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# Copyright 2017-2020 Spotify AB 

# 

# Licensed under the Apache License, Version 2.0 (the "License"); 

# you may not use this file except in compliance with the License. 

# You may obtain a copy of the License at 

# 

# http://www.apache.org/licenses/LICENSE-2.0 

# 

# Unless required by applicable law or agreed to in writing, software 

# distributed under the License is distributed on an "AS IS" BASIS, 

# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 

# See the License for the specific language governing permissions and 

# limitations under the License. 

 

from typing import (Union, Iterable, List, Tuple) 

from warnings import warn 

 

import numpy as np 

from pandas import DataFrame, Series, concat 

from statsmodels.stats.multitest import multipletests 

 

from spotify_confidence.analysis.abstract_base_classes.confidence_computer_abc import \ 

ConfidenceComputerABC 

from spotify_confidence.analysis.confidence_utils import (get_remaning_groups, validate_levels, 

level2str, listify, add_nim_columns, 

validate_and_rename_nims, 

validate_and_rename_column, 

add_mde_columns, 

get_all_categorical_group_columns, get_all_group_columns, 

validate_data, remove_group_columns) 

from spotify_confidence.analysis.constants import (POINT_ESTIMATE, VARIANCE, CI_LOWER, CI_UPPER, 

DIFFERENCE, P_VALUE, SFX1, SFX2, STD_ERR, ALPHA, 

ADJUSTED_ALPHA, POWER, POWERED_EFFECT, 

ADJUSTED_POWER, ADJUSTED_P, 

ADJUSTED_LOWER, ADJUSTED_UPPER, IS_SIGNIFICANT, 

REQUIRED_SAMPLE_SIZE, 

NULL_HYPOTHESIS, NIM, PREFERENCE, 

PREFERENCE_TEST, TWO_SIDED, 

PREFERENCE_DICT, BONFERRONI, HOLM, HOMMEL, 

SIMES_HOCHBERG, SIDAK, 

HOLM_SIDAK, FDR_BH, FDR_BY, FDR_TSBH, 

FDR_TSBKY, 

SPOT_1_HOLM, SPOT_1_HOMMEL, 

SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, 

SPOT_1_FDR_TSBKY, 

BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, 

SPOT_1, CORRECTION_METHODS, BOOTSTRAP, CHI2, 

TTEST, ZTEST, NIM_TYPE, 

CORRECTION_METHODS_THAT_REQUIRE_METRIC_INFO) 

from spotify_confidence.analysis.frequentist.confidence_computers.bootstrap_computer import BootstrapComputer 

from spotify_confidence.analysis.frequentist.confidence_computers.chi_squared_computer import ChiSquaredComputer 

from spotify_confidence.analysis.frequentist.confidence_computers.t_test_computer import TTestComputer 

from spotify_confidence.analysis.frequentist.confidence_computers.z_test_computer import ZTestComputer 

from spotify_confidence.analysis.frequentist.sequential_bound_solver import bounds 

 

 

def sequential_bounds(t: np.array, alpha: float, sides: int): 

return bounds(t, alpha, rho=2, ztrun=8, sides=sides, max_nints=1000) 

 

 

class GenericComputer(ConfidenceComputerABC): 

def __init__(self, data_frame: DataFrame, numerator_column: str, 

numerator_sum_squares_column: str, 

denominator_column: str, 

categorical_group_columns: Union[str, Iterable], 

ordinal_group_column: str, 

interval_size: float, 

correction_method: str, 

method_column: str, 

bootstrap_samples_column: str, 

metric_column: Union[str, None], 

treatment_column: Union[str, None], 

power: float): 

 

self._df = data_frame 

self._numerator = numerator_column 

self._numerator_sumsq = numerator_sum_squares_column 

if self._numerator is not None and (self._numerator_sumsq is None or self._numerator_sumsq == self._numerator): 

if (data_frame[numerator_column] <= 

data_frame[denominator_column]).all(): 

# Treat as binomial data 

self._numerator_sumsq = self._numerator 

else: 

raise ValueError( 

f'numerator_sum_squares_column missing or same as ' 

f'numerator_column, but since {numerator_column} is not ' 

f'always smaller than {denominator_column} it can\'t be ' 

f'binomial data. Please check your data.') 

