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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 ipywidgets import widgets 

from IPython.display import display 

import scipy.stats as st 

import numpy as np 

import math 

 

 

class SampleSize(object): 

"""Frequentist sample size calculations. 

 

See: Duflo, E., Glennerster, R., & Kremer, M. (2007). Using 

randomization in development economics research: A toolkit. 

Handbook of Development Economics, 4, 3895–3962. pp28-31. 

 

Methods 

------- 

binomial() 

Calculate the required sample size for a binomial metric. 

binomial_interactive() 

Interactive version of the binomial() function for notebook use. 

continuous() 

Calculate the required sample size for a continuous metric. 

continuous_interactive() 

Interactive version of the continuous() function for notebook use. 

achieved_power() 

TODO: Calculate achieved power given reached sample size. 

 

""" 

default_alpha = 0.05 

default_power = 0.85 

default_treatments = 2 

default_comparisons = 'control_vs_all' 

default_treatment_costs = None 

default_treatment_allocations = None 

default_bonferroni = False 

 

@staticmethod 

def continuous(average_absolute_mde, 

baseline_variance, 

alpha=default_alpha, 

power=default_power, 

treatments=default_treatments, 

comparisons=default_comparisons, 

treatment_costs=default_treatment_costs, 

treatment_allocations=default_treatment_allocations, 

bonferroni_correction=default_bonferroni): 

"""Calculate the required sample size for a binomial metric. 

 

Args: 

average_absolute_mde (float): Average absolute minimal detectable 

effect size (mean difference) across all tests. 

baseline_variance (float): Baseline metric variance in 

target population. 

alpha (float, optional): Probability of Type I error 

(false positive). Defaults to 0.05. 

power (float, optional): 1 - B, where B is the probability of 

Type II error (false negative). Defaults to 0.85. 

treatments (int, optional): Number of treatment variants 

in the a/b test, including control. Defaults to 2. 

comparisons ({'control_vs_all', 'all_vs_all'}, optional): Which 

treatments to compare. Defaults to 'control_vs_all'. 

treatment_costs (numpy.ndarray, optional): Array with same length 

as the number of treatments containing positive floats 

specifying the treatments' relative costs. Defaults to equal 

cost for all treatments. 

treatment_allocations (numpy.ndarray, optional): Array with same 

length as the number of treatments containing proportion of 

sample allocated to each treatment. If not specified defaults 

to automatic allocation. 

bonferroni_correction (bool): Whether Bonferroni correction should 

be applied to control the false positive rate across all 

comparisons. Defaults to false. 

 

Returns: 

int: Total required sample size across all treatments. 

list of int: Required sample size for each treatment. 

list of float: Proportion of total sample allocated 

to each treatment. 

 

Raises: 

ValueError: If `power` is less than or equal to`alpha`. 

 

""" 

mde = SampleSize._clean_continuous_mde(average_absolute_mde) 

baseline_variance = SampleSize._validate_positive(baseline_variance) 

 

return SampleSize._calculate_samplesize(mde, 

baseline_variance, 

alpha, 

power, 

treatments, 

comparisons, 

treatment_costs, 

treatment_allocations, 

bonferroni_correction) 

 

@staticmethod 

def continuous_interactive(): 

SampleSize._calculate_sample_size_interactive('continuous') 

 

@staticmethod 

def binomial(absolute_percentage_mde, 

baseline_proportion, 

alpha=default_alpha, 

power=default_power, 

treatments=default_treatments, 

comparisons=default_comparisons, 

treatment_costs=default_treatment_costs, 

treatment_allocations=default_treatment_allocations, 

bonferroni_correction=default_bonferroni): 

"""Calculate the required sample size for a binomial metric. 

 

Args: 

absolute_percentage_mde (float): Average absolute minimal 

detectable effect size across all tests. 

baseline_proportion (float): Baseline metric proportion in 

target population. 

alpha (float, optional): Probability of Type I error 

(false positive). Defaults to 0.05. 

power (float, optional): 1 - B, where B is the probability of 

Type II error (false negative). Defaults to 0.85. 

treatments (int, optional): Number of treatment variants 

in the a/b test, including control. Defaults to 2. 

comparisons ({'control_vs_all', 'all_vs_all'}, optional): Which 

treatments to compare. Defaults to 'control_vs_all'. 

treatment_costs (numpy.ndarray, optional): Array with same length 

as the number of treatments containing positive floats 

specifying the treatments' relative costs. Defaults to equal 

cost for all treatments. 

treatment_allocations (numpy.ndarray, optional): Array with same 

length as the number of treatments containing proportion of 

sample allocated to each treatment. If not specified defaults 

to automatic allocation. 

bonferroni_correction (bool): Whether Bonferroni correction should 

be applied to control the false positive rate across all 

comparisons. Defaults to false. 

