pystatpower.models.proportion.independent.inequality ¶

Functions:

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

solve_power ¶

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

Calculate the 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 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`	`float`	Sample size for the treatment group (\(n_1\)).	required
`reference_size`	`float`	Sample size for the reference group (\(n_2\)).	required
`alpha`	`float`	Significance level. Defaults to 0.05.	`0.05`
`pooled`	`bool`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis. Defaults to False.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction. Defaults to False.	`False`

Returns:

Name	Type	Description
`float`	`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 sample size required 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 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 (\(k = n_1 / n_2\)). Defaults to 1.	`1`
`alpha`	`float`	Significance level. Defaults to 0.05.	`0.05`
`power`	`float`	Desired statistical power. Defaults to 0.80.	`0.8`
`pooled`	`bool`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis. Defaults to False.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction. Defaults to False.	`False`

Returns:

Type	Description
`tuple[int, int]`	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: float, reference_size: float, 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 proportion required 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`	`float`	Sample size for the treatment group (\(n_1\)).	required
`reference_size`	`float`	Sample size for the reference group (\(n_2\)).	required
`alternative`	`Literal['one-sided', 'two-sided']`	Type of 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. Defaults to 0.05.	`0.05`
`power`	`float`	Desired statistical power. Defaults to 0.80.	`0.8`
`pooled`	`bool`	If True, use the pooled variance estimator (\(\bar{p}\)) under the null hypothesis. Defaults to False.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction. Defaults to False.	`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 \(p_1 > p_2\). Defaults to "upper".	`'upper'`

Returns:

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

solve_reference_proportion ¶

solve_reference_proportion(treatment_proportion: float, treatment_size: float, reference_size: float, 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 proportion required 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`	`float`	Sample size for the treatment group (\(n_1\)).	required
`reference_size`	`float`	Sample size for the reference group (\(n_2\)).	required
`alternative`	`Literal['one-sided', 'two-sided']`	Type of 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. Defaults to False.	`0.05`
`power`	`float`	Desired statistical power. Defaults to 0.80.	`0.8`
`pooled`	`bool`	If True, use the pooled variance estimator. Defaults to False.	`False`
`continuity_correction`	`bool`	If True, applies Yates' continuity correction. Defaults to False.	`False`
`search_direction`	`Literal['lower', 'upper']`	Which solution to search for relative to \(p_1\). "lower": Finds \(p_2\) where \(p_2 < p_1\). Defaults to "lower". "upper": Finds \(p_2\) where \(p_2 > p_1\).	`'lower'`

Returns:

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