 

self._denominator = denominator_column 

self._categorical_group_columns = get_all_categorical_group_columns( 

categorical_group_columns, metric_column, 

treatment_column) 

self._segments = remove_group_columns(self._categorical_group_columns, metric_column) 

self._segments = remove_group_columns(self._segments, treatment_column) 

self._ordinal_group_column = ordinal_group_column 

self._metric_column = metric_column 

self._interval_size = interval_size 

self._power = power 

self._treatment_column = treatment_column 

 

if correction_method.lower() not in CORRECTION_METHODS: 

raise ValueError(f'Use one of the correction methods ' + 

f'in {CORRECTION_METHODS}') 

self._correction_method = correction_method 

self._method_column = method_column 

 

self._single_metric = True 

if self._metric_column is not None: 

if data_frame.groupby(self._metric_column).ngroups == 1: 

self._categorical_group_columns = remove_group_columns(self._categorical_group_columns, self._metric_column) 

else: 

self._single_metric = False 

 

self._all_group_columns = get_all_group_columns( 

self._categorical_group_columns, self._ordinal_group_column) 

 

self._bootstrap_samples_column = bootstrap_samples_column 

 

columns_that_must_exist = [] 

if (CHI2 in self._df[self._method_column] or TTEST in self._df[self._method_column] 

or ZTEST in self._df[self._method_column]): 

columns_that_must_exist += [self._numerator, self._denominator] 

columns_that_must_exist += [] if self._numerator_sumsq is None else [self._numerator_sumsq] 

if BOOTSTRAP in self._df[self._method_column]: 

columns_that_must_exist += [self._bootstrap_samples_column] 

 

validate_data(self._df, columns_that_must_exist, self._all_group_columns, self._ordinal_group_column) 

 

self._sufficient = None 

self._computers = { 

CHI2: ChiSquaredComputer(self._numerator, self._numerator_sumsq, self._denominator, 

self._ordinal_group_column, self._interval_size), 

TTEST: TTestComputer(self._numerator, self._numerator_sumsq, self._denominator, 

self._ordinal_group_column, self._interval_size), 

ZTEST: ZTestComputer(self._numerator, self._numerator_sumsq, self._denominator, 

self._ordinal_group_column, self._interval_size), 

BOOTSTRAP: BootstrapComputer(self._bootstrap_samples_column, self._interval_size), 

} 

 

@property 

def _confidence_computers(self): 

return self._computers 

 

def compute_summary(self, verbose: bool) -> DataFrame: 

return ( 

self._sufficient_statistics if verbose else 

self._sufficient_statistics[ 

self._all_group_columns + [c for c in [self._numerator, self._denominator] if c is not None] 

+ [POINT_ESTIMATE, CI_LOWER, CI_UPPER] 

] 

) 

 

@property 

def _sufficient_statistics(self) -> DataFrame: 

if self._sufficient is None: 

self._sufficient = ( 

self._df 

.assign(**{POINT_ESTIMATE: self._point_estimate}) 

.assign(**{VARIANCE: self._variance}) 

.pipe(self._add_point_estimate_ci) 

) 

return self._sufficient 

 

def compute_difference(self, 

level_1: Union[str, Iterable], 

level_2: Union[str, Iterable], 

absolute: bool, 

groupby: Union[str, Iterable], 

nims: NIM_TYPE, 

mdes: bool, 

final_expected_sample_size_column: str, 

verbose: bool) -> DataFrame: 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

difference_df = self._compute_differences(level_columns, 

[(level_1, level_2)], 

absolute, 

groupby, 

level_as_reference=True, 

nims=nims, 

mdes=mdes, 

final_expected_sample_size_column=final_expected_sample_size_column) 

return (difference_df if verbose else 

difference_df[listify(groupby) + 

['level_1', 'level_2', 'absolute_difference', 

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P, IS_SIGNIFICANT, 

POWERED_EFFECT, REQUIRED_SAMPLE_SIZE] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])]) 

