pystatpower.mean.single.inequality ¶

FUNCTION	DESCRIPTION
`solve_power`	Calculate the statistical power.
`solve_size`	Estimate the required sample size.
`solve_mean`	Estimate the required mean under the alternative hypothesis.
`solve_null_mean`	Estimate the required mean under the null hypothesis.
`solve_diff`	Estimate the required mean difference.
`solve_std`	Estimate the required standard deviation.

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"] = "two-sided",
    alpha: float = 0.05,
    dist: Literal["z", "t"] = "t",
) -> float

Calculate the statistical power.

PARAMETER	DESCRIPTION
`mean`	Mean under the alternative hypothesis. This parameter must be used in conjuction with `null_mean` to compute the `diff`, where `diff` = `mean` - `null_mean`. TYPE: `float \| None` DEFAULT: `None`
`null_mean`	Mean under the null hypothesis. This parameter must be used in conjuction with `mean` to compute the `diff`, where `diff` = `mean` - `null_mean`. TYPE: `float \| None` DEFAULT: `None`
`diff`	Mean difference between the alternative hypothesis and the null hypothesis. If this parameter is specified, both `mean` and `null_mean` are ignored. TYPE: `float \| None` DEFAULT: `None`
`std`	Standard deviation. TYPE: `float`
`size`	Sample size. TYPE: `int`
`alternative`	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 \(\mu < \mu_0\) TYPE: `Literal['two-sided', 'greater', 'less']` DEFAULT: `'two-sided'`
`alpha`	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. TYPE: `float` DEFAULT: `0.05`
`dist`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution. TYPE: `Literal['z', 't']` DEFAULT: `'t'`

RETURNS	DESCRIPTION
`float`	The statistical power of the test.

RAISES	DESCRIPTION
`ValueError`	The given set of parameters is insufficient to determine the mean difference.

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"] = "two-sided",
    alpha: float = 0.05,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
) -> int

Estimate the required sample size.

PARAMETER	DESCRIPTION
`mean`	Mean under the alternative hypothesis. This parameter must be used in conjuction with `null_mean` to compute the `diff`, where `diff` = `mean` - `null_mean`. TYPE: `float \| None` DEFAULT: `None`
`null_mean`	Mean under the null hypothesis. This parameter must be used in conjuction with `mean` to compute the `diff`, where `diff` = `mean` - `null_mean`. TYPE: `float \| None` DEFAULT: `None`
`diff`	Mean difference between the alternative hypothesis and the null hypothesis. If this parameter is specified, both `mean` and `null_mean` are ignored. TYPE: `float \| None` DEFAULT: `None`
`std`	Standard deviation. TYPE: `float`
`alternative`	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 \(\mu < \mu_0\) TYPE: `Literal['two-sided', 'greater', 'less']` DEFAULT: `'two-sided'`
`alpha`	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. TYPE: `float` DEFAULT: `0.05`
`power`	Expected statistical power. 0.8 is a commonly used value for statistical power. TYPE: `float` DEFAULT: `0.8`
`dist`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution. TYPE: `Literal['z', 't']` DEFAULT: `'t'`

RETURNS	DESCRIPTION
`int`	The required sample size.

RAISES	DESCRIPTION
`ValueError`	The given set of parameters is insufficient to determine the mean difference.

solve_mean ¶

solve_mean(
    *,
    null_mean: float,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"] = "two-sided",
    alpha: float = 0.05,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
    direction: Literal["greater", "less"] | None = None,
) -> float

Estimate the required mean under the alternative hypothesis.

PARAMETER	DESCRIPTION
`null_mean`	Mean under the null hypothesis. TYPE: `float`
`std`	Standard deviation. TYPE: `float`
`size`	Sample size. TYPE: `int`
`alternative`	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 \(\mu < \mu_0\) TYPE: `Literal['two-sided', 'greater', 'less']` DEFAULT: `'two-sided'`
`alpha`	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. TYPE: `float` DEFAULT: `0.05`
`power`	Expected statistical power. 0.8 is a commonly used value for statistical power. TYPE: `float` DEFAULT: `0.8`
`dist`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution. TYPE: `Literal['z', 't']` DEFAULT: `'t'`
`direction`	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. TYPE: `Literal['greater', 'less'] \| None` DEFAULT: `None`

RETURNS	DESCRIPTION
`float`	The required mean under the alternative hypothesis.