 

Returns: 

int: Total required sample size across all treatments. 

list of int: Required sample size for each treatment. 

list of float: Proportion of total sample allocated 

to each treatment. 

 

Raises: 

ValueError: If `power` is less than or equal to`alpha`. 

ValueError: If `baseline_proportion` - `absolute_percentage_mde` 

< 0 and `baseline_proportion` + `absolute_percentage_mde` > 1. 

I.e. if the mde always implies a non-valid percentage. 

 

""" 

baseline = SampleSize._validate_percentage(baseline_proportion) 

mde = SampleSize._clean_binomial_mde(absolute_percentage_mde, baseline) 

baseline_variance = baseline * (1 - baseline) 

 

return SampleSize._calculate_samplesize(mde, 

baseline_variance, 

alpha, 

power, 

treatments, 

comparisons, 

treatment_costs, 

treatment_allocations, 

bonferroni_correction) 

 

@staticmethod 

def binomial_interactive(): 

SampleSize._calculate_sample_size_interactive('binomial') 

 

@staticmethod 

def _calculate_samplesize(mde, baseline_variance, alpha, power, treatments, 

comparisons, treatment_costs, 

treatment_allocations, bonferroni): 

power = SampleSize._validate_percentage(power) 

treatments = SampleSize._clean_treatments(treatments) 

comparisons = SampleSize._clean_comparisons(comparisons) 

treatment_costs = SampleSize._clean_treatment_costs(treatments, 

treatment_costs) 

 

alpha = SampleSize._get_alpha(alpha, power, bonferroni, 

treatments, comparisons) 

treatment_allocations = ( 

SampleSize._get_treatment_allocations(treatments, 

comparisons, 

treatment_costs, 

treatment_allocations)) 

 

num_comparisons = SampleSize._num_comparisons(treatments, comparisons) 

comparison_matrix = SampleSize._get_comparison_matrix(treatments, 

comparisons) 

 

z_alpha = st.norm.ppf(1 - alpha / 2) 

z_power = st.norm.ppf(power) 

 

a = np.power(1. / (num_comparisons * mde), 2) 

b = np.power(z_power + z_alpha, 2) 

c = baseline_variance 

d = 0 

for i in range(treatments): 

for j in range(treatments): 

if comparison_matrix[i, j] > 0: 

d += np.sqrt( 

1. / treatment_allocations[i] + 

1. / treatment_allocations[j]) 

d = np.power(d, 2) 

 

n_total = np.ceil(a * b * c * d).astype(int) 

n_allocation = np.ceil(treatment_allocations * n_total).astype(int) 

return n_total, n_allocation, treatment_allocations 

 

@staticmethod 

def _calculate_sample_size_interactive(metric): 

style = {'description_width': 'initial'} 

desc_layout = widgets.Layout(width='50%') 

if metric == 'continuous': 

mde_widget = widgets.FloatText( 

value=0.01, 

description='', 

) 

 

mde_desc = widgets.HTML(""" 

<small> 

This is the smallest absolute difference in averages that 

any of your comparisons can detect at the given statistical 

rigour. 

</small> 

""", layout=desc_layout) 

 

baseline_title = widgets.HTML("<strong>Baseline variance</strong>") 

baseline_widget = widgets.BoundedFloatText( 

value=1.0, 

min=0.00001, 

max=1000000000.0, 

description='', 

) 

baseline_desc = widgets.HTML(""" 

<small> 

This is the expected variance of the metric among 

users in your control group. 

</small> 

""", layout=desc_layout) 

 

elif metric == 'binomial': 

mde_widget = widgets.FloatLogSlider( 

value=0.003, 

base=10, 

min=-4, 

max=np.log10(0.5), 

step=0.001, 

description='', 

readout_format='.4f' 

) 

 

mde_desc = widgets.HTML(""" 

<small> 

This is the smallest absolute difference (percentage 

point / 100) that any of your comparisons can detect 

at the given statistical rigour. 