 

def compute_multiple_difference(self, 

level: Union[str, Iterable], 

absolute: bool, 

groupby: Union[str, Iterable], 

level_as_reference: bool, 

nims: NIM_TYPE, 

minimum_detectable_effect: bool, 

final_expected_sample_size_column: str, 

verbose: bool) -> DataFrame: 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

other_levels = [other for other in self._sufficient_statistics 

.groupby(level_columns).groups.keys() if other != level] 

levels = [(level, other) for other in other_levels] 

difference_df = self._compute_differences(level_columns, 

levels, 

absolute, 

groupby, 

level_as_reference, 

nims, 

minimum_detectable_effect, 

final_expected_sample_size_column) 

return (difference_df if verbose else 

difference_df[listify(groupby) + 

['level_1', 'level_2', 'absolute_difference', 

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE, POWERED_EFFECT, REQUIRED_SAMPLE_SIZE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P, IS_SIGNIFICANT] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])]) 

 

def compute_differences(self, 

levels: List[Tuple], 

absolute: bool, 

groupby: Union[str, Iterable], 

nims: NIM_TYPE, 

final_expected_sample_size_column: str, 

verbose: bool 

) -> DataFrame: 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

difference_df = self._compute_differences( 

level_columns, 

[levels] if type(levels) == tuple else levels, 

absolute, 

groupby, 

level_as_reference=True, 

nims=nims, 

final_expected_sample_size_column=final_expected_sample_size_column) 

return (difference_df if verbose else 

difference_df[listify(groupby) + 

['level_1', 'level_2', 'absolute_difference', 

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P, IS_SIGNIFICANT, 

POWERED_EFFECT, REQUIRED_SAMPLE_SIZE] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])]) 

 

def _compute_differences(self, 

level_columns: Iterable, 

levels: Union[str, Iterable], 

absolute: bool, 

groupby: Union[str, Iterable], 

level_as_reference: bool, 

nims: NIM_TYPE, 

mdes: bool, 

final_expected_sample_size_column: str): 

if type(level_as_reference) is not bool: 

raise ValueError( 

f'level_is_reference must be either True or False, but is {level_as_reference}.') 

groupby = listify(groupby) 

unique_levels = set([l[0] for l in levels] + [l[1] for l in levels]) 

validate_levels(self._sufficient_statistics, 

level_columns, 

unique_levels) 

str2level = {level2str(lv): lv for lv in unique_levels} 

filtered_sufficient_statistics = concat( 

[self._sufficient_statistics.groupby(level_columns).get_group(group) for group in 

unique_levels]) 

levels = [(level2str(l[0]), level2str(l[1])) 

if level_as_reference 

else (level2str(l[1]), level2str(l[0])) 

for l in levels] 

return ( 

self._sufficient_statistics 

.assign(level=self._sufficient_statistics[level_columns] 

.agg(level2str, axis='columns')) 

.pipe(lambda df: df if groupby == [] else df.set_index(groupby)) 

.pipe(self._create_comparison_df, 

groups_to_compare=levels, 

absolute=absolute, 

nims=nims, 

mdes=mdes, 

final_expected_sample_size_column=final_expected_sample_size_column, 

filtered_sufficient_statistics=filtered_sufficient_statistics) 

.assign(level_1=lambda df: 

df['level_1'].map(lambda s: str2level[s])) 

.assign(level_2=lambda df: 

df['level_2'].map(lambda s: str2level[s])) 

.reset_index() 

.sort_values(by=groupby + ['level_1', 'level_2']) 

) 