RAISES	DESCRIPTION
`ValueError`	If `alternative` is `'two-sided'` and `direction` is omitted.

solve_null_mean ¶

solve_null_mean(
    *,
    mean: float,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"] = "two-sided",
    alpha: float = 0.05,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
    direction: Literal["greater", "less"] | None = None,
) -> float

Estimate the required mean under the null hypothesis.

PARAMETER	DESCRIPTION
`mean`	Mean under the alternative hypothesis. TYPE: `float`
`std`	Standard deviation. TYPE: `float`
`size`	Sample size. TYPE: `int`
`alternative`	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 \(\mu < \mu_0\) TYPE: `Literal['two-sided', 'greater', 'less']` DEFAULT: `'two-sided'`
`alpha`	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. TYPE: `float` DEFAULT: `0.05`
`power`	Expected statistical power. 0.8 is a commonly used value for statistical power. TYPE: `float` DEFAULT: `0.8`
`dist`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution. TYPE: `Literal['z', 't']` DEFAULT: `'t'`
`direction`	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. TYPE: `Literal['greater', 'less'] \| None` DEFAULT: `None`

RETURNS	DESCRIPTION
`float`	The required mean under the null hypothesis.

RAISES	DESCRIPTION
`ValueError`	If `alternative` is `'two-sided'` and `direction` is omitted.

solve_diff ¶

solve_diff(
    *,
    std: float,
    size: int,
    alternative: Literal["two-sided", "greater", "less"] = "two-sided",
    alpha: float = 0.05,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
    direction: Literal["greater", "less"] | None = None,
) -> float

Estimate the required mean difference.

PARAMETER	DESCRIPTION
`std`	Standard deviation. TYPE: `float`
`size`	Sample size. TYPE: `int`
`alternative`	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 \(\mu < \mu_0\) TYPE: `Literal['two-sided', 'greater', 'less']` DEFAULT: `'two-sided'`
`alpha`	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. TYPE: `float` DEFAULT: `0.05`
`power`	Expected statistical power. 0.8 is a commonly used value for statistical power. TYPE: `float` DEFAULT: `0.8`
`dist`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution. TYPE: `Literal['z', 't']` DEFAULT: `'t'`
`direction`	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. TYPE: `Literal['greater', 'less'] \| None` DEFAULT: `None`

RETURNS	DESCRIPTION
`float`	The required mean difference between the alternative hypothesis and the null hypothesis.

RAISES	DESCRIPTION
`ValueError`	If `alternative` is `'two-sided'` and `direction` is omitted.

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"] = "two-sided",
    alpha: float = 0.05,
    power: float = 0.8,
    dist: Literal["z", "t"] = "t",
) -> float

Estimate the required standard deviation.

PARAMETER	DESCRIPTION
`mean`	Mean under the alternative hypothesis. This parameter must be used in conjuction with `null_mean` to compute the `diff`, where `diff` = `mean` - `null_mean`. TYPE: `float \| None` DEFAULT: `None`
`null_mean`	Mean under the null hypothesis. This parameter must be used in conjuction with `mean` to compute the `diff`, where `diff` = `mean` - `null_mean`. TYPE: `float \| None` DEFAULT: `None`
`diff`	Mean difference between the alternative hypothesis and the null hypothesis. If this parameter is specified, both `mean` and `null_mean` are ignored. TYPE: `float \| None` DEFAULT: `None`
`size`	Sample size. TYPE: `int`
`alternative`	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 \(\mu < \mu_0\) TYPE: `Literal['two-sided', 'greater', 'less']` DEFAULT: `'two-sided'`
`alpha`	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. TYPE: `float` DEFAULT: `0.05`
`power`	Expected statistical power. 0.8 is a commonly used value for statistical power. TYPE: `float` DEFAULT: `0.8`
`dist`	The distribution used for the test. `'z'`: Normal distribution. `'t'`: Student's t distribution. TYPE: `Literal['z', 't']` DEFAULT: `'t'`

RETURNS	DESCRIPTION
`float`	The required standard deviation.

RAISES	DESCRIPTION
`ValueError`	The given set of parameters is insufficient to determine the mean difference.