</small> 

""", layout=desc_layout) 

 

baseline_title = widgets.HTML("<strong>Baseline " 

"proportion</strong>") 

baseline_widget = widgets.FloatSlider( 

value=0.5, 

min=0.00001, 

max=0.99999, 

step=0.01, 

description='' 

) 

baseline_desc = widgets.HTML(""" 

<small> 

This is the expected value of the metric among 

users in your control group. 

</small> 

""", layout=desc_layout) 

 

else: 

raise ValueError('metric must be `continuous` or `binomial`') 

 

alpha_widget = widgets.FloatSlider( 

value=0.05, 

min=0.001, 

max=0.10, 

step=0.001, 

description=r'\(\alpha\)', 

readout_format='.3f') 

 

power_widget = widgets.FloatSlider( 

value=0.85, 

min=0.8, 

max=0.99, 

step=0.01, 

description=r'Power, \( 1-\beta\)') 

 

treatments_widget = widgets.IntSlider( 

value=2, 

min=2, 

max=20, 

step=1, 

description='Groups (including control)', 

style=style) 

 

comparisons_widget = widgets.RadioButtons( 

options=['Control vs. All', 'All vs. All'], 

value='Control vs. All', 

description='Groups to compare', 

style=style) 

 

control_group_widget = widgets.FloatLogSlider( 

value=1, 

step=0.1, 

base=10, 

min=0, 

max=4, 

description='Control group advantage', 

readout=False, 

style=style, 

) 

control_group_description = widgets.HTML(""" 

<small> 

Sometime we want the control group to be bigger than what is 

strictly optimal. This can be either because we can collect 

samples quickly enough anyway or because we believe the 

treatment variants are riskier. Boosting the size of the 

control group comes at the cost of an increased total 

required sample. 

</small> 

""", layout=desc_layout) 

 

bonferroni_widget = widgets.Checkbox( 

value=False, 

description='Apply Bonferroni correction') 

 

risk_reset_btn = widgets.Button( 

description=' ', 

disabled=False, 

button_style='', 

tooltip='Reset variant risk', 

icon='repeat', 

layout=widgets.Layout(width="40px") 

) 

 

def reset_widget(b): 

control_group_widget.value = 1 

risk_reset_btn.on_click(reset_widget) 

 

ui = widgets.VBox([ 

widgets.HTML('<h4>Target metric</h4>'), 

widgets.VBox( 

children=[ 

widgets.HTML("<strong>Minimal Detectable Effect " 

"size</strong>"), 

mde_widget, 

mde_desc], 

), 

widgets.VBox( 

children=[ 

baseline_title, 

baseline_widget, 

baseline_desc], 

), 

widgets.HTML('<h4>Statistical rigour</h4>'), 

alpha_widget, 

power_widget, 

bonferroni_widget, 

widgets.HTML('<h4>Treatment groups</h4>'), 

treatments_widget, 

comparisons_widget, 

widgets.VBox( 

children=[ 

widgets.HBox([control_group_widget, risk_reset_btn]), 

control_group_description 

] 

)]) 

 

def show_samplesize(mde, 

baseline, 

alpha, 

power, 

treatments, 

comparisons_readable, 

bonferroni_correction, 

relative_risk): 

if comparisons_readable == 'Control vs. All': 

comparisons = 'control_vs_all' 

else: 

comparisons = 'all_vs_all' 

 

treatment_costs = np.ones(treatments) 

treatment_costs[1:] = relative_risk 

treatment_allocations = None 

 

if metric == 'continuous': 

n_optimal, _, _ = SampleSize.continuous( 

mde, baseline, alpha, power, 

treatments, comparisons, None, 

treatment_allocations, bonferroni_correction) 

n_tot, n_cell, prop_cell = SampleSize.continuous( 

mde, baseline, alpha, power, 

treatments, comparisons, treatment_costs, 

treatment_allocations, bonferroni_correction) 

code_html = widgets.HTML( 

"<pre><code>" 

f"SampleSize.continuous(average_absolute_mde={ mde },\n" 

f" baseline_variance={ baseline },\n" 

f" alpha={ alpha },\n" 

f" power={ power },\n" 

f" treatments={ treatments },\n" 

f" comparisons=" 

f"'{ comparisons }',\n" 

f" treatment_costs=" 

f"{ list(treatment_costs) },\n" 

f" treatment_allocations=None,\n" 

f" bonferroni_correction=" 

f"{ bonferroni_correction })" 