 

def _create_comparison_df(self, 

df: DataFrame, 

groups_to_compare: List[Tuple[str, str]], 

absolute: bool, 

nims: NIM_TYPE, 

mdes: bool, 

final_expected_sample_size_column: str, 

filtered_sufficient_statistics: DataFrame 

) -> DataFrame: 

 

def join(df: DataFrame) -> DataFrame: 

has_index = not all(idx is None for idx in df.index.names) 

if has_index: 

# self-join on index (the index will typically model the date, 

# i.e., rows with the same date are joined) 

return df.merge(df, 

left_index=True, 

right_index=True, 

suffixes=(SFX1, SFX2)) 

else: 

# join on dummy column, i.e. conduct a cross join 

return ( 

df.assign(dummy_join_column=1) 

.merge(right=df.assign(dummy_join_column=1), 

on='dummy_join_column', 

suffixes=(SFX1, SFX2)) 

.drop(columns='dummy_join_column') 

) 

 

comparison_df = ( 

df.pipe(add_nim_columns, nims=nims) 

.pipe(add_mde_columns, mdes=mdes) 

.pipe(join) 

.query(f'level_1 in {[l1 for l1, l2 in groups_to_compare]} and ' + 

f'level_2 in {[l2 for l1, l2 in groups_to_compare]}' + 

'and level_1 != level_2') 

.pipe(validate_and_rename_nims) 

.pipe(validate_and_rename_column, final_expected_sample_size_column) 

.pipe(validate_and_rename_column, self._method_column) 

.assign(**{DIFFERENCE: lambda df: df[POINT_ESTIMATE + SFX2] - 

df[POINT_ESTIMATE + SFX1]}) 

.assign(**{STD_ERR: self._std_err}) 

.pipe(self._add_p_value_and_ci, 

final_expected_sample_size_column=final_expected_sample_size_column, 

filtered_sufficient_statistics=filtered_sufficient_statistics) 

.pipe(self._adjust_if_absolute, absolute=absolute) 

.pipe(self._add_adjusted_power) 

.apply(self._powered_effect_and_required_sample_size, axis=1) 

.assign(**{PREFERENCE: lambda df: 

df[PREFERENCE].map(PREFERENCE_DICT)})) 

 

return comparison_df 

 

@staticmethod 

def _adjust_if_absolute(df: DataFrame, absolute: bool) -> DataFrame: 

if absolute: 

return df.assign(absolute_difference=absolute) 

else: 

return ( 

df.assign(absolute_difference=absolute) 

.assign(**{DIFFERENCE: 

df[DIFFERENCE] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{CI_LOWER: 

df[CI_LOWER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{CI_UPPER: 

df[CI_UPPER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{ADJUSTED_LOWER: 

df[ADJUSTED_LOWER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{ADJUSTED_UPPER: 

df[ADJUSTED_UPPER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{NULL_HYPOTHESIS: 

df[NULL_HYPOTHESIS] / df[POINT_ESTIMATE + SFX1]}) 

) 

 

def _std_err(self, df: DataFrame) -> Series: 

return np.sqrt(df[VARIANCE + SFX1] / df[self._denominator + SFX1] + 

df[VARIANCE + SFX2] / df[self._denominator + SFX2]) 

 

def _corrections_power(self, number_of_success_metrics: int, 

number_of_guardrail_metrics: int) -> int: 

return number_of_guardrail_metrics if number_of_success_metrics == 0 else \ 

number_of_guardrail_metrics + 1 

 

def _add_adjusted_power(self, df: DataFrame) -> DataFrame: 

