pystatpower.models.proportion.independent.ci ¶

Functions:

Name	Description
`solve_distance`	Calculate the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between two independent proportions.
`solve_size`	Estimate the required sample size, given either the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between two independent proportions.
`solve_treatment_proportion`	Estimate the required proportion in the treatment group (\(p_1\)), given either the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between two independent proportions.
`solve_reference_proportion`	Estimate the required proportion in the reference group (\(p_2\)), given either the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between two independent proportions.

solve_distance ¶

solve_distance(
    *,
    treatment_proportion: float,
    reference_proportion: float,
    treatment_size: int,
    reference_size: int,
    conf_level: float = 0.95,
    interval_type: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ] = "two-sided",
    method: Literal[
        "chisq",
        "chisq_cc",
        "newcombe_wilson",
        "newcombe_wilson_cc",
        "farrington_manning",
        "miettinen_nurminen",
    ] = "chisq",
) -> float

Calculate the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between 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
`treatment_size`	`int`	Sample size in the treatment group (\(n_1\)). Must be greater than 0.	required
`reference_size`	`int`	Sample size in the reference group (\(n_2\)). Must be greater than 0.	required
`conf_level`	`float`	Confidence level.	`0.95`
`interval_type`	`Literal['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the confidence interval. `'two-sided'`: Two-sided confidence interval. `'lower one-sided'`: Lower one-sided confidence interval. `'upper one-sided'`: Upper one-sided confidence interval.	`'two-sided'`
`method`	`Literal['chisq', 'chisq_cc', 'newcombe_wilson', 'newcombe_wilson_cc', 'farrington_manning', 'miettinen_nurminen']`	Method to calculate the confidence interval. `'chisq'`: Pearson's chi-square method. `'chisq_cc'`: Yate's chi-square with continuity correction method. `'newcombe_wilson'`: Newcombe-Wilson method. `'newcombe_wilson_cc'`: Newcombe-Wilson with continuity correction method. `'farrington_manning'`: Farrington and Manning's score method. `'miettinen_nurminen'`: Miettinen and Nurminen's score method.	`'chisq'`

Returns:

Type	Description
`float`	The confidence interval width or the distance from the proportion difference to the confidence bound.

solve_size ¶

solve_size(
    *,
    treatment_proportion: float,
    reference_proportion: float,
    distance: float,
    ratio: float = 1,
    conf_level: float = 0.95,
    interval_type: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ] = "two-sided",
    method: Literal[
        "chisq",
        "chisq_cc",
        "newcombe_wilson",
        "newcombe_wilson_cc",
        "farrington_manning",
        "miettinen_nurminen",
    ] = "chisq",
) -> tuple[int, int]

Estimate the required sample size, given either the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between 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
`distance`	`float`	Confidence interval width or the distance from the proportion difference to the confidence bound. If `interval_type='two-sided'`, provide confidence interval width. If `interval_type='lower one-sided'`, provide the distance from the proportion difference to the lower one-side confidence bound. If `interval_type='upper one-sided'`, provide the distance from the proportion difference to the upper one-side confidence bound.	required
`ratio`	`float`	Ratio of the sample size in the treatment group to the sample size in the reference group (\(k = n_1 / n_2\)).	`1`
`conf_level`	`float`	Confidence level.	`0.95`
`interval_type`	`Literal['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the confidence interval. `'two-sided'`: Two-sided confidence interval. `'lower one-sided'`: Lower one-sided confidence interval. `'upper one-sided'`: Upper one-sided confidence interval.	`'two-sided'`
`method`	`Literal['chisq', 'chisq_cc', 'newcombe_wilson', 'newcombe_wilson_cc', 'farrington_manning', 'miettinen_nurminen']`	Method to calculate the confidence interval. `'chisq'`: Pearson's chi-square method. `'chisq_cc'`: Yate's chi-square with continuity correction method. `'newcombe_wilson'`: Newcombe-Wilson method. `'newcombe_wilson_cc'`: Newcombe-Wilson with continuity correction method. `'farrington_manning'`: Farrington and Manning's score method. `'miettinen_nurminen'`: Miettinen and Nurminen's score method.	`'chisq'`

Returns:

Type	Description
`tuple[int, int]`	The required sample size.

solve_treatment_proportion ¶

solve_treatment_proportion(
    *,
    reference_proportion: float,
    treatment_size: int,
    reference_size: int,
    distance: float,
    conf_level: float = 0.95,
    interval_type: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ] = "two-sided",
    method: Literal[
        "chisq",
        "chisq_cc",
        "newcombe_wilson",
        "newcombe_wilson_cc",
        "farrington_manning",
        "miettinen_nurminen",
    ] = "chisq",
) -> float | tuple[float, float]

Estimate the required proportion in the treatment group (\(p_1\)), given either the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between two independent proportions.