"<code></pre>") 

else: 

n_tot, n_cell, prop_cell = SampleSize.binomial( 

mde, baseline, alpha, power, 

treatments, comparisons, treatment_costs, 

treatment_allocations, bonferroni_correction) 

n_optimal, _, _ = SampleSize.binomial( 

mde, baseline, alpha, power, 

treatments, comparisons, None, 

treatment_allocations, bonferroni_correction) 

code_html = widgets.HTML( 

"<pre><code>" 

f"SampleSize.binomial(absolute_percentage_mde={ mde },\n" 

f" baseline_proportion=" 

f"{ baseline },\n" 

f" alpha={ alpha },\n" 

f" power={ power },\n" 

f" treatments={ treatments },\n" 

f" comparisons=" 

f"'{ comparisons }',\n" 

f" treatment_costs=" 

f"{ list(treatment_costs) },\n" 

f" treatment_allocations=None,\n" 

f" bonferroni_correction=" 

f"{ bonferroni_correction })" 

"<code></pre>") 

 

def compare_against_optimal(current, optimal): 

if current == optimal: 

return '' 

else: 

return (f"<br><small><em>{current/optimal:.1f}x " 

f"optimal group allocation of {optimal:,}." 

f"</em></small>") 

 

display(widgets.HTML( 

f"<h4>Required sample size</h4>" 

f"<strong>Total:</strong><br>{n_tot:,}" 

f"{compare_against_optimal(n_tot, n_optimal)}")) 

cell_str = '<strong>Sample size in each cell</strong>' 

for i in range(len(n_cell)): 

if i == 0: 

treatment = 'Control' 

else: 

treatment = 'Variant ' + str(i) 

 

cell_str += (f"<br><em>{treatment}:</em> " 

f"{n_cell[i]:,} ({prop_cell[i]*100:.1f}%)") 

 

display(widgets.HTML(cell_str)) 

display(code_html) 

 

out = widgets.interactive_output(show_samplesize, { 

'mde': mde_widget, 

'baseline': baseline_widget, 

'alpha': alpha_widget, 

'power': power_widget, 

'treatments': treatments_widget, 

'comparisons_readable': comparisons_widget, 

'bonferroni_correction': bonferroni_widget, 

'relative_risk': control_group_widget 

}) 

 

display(ui, out) 

 

@staticmethod 

def _clean_treatments(treatments): 

"""Validate treatments input. 

 

Args: 

treatments (int): Number of treatment variants in the a/b test, 

including control. Defaults to 2. 

 

Returns: 

int: Number of treatment variants. 

 

Raises: 

TypeError: If `treatments` is not a number. 

ValueError: If `treatments` is not an integer greater than or 

equal to two. 

 

""" 

error_string = 'Treatments must be a whole number ' \ 

'greater than or equal to two' 

try: 

remainder = treatments % 1 

except TypeError: 

raise TypeError(error_string) 

 

if remainder != 0: 

raise ValueError(error_string) 

elif treatments < 2: 

raise ValueError(error_string) 

else: 

return int(treatments) 

 

@staticmethod 

def _clean_comparisons(comparisons): 

"""Validate comparisons input. 

 

Args: 

comparisons ({'control_vs_all', 'all_vs_all'}): Which treatments 

to compare. 

 

Returns: 

str: Which treatments to compare. 

 

Raises: 

ValueError: If `comparisons` is not one of 'control_vs_all' or 

'all_vs_all'. 

 

""" 

if comparisons not in ('control_vs_all', 'all_vs_all'): 

raise ValueError('comparisons must be either ' 

'"control_vs_all" or "all_vs_all"') 

else: 

return comparisons 

 

@staticmethod 

def _num_comparisons(treatments, comparisons): 

"""Calculate the number of hypothesis tests. 

 

When comparing all treatments against each other, calculating 

the number of hypothesis tests is an n-choose-k problem with 

n=treatments, and k=2: https://en.wikipedia.org/wiki/Combination. 

 

Args: 

treatments (int): Number of treatment variants in the a/b test, 

including control. 

comparisons ({'control_vs_all', 'all_vs_all'}): Which treatments 

to compare. 

 

Returns: 

int: Number of hypothesis tests to conduct. 

 

""" 

treatments = SampleSize._clean_treatments(treatments) 

comparisons = SampleSize._clean_comparisons(comparisons) 

 

if comparisons == 'control_vs_all': 

num_comparisons = treatments - 1 

else: 

num_comparisons = math.factorial(treatments) /\ 

(2 * math.factorial(treatments - 2)) 

 

return int(num_comparisons) 

 

@staticmethod 

def _get_comparison_matrix(treatments, comparisons): 

"""Transform categorical comparison to matrix. 