 

if self._correction_method in CORRECTION_METHODS_THAT_REQUIRE_METRIC_INFO: 

if self._metric_column is None or self._treatment_column is None: 

return df.assign(**{ADJUSTED_POWER: None}) 

else: 

self._number_total_metrics = 1 if self._single_metric else df.groupby( self._metric_column).ngroups 

if self._single_metric: 

if df[df[NIM].isnull()].shape[0] > 0: 

self._number_success_metrics = 1 

else: 

self._number_success_metrics = 0 

else: 

self._number_success_metrics = df[df[NIM].isnull()].groupby( 

self._metric_column).ngroups 

 

self._number_guardrail_metrics = self._number_total_metrics - \ 

self._number_success_metrics 

power_correction = self._corrections_power( 

number_of_guardrail_metrics=self._number_guardrail_metrics, 

number_of_success_metrics=self._number_success_metrics) 

return df.assign(**{ADJUSTED_POWER: 1 - (1 - df[POWER]) / power_correction}) 

else: 

return df.assign(**{ADJUSTED_POWER:df[POWER]}) 

 

def _add_p_value_and_ci(self, 

df: DataFrame, 

final_expected_sample_size_column: str, 

filtered_sufficient_statistics: DataFrame) -> DataFrame: 

 

def set_alpha_and_adjust_preference(df: DataFrame) -> DataFrame: 

alpha_0 = 1 - self._interval_size 

return ( 

df.assign( 

**{ALPHA: df.apply(lambda row: 2 * alpha_0 if self._correction_method == SPOT_1 

and row[PREFERENCE] != TWO_SIDED 

else alpha_0, axis=1)}) 

.assign(**{POWER: self._power}) 

.assign(**{PREFERENCE_TEST: df.apply( 

lambda row: TWO_SIDED if self._correction_method == SPOT_1 

else row[PREFERENCE], axis=1)}) 

) 

 

def _add_adjusted_p_and_is_significant(df: DataFrame) -> DataFrame: 

if (final_expected_sample_size_column is not None): 

if self._correction_method not in [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, 

SPOT_1]: 

raise ValueError( 

f"{self._correction_method} not supported for sequential tests. Use one of" 

f"{BONFERRONI}, {BONFERRONI_ONLY_COUNT_TWOSIDED}, " 

f"{BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY}, {SPOT_1}") 

 

groups_except_ordinal = [ 

column for column in df.index.names if column != self._ordinal_group_column] 

n_comparisons = self._get_num_comparisons(df, self._correction_method, 

['level_1', 'level_2'] + groups_except_ordinal) 

 

df[ADJUSTED_ALPHA] = self._compute_sequential_adjusted_alpha(df, 

final_expected_sample_size_column, 

filtered_sufficient_statistics, 

n_comparisons) 

df[IS_SIGNIFICANT] = df[P_VALUE] < df[ADJUSTED_ALPHA] 

df[P_VALUE] = None 

df[ADJUSTED_P] = None 

elif self._correction_method in [HOLM, HOMMEL, SIMES_HOCHBERG, 

SIDAK, HOLM_SIDAK, FDR_BH, FDR_BY, FDR_TSBH, 

FDR_TSBKY, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY]: 

if self._correction_method.startswith('spot-'): 

correction_method = self._correction_method[7:] 

else: 

correction_method = self._correction_method 

 

groupby = ['level_1', 'level_2'] + [column for column in df.index.names if 

column is not None] 

df[ADJUSTED_ALPHA] = df[ALPHA] / self._get_num_comparisons(df, 

self._correction_method, 

groupby) 

is_significant, adjusted_p, _, _ = multipletests(pvals=df[P_VALUE], 

alpha=1 - self._interval_size, 

method=correction_method) 

df[ADJUSTED_P] = adjusted_p 

df[IS_SIGNIFICANT] = is_significant 

elif self._correction_method in [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1]: 

groupby = ['level_1', 'level_2'] + [column for column in df.index.names if 

column is not None] 

n_comparisons = self._get_num_comparisons(df, self._correction_method, groupby) 

df[ADJUSTED_ALPHA] = df[ALPHA] / n_comparisons / (1 + (df[PREFERENCE_TEST] == 'two-sided').astype(int)) 

df[ADJUSTED_P] = df.apply( 

lambda row: min(row[P_VALUE] * n_comparisons * (1 + (row[PREFERENCE_TEST] == 'two-sided')), 1), 

axis=1) 

