sig_pow.md

Reproduce the "R from Python" plot in Python using plotnine. This is a line for line tranlation of significance_power_visuals.R.

# import our modules
import numpy as np
import pandas as pd
from IPython.display import display, HTML
from scipy.stats import norm
from data_algebra.cdata import RecordSpecification
from plotnine import (
    aes, 
    ggplot, 
    geom_line, geom_point, geom_ribbon, geom_vline,
    scale_color_manual, scale_fill_manual,
    xlab, ylab,
    ggtitle,
    theme
)

# our parameters of interest
n = 557
r = 0.1
t = 0.061576