 

Args: 

treatments (int): Number of treatment variants in the a/b test, 

including control. 

comparisons ({'control_vs_all', 'all_vs_all'}): Which treatments 

to compare. 

 

Returns: 

numpy.ndarray: Lower triangular matrix of size 

`treatments x treatments` with 1 in position i, j 

if treatment i is to be compared with treatment j. 

 

""" 

treatments = SampleSize._clean_treatments(treatments) 

comparisons = SampleSize._clean_comparisons(comparisons) 

 

if comparisons == 'control_vs_all': 

comparison_matrix = np.zeros((treatments, treatments)) 

comparison_matrix[1:, 0] = 1 

 

else: 

comparison_matrix = np.ones((treatments, treatments)) 

comparison_matrix = np.tril(comparison_matrix, -1) 

 

return comparison_matrix 

 

@staticmethod 

def _clean_treatment_costs(treatments, treatment_costs): 

"""Validate or generate treatment cost array. 

 

Args: 

treatment_costs (numpy.ndarray, None): Array with same length as 

the number of treatments containing positive floats specifying 

the treatments' relative costs. None also accepted in which 

case equal relative costs are returned. 

treatments (int): Number of treatment variants in the a/b test, 

including control. 

 

Returns: 

numpy.ndarray: Array with each treatment's cost. 

 

Raises: 

TypeError: If `treatment_costs` is not None or a numpy.ndarray. 

TypeError: If the length of customs `treatment_costs` is not the 

same as the number of treatments. 

ValueError: If the values of custom `treatment_costs` are not all 

positive and sum to one. 

 

""" 

treatments = SampleSize._clean_treatments(treatments) 

 

if treatment_costs is None: 

# Default equal cost of all cells 

return np.ones(treatments) 

 

elif (not (isinstance(treatment_costs, np.ndarray) or 

isinstance(treatment_costs, list)) or 

len(treatment_costs) != treatments): 

raise TypeError('treatment_costs must be a list or numpy array of' 

'the same length as the number of treatments') 

 

try: 

treatment_costs = np.array(treatment_costs) 

if not (treatment_costs > 0).all(): 

raise ValueError('treatment_costs values must all be positive') 

 

except TypeError: 

raise TypeError('treatment_costs array must only contain numbers') 

 

return treatment_costs 

 

@staticmethod 

def _get_treatment_allocations(treatments, comparisons, treatment_costs, 

treatment_allocations): 

"""Validate or generate treatment allocation array. 

 

See the footnote on page 31 of "Duflo, E., Glennerster, R., & Kremer, 

M. (2007). Using randomization in development economics research: A 

toolkit. Handbook of Development Economics, 4, 3895–3962." for math. 

 

Args: 

treatments (int, optional): Number of treatment variants in the a/b 

test, including control. Defaults to 2. 

comparisons ({'control_vs_all', 'all_vs_all'}, optional): Which 

treatments to compare. Defaults to 'control_vs_all'. 

treatment_costs (numpy.ndarray, optional): Array with same length 

as the number of treatments containing positive floats 

specifying the treatments' relative costs. Defaults to equal 

cost for all treatments. 

treatment_allocations (numpy.ndarray/list/tuple, optional): Array 

with same length as the number of treatments containing 

proportion of sample allocated to each treatment. If not 

specified defaults to automatic allocation. 

 

Returns: 

numpy.ndarray: Array with same length as the number of treatments 

containing proportion of sample allocated to each treatment. 

 

Raises: 

TypeError: If `treatment_allocations` is not None or a 

numpy.ndarray. 

TypeError: If the length of custom `treatment_allocations` is not 

the same as the number of treatments. 

ValueError: If the values of custom `treatment_allocations` are 

not all positive and sum to one. 