# df[ADJUSTED_P] = df[P_VALUE].map(lambda p: min(p * n_comparisons , 1)) 

df[IS_SIGNIFICANT] = df[P_VALUE] < df[ADJUSTED_ALPHA] 

else: 

raise ValueError("Can't figure out which correction method to use :(") 

 

return df 

 

def _add_ci(df: DataFrame) -> DataFrame: 

ci = df.apply(self._ci, axis=1, alpha_column=ALPHA) 

ci_df = DataFrame(index=ci.index, 

columns=[CI_LOWER, CI_UPPER], 

data=list(ci.values)) 

 

if self._correction_method in [HOLM, HOMMEL, SIMES_HOCHBERG, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG] \ 

and all(df[PREFERENCE_TEST] != TWO_SIDED): 

adjusted_ci = self._ci_for_multiple_comparison_methods( 

df, 

correction_method=self._correction_method, 

alpha=1 - self._interval_size, 

) 

elif self._correction_method in [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY]: 

adjusted_ci = df.apply(self._ci, axis=1, alpha_column=ADJUSTED_ALPHA) 

else: 

warn(f"Confidence intervals not supported for {self._correction_method}") 

adjusted_ci = Series(index=df.index, data=[(None, None) for i in range(len(df))]) 

 

adjusted_ci_df = DataFrame(index=adjusted_ci.index, 

columns=[ADJUSTED_LOWER, ADJUSTED_UPPER], 

data=list(adjusted_ci.values)) 

 

return ( 

df.assign(**{CI_LOWER: ci_df[CI_LOWER]}) 

.assign(**{CI_UPPER: ci_df[CI_UPPER]}) 

.assign(**{ADJUSTED_LOWER: adjusted_ci_df[ADJUSTED_LOWER]}) 

.assign(**{ADJUSTED_UPPER: adjusted_ci_df[ADJUSTED_UPPER]}) 

) 

 

return ( 

df.pipe(set_alpha_and_adjust_preference) 

.assign(**{P_VALUE: lambda df: df.apply(self._p_value, axis=1)}) 

.pipe(_add_adjusted_p_and_is_significant) 

.pipe(_add_ci) 

) 

 

def _get_num_comparisons(self, df: DataFrame, correction_method: str, 

groupby: Iterable) -> int: 

if correction_method == BONFERRONI: 

return max(1, df.groupby(groupby).ngroups) 

elif correction_method == BONFERRONI_ONLY_COUNT_TWOSIDED: 

return max(df.query(f'{PREFERENCE_TEST} == "{TWO_SIDED}"').groupby(groupby).ngroups, 1) 

elif correction_method in [HOLM, HOMMEL, SIMES_HOCHBERG, 

SIDAK, HOLM_SIDAK, FDR_BH, FDR_BY, FDR_TSBH, FDR_TSBKY]: 

return 1 

elif correction_method in [BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY]: 

if self._metric_column is None or self._treatment_column is None: 

return max(1, df[df[NIM].isnull()].groupby(groupby).ngroups) 

else: 

if self._single_metric: 

if df[df[NIM].isnull()].shape[0] > 0: 

self._number_success_metrics = 1 

else: 

self._number_success_metrics = 0 

else: 

self._number_success_metrics = df[df[NIM].isnull()].groupby( 

self._metric_column).ngroups 

 

number_comparions = len((df[self._treatment_column + SFX1] + df[self._treatment_column + SFX2]).unique()) 

number_segments = (1 if len(self._segments) is 0 or not all(item in df.index.names for item in self._segments) else df.groupby(self._segments).ngroups) 

 

return max(1, number_comparions * max(1, self._number_success_metrics) * number_segments) 

else: 

raise ValueError(f"Unsupported correction method: {correction_method}.") 