Parameters:

Name	Type	Description	Default
`reference_proportion`	`float`	Actual proportion in the reference group (\(p_2\)). Must be between 0 and 1.	required
`treatment_size`	`int`	Sample size in the treatment group (\(n_1\)). Must be greater than 0.	required
`reference_size`	`int`	Sample size in the reference group (\(n_2\)). Must be greater than 0.	required
`distance`	`float`	Confidence interval width or the distance from the proportion difference to the confidence bound. If `interval_type='two-sided'`, provide confidence interval width. If `interval_type='lower one-sided'`, provide the distance from the proportion difference to the lower one-side confidence bound. If `interval_type='upper one-sided'`, provide the distance from the proportion difference to the upper one-side confidence bound.	required
`conf_level`	`float`	Confidence level.	`0.95`
`interval_type`	`Literal['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the confidence interval. `'two-sided'`: Two-sided confidence interval. `'lower one-sided'`: Lower one-sided confidence interval. `'upper one-sided'`: Upper one-sided confidence interval.	`'two-sided'`
`method`	`Literal['chisq', 'chisq_cc', 'newcombe_wilson', 'newcombe_wilson_cc', 'farrington_manning', 'miettinen_nurminen']`	Method to calculate the confidence interval. `'chisq'`: Pearson's chi-square method. `'chisq_cc'`: Yate's chi-square with continuity correction method. `'newcombe_wilson'`: Newcombe-Wilson method. `'newcombe_wilson_cc'`: Newcombe-Wilson with continuity correction method. `'farrington_manning'`: Farrington and Manning's score method. `'miettinen_nurminen'`: Miettinen and Nurminen's score method.	`'chisq'`

Returns:

Type	Description
`float \| tuple[float, float]`	The required proportion in the treatment group (\(p_1\)), or a tuple of proportions if two solutions found.

solve_reference_proportion ¶

solve_reference_proportion(
    *,
    treatment_proportion: float,
    treatment_size: int,
    reference_size: int,
    distance: float,
    conf_level: float = 0.95,
    interval_type: Literal[
        "two-sided", "lower one-sided", "upper one-sided"
    ] = "two-sided",
    method: Literal[
        "chisq",
        "chisq_cc",
        "newcombe_wilson",
        "newcombe_wilson_cc",
        "farrington_manning",
        "miettinen_nurminen",
    ] = "chisq",
) -> float | tuple[float, float]

Estimate the required proportion in the reference group (\(p_2\)), given either the confidence interval width or the distance from the proportion difference to the confidence bound for the difference between 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
`treatment_size`	`int`	Sample size in the treatment group (\(n_1\)). Must be greater than 0.	required
`reference_size`	`int`	Sample size in the reference group (\(n_2\)). Must be greater than 0.	required
`distance`	`float`	Confidence interval width or the distance from the proportion difference to the confidence bound. If `interval_type='two-sided'`, provide confidence interval width. If `interval_type='lower one-sided'`, provide the distance from the proportion difference to the lower one-side confidence bound. If `interval_type='upper one-sided'`, provide the distance from the proportion difference to the upper one-side confidence bound.	required
`conf_level`	`float`	Confidence level.	`0.95`
`interval_type`	`Literal['two-sided', 'lower one-sided', 'upper one-sided']`	Type of the confidence interval. `'two-sided'`: Two-sided confidence interval. `'lower one-sided'`: Lower one-sided confidence interval. `'upper one-sided'`: Upper one-sided confidence interval.	`'two-sided'`
`method`	`Literal['chisq', 'chisq_cc', 'newcombe_wilson', 'newcombe_wilson_cc', 'farrington_manning', 'miettinen_nurminen']`	Method to calculate the confidence interval. `'chisq'`: Pearson's chi-square method. `'chisq_cc'`: Yate's chi-square with continuity correction method. `'newcombe_wilson'`: Newcombe-Wilson method. `'newcombe_wilson_cc'`: Newcombe-Wilson with continuity correction method. `'farrington_manning'`: Farrington and Manning's score method. `'miettinen_nurminen'`: Miettinen and Nurminen's score method.	`'chisq'`

Returns:

Type	Description
`float \| tuple[float, float]`	The required proportion in the reference group (\(p_2\)), or a tuple of proportions if two solutions found.