    null_mean: float | None = None,
    diff: float | None = None,
    size: int,
    alternative: Literal["two-sided", "greater", "less"],
    alpha: float,
    power: float,
    dist: Literal["z", "t"],
) -> float

Estimate the required standard deviation for an inequality test of one mean.

Parameters:

Name	Type	Description	Default
`mean`	`float \| None`	Mean under the alternative hypothesis. If `diff` is not specified, this parameter and `null_mean` are required.	`None`
`null_mean`	`float \| None`	Mean under the null hypothesis. If `diff` is not specified, this parameter and `mean` are required.	`None`
`diff`	`float \| None`	Mean difference between the alternative hypothesis and the null hypothesis. If both `mean` and `null_mean` are not specified, this parameter is required.	`None`
`size`	`int`	Sample size.	required
`alternative`	`Literal['two-sided', 'greater', 'less']`	Type of the alternative hypothesis. If `alternative` is `'two-sided'`, the alternative hypothesis is \(\mu \neq \mu_0\) If `alternative` is `'greater'`, the alternative hypothesis is \(\mu > \mu_0\) If `alternative` is `'less'`, the alternative hypothesis is \(\mu < \mu_0\)	required
`alpha`	`float`	Significance level. If `alternative` is `'two-sided'`, `alpha` represents the two-sided significance level. If `alternative` is `'greater'` or `'less'`, `alpha` represents the one-sided significance level.	required
`power`	`float`	Expected statistical power. 0.8 is a commonly used statistical power.	required
`dist`	`Literal['z', 't']`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution.	required

Returns:

Name	Type	Description
`float`	`float`	The required standard deviation.

Raises:

Type	Description
`ValueError`	If `diff` is not specified, and either `mean` or `null_mean` is not specified.