 

def achieved_power(self, level_1, level_2, mde, alpha, groupby): 

"""Calculated the achieved power of test of differences between 

level 1 and level 2 given a targeted MDE. 

 

Args: 

level_1 (str, tuple of str): Name of first level. 

level_2 (str, tuple of str): Name of second level. 

mde (float): Absolute minimal detectable effect size. 

alpha (float): Type I error rate, cutoff value for determining 

statistical significance. 

groupby (str): Name of column. 

If specified, will return the difference for each level 

of the grouped dimension. 

 

Returns: 

Pandas DataFrame with the following columns: 

- level_1: Name of level 1. 

- level_2: Name of level 2. 

- power: 1 - B, where B is the likelihood of a Type II (false 

negative) error. 

 

""" 

groupby = listify(groupby) 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

return ( 

self._compute_differences(level_columns, 

[(level_1, level_2)], 

True, 

groupby, 

level_as_reference=True, 

nims=None, # TODO: IS this right? 

final_expected_sample_size_column=None) # TODO: IS this 

# right? 

.pipe(lambda df: df if groupby == [] else df.set_index(groupby)) 

.assign(achieved_power=lambda df: df.apply(self._achieved_power, mde=mde, alpha=alpha, axis=1)) 

)[['level_1', 'level_2', 'achieved_power']] 

 

def _point_estimate(self, df: DataFrame) -> Series: 

return df.apply(lambda row: self._confidence_computers[row[self._method_column]]._point_estimate(row), axis=1) 

 

def _variance(self, df: DataFrame) -> Series: 

return df.apply(lambda row: self._confidence_computers[row[self._method_column]]._variance(row), axis=1) 

 

def _std_err(self, df: DataFrame) -> Series: 

return df.apply(lambda row: self._confidence_computers[row[self._method_column]]._std_err(row), axis=1) 

 

def _add_point_estimate_ci(self, df: DataFrame) -> DataFrame: 

return df.apply(lambda row: self._confidence_computers[row[self._method_column]]._add_point_estimate_ci(row), 

axis=1) 

 

def _p_value(self, row) -> float: 

return self._confidence_computers[row[self._method_column]]._p_value(row) 

 

def _ci(self, row, alpha_column: str) -> Tuple[float, float]: 

return self._confidence_computers[row[self._method_column]]._ci(row, alpha_column=alpha_column) 

 

def _powered_effect_and_required_sample_size(self, row ) -> DataFrame: 

if row[ADJUSTED_POWER] is None: 

row['powered_effect'] = None 

row['required_sample_size'] = None 

return row 

else: 

return self._confidence_computers[row[self._method_column]]._powered_effect_and_required_sample_size(row) 

 

def _achieved_power(self, 

row: Series, 

mde: float, 

alpha: float) -> DataFrame: 

return self._confidence_computers[row[self._method_column]]._achieved_power(row, mde, alpha) 

 

def _compute_sequential_adjusted_alpha(self, 

df: DataFrame, 

final_expected_sample_size_column: str, 

filtered_sufficient_statistics: DataFrame, 

n_comparisons: int) -> Series: 

if all(df[self._method_column] == 'z-test'): 

return self._confidence_computers['z-test']._compute_sequential_adjusted_alpha( 

df, final_expected_sample_size_column, filtered_sufficient_statistics, n_comparisons) 

else: 

raise NotImplementedError("Sequential testing is only supported for z-tests") 

 

def _ci_for_multiple_comparison_methods( 

self, 

df: DataFrame, 

correction_method: str, 

alpha: float, 

w: float = 1.0, 

) -> Tuple[Union[Series, float], Union[Series, float]]: 

if all(df[self._method_column] == 'z-test'): 

return self._confidence_computers['z-test']._ci_for_multiple_comparison_methods( 

df, correction_method, alpha, w) 

else: 

raise NotImplementedError(f"{self._correction_method} is only supported for ZTests")