 

""" 

treatments = SampleSize._clean_treatments(treatments) 

 

if treatment_allocations is not None: 

if (isinstance(treatment_allocations, list) or 

isinstance(treatment_allocations, tuple)): 

treatment_allocations = np.array(treatment_allocations) 

 

if (not isinstance(treatment_allocations, np.ndarray) or 

len(treatment_allocations) != treatments): 

raise TypeError('treatment_allocations must be a numpy array ' 

'or list of the same length as the number of ' 

'treatments') 

 

elif not (treatment_allocations > 0).all(): 

raise ValueError('treatment_allocations values ' 

'must all be positive') 

 

elif not math.isclose(treatment_allocations.sum(), 1.0): 

raise ValueError('treatment_allocations values ' 

'must sum to one') 

 

else: 

return np.array(treatment_allocations) 

 

comparisons = SampleSize._get_comparison_matrix(treatments, 

comparisons) 

weighted_comparisons = comparisons/np.sum(comparisons) 

treatment_costs = SampleSize._clean_treatment_costs(treatments, 

treatment_costs) 

 

ratios = np.zeros((treatments, treatments)) 

for i in range(treatments): 

sum_importance_i = (np.sum(weighted_comparisons[:, i]) + 

np.sum(weighted_comparisons[i, :])) 

for j in range(treatments): 

sum_importance_j = (np.sum(weighted_comparisons[:, j]) + 

np.sum(weighted_comparisons[j, :])) 

ratios[i, j] = (sum_importance_i / sum_importance_j * 

np.sqrt(treatment_costs[j] / 

treatment_costs[i])) 

 

treatment_allocations = ratios[:, 0] / np.sum(ratios[:, 0]) 

 

return treatment_allocations 

 

@staticmethod 

def _get_alpha(alpha, power, bonferroni, treatments, comparisons): 

"""Validate and potentially correct false positive rate. 

 

Args: 

alpha (float): Probability of Type I error (false positive). 

bonferroni (bool): Whether Bonferroni correction should be applied 

to control the false positive rate across all comparisons. 

treatments (int): Number of treatment variants in the a/b test, 

including control. 

comparisons ({'control_vs_all', 'all_vs_all'}, optional): Which 

treatments to compare. 

 

Returns: 

float: False positive rate, potentially Bonferroni corrected. 

 

Raises: 

ValueError: If `power` is less than or equal to `alpha`. 

TypeError: If `bonferroni` is not a bool. 

 

""" 

power = SampleSize._validate_percentage(power) 

alpha = SampleSize._validate_percentage(alpha) 

 

if power <= alpha: 

raise ValueError('alpha must be less than power') 

elif not isinstance(bonferroni, bool): 

raise TypeError('bonferroni must be a bool') 

 

num_comparisons = SampleSize._num_comparisons(treatments, comparisons) 

 

if bonferroni: 

return alpha / num_comparisons 

else: 

return alpha 

 

@staticmethod 

def _validate_percentage(num): 

"""Validate that num is a percentage. 

 

Args: 

num(float): Valid percentage. 

 

Returns: 

float: Valid percentage. 

 

Raises: 

TypeError: If `num` is not a float. 

ValueError: If `num` is not between zero and one. 

 

""" 

if not isinstance(num, float): 

raise TypeError('num must be a float') 

elif not 0 < num < 1: 

raise ValueError('num must be between 0 and 1') 

else: 

return num 

 

@staticmethod 

def _validate_positive(val): 

"""Validate that val is positive. 

 

Args: 

val (float): Value to validate. 

 

Returns: 

float: Value. 

 

Raises: 

ValueError: If value is non-positive. 

 

""" 

if not val > 0: 

raise ValueError('value must be positive') 

else: 

return val 

 

@staticmethod 

def _clean_continuous_mde(average_absolute_mde): 

"""Validate that mde is not equal to zero. 

 

Args: 

average_absolute_mde (float): Average absolute minimal detectable 

effect size (mean difference) across all tests. 

 

Returns: 

float: Average absolute minimal detectable effect size. 

 

Raises: 

ValueError: If `average_absolute_mde` is zero. 

 

""" 

if math.isclose(average_absolute_mde, 0.): 

raise ValueError('average_absolute_mde cannot be zero') 

else: 

return average_absolute_mde 

 

@staticmethod 

def _clean_binomial_mde(absolute_percentage_mde, baseline_proportion): 

"""Validate that mde is percentage and not too large. 

 

Args: 

absolute_percentage_mde (float): Average absolute minimal 

detectable effect size across all tests. 

baseline_proportion (float): Baseline metric proportion in 

target population. 

 

Returns: 

float: Average absolute minimal detectable effect size. 

 

""" 

mde = SampleSize._validate_percentage(absolute_percentage_mde) 

baseline = SampleSize._validate_percentage(baseline_proportion) 

 

if baseline - mde < 0 and baseline + mde > 1: 

raise ValueError('absolute_percentage_mde is too large ' 

'given baseline_proportion') 

else: 

return mde