pystatpower.models.proportion.independent.inequality ¶

Functions:

Name	Description
`solve_power`	Calculate the statistical power for an inequality test of two independent proportions.
`solve_size`	Estimate the required sample size for an inequality test of two independent proportions.
`solve_treatment_proportion`	Estimate the required proportion in the treatment group for an inequality test of two independent proportions.
`solve_reference_proportion`	Estimate the required proportion in the reference group for an inequality test of two independent proportions.

solve_power ¶

solve_power(
    *,
    treatment_proportion: float,
    reference_proportion: float,
    treatment_size: int,
    reference_size: int,
    alternative: Literal["one-sided", "two-sided"],
    alpha: float = 0.05,
    pooled: bool = False,
    continuity_correction: bool = False,
) -> float

Calculate the statistical power for an inequality test of two independent proportions.

Parameters:

Name	Type	Description	Default
`treatment_proportion`	`float`	Actual proportion in the treatment group (\(p_1\)). Must be between 0 and 1.	required
`reference_proportion`	`float`	Actual proportion in the reference group (\(p_2\)). Must be between 0 and 1.	required
`alternative`	`Literal['one-sided', 'two-sided']`	Type of the alternative hypothesis. `'one-sided'`: Tests for a difference in one direction (uses \(\alpha\)). `'two-sided'`: Tests for any difference (uses \(\alpha/2\) per tail).	required
`treatment_size`	`int`	Sample size for the treatment group (\(n_1\)).	required
`reference_size`	`int`	Sample size for the reference group (\(n_2\)).	required
`alpha`	`float`	Significance level.	`0.05`
`pooled`	`bool`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction.	`False`

Returns:

Type	Description
`float`	Power of the test.

solve_size ¶

solve_size(
    *,
    treatment_proportion: float,
    reference_proportion: float,
    alternative: Literal["one-sided", "two-sided"],
    ratio: float = 1,
    alpha: float = 0.05,
    power: float = 0.8,
    pooled: bool = False,
    continuity_correction: bool = False,
) -> tuple[int, int]

Estimate the required sample size for an inequality test of two independent proportions.

Parameters:

Name	Type	Description	Default
`treatment_proportion`	`float`	Expected proportion in the treatment group (\(p_1\)). Must be between 0 and 1.	required
`reference_proportion`	`float`	Expected proportion in the reference group (\(p_2\)). Must be between 0 and 1.	required
`alternative`	`Literal['one-sided', 'two-sided']`	Type of the alternative hypothesis. `'one-sided'`: Tests for a difference in one direction (uses \(\alpha\)). `'two-sided'`: Tests for any difference (uses \(\alpha/2\) per tail).	required
`ratio`	`float`	Ratio of treatment sample size to reference sample size (\(k = n_1 / n_2\)).	`1`
`alpha`	`float`	Significance level.	`0.05`
`power`	`float`	Desired statistical power.	`0.8`
`pooled`	`bool`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction.	`False`

Returns:

Type	Description
`tuple[int, int]`	The required sample sizes for the treatment and reference groups, respectively.

solve_treatment_proportion ¶

solve_treatment_proportion(
    *,
    reference_proportion: float,
    treatment_size: int,
    reference_size: int,
    alternative: Literal["one-sided", "two-sided"],
    alpha: float = 0.05,
    power: float = 0.8,
    pooled: bool = False,
    continuity_correction: bool = False,
    search_direction: Literal["lower", "upper"] = "upper",
) -> float

Estimate the required proportion in the treatment group for an inequality test of two independent proportions.

Parameters:

Name	Type	Description	Default
`reference_proportion`	`float`	Expected proportion in the reference group (\(p_2\)). Must be between 0 and 1.	required
`treatment_size`	`int`	Sample size for the treatment group (\(n_1\)).	required
`reference_size`	`int`	Sample size for the reference group (\(n_2\)).	required
`alternative`	`Literal['one-sided', 'two-sided']`	Type of the alternative hypothesis. `'one-sided'`: Tests for a difference in one direction (uses \(\alpha\)). `'two-sided'`: Tests for any difference (uses \(\alpha/2\) per tail).	required
`alpha`	`float`	Significance level.	`0.05`
`power`	`float`	Desired statistical power.	`0.8`
`pooled`	`bool`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction.	`False`
`search_direction`	`Literal['lower', 'upper']`	Which solution to search for relative to \(p_2\). "lower": Finds \(p_1\) where \(p_1 < p_2\). "upper": Finds \(p_1\) where \(p_1 > p_2\).	`'upper'`

Returns:

Type	Description
`float`	The required proportion in the treatment group.

solve_reference_proportion ¶

solve_reference_proportion(
    *,
    treatment_proportion: float,
    treatment_size: int,
    reference_size: int,
    alternative: Literal["one-sided", "two-sided"],
    alpha: float = 0.05,
    power: float = 0.8,
    pooled: bool = False,
    continuity_correction: bool = False,
    search_direction: Literal["lower", "upper"] = "lower",
) -> float

Estimate the required proportion in the reference group for an inequality test of two independent proportions.

Parameters:

Name	Type	Description	Default
`treatment_proportion`	`float`	Expected proportion in the treatment group (\(p_1\)). Must be between 0 and 1.	required
`treatment_size`	`int`	Sample size for the treatment group (\(n_1\)).	required
`reference_size`	`int`	Sample size for the reference group (\(n_2\)).	required
`alternative`	`Literal['one-sided', 'two-sided']`	Type of the alternative hypothesis. `'one-sided'`: Tests for a difference in one direction (uses \(\alpha\)). `'two-sided'`: Tests for any difference (uses \(\alpha/2\) per tail).	required
`alpha`	`float`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis.	`0.05`
`power`	`float`	Desired statistical power.	`0.8`
`pooled`	`bool`	If True, use the pooled variance estimator.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction.	`False`
`search_direction`	`Literal['lower', 'upper']`	Which solution to search for relative to \(p_1\). "lower": Finds \(p_2\) where \(p_2 < p_1\). "upper": Finds \(p_2\) where \(p_2 > p_1\).	`'lower'`

Returns:

Type	Description
`float`	The required proportion in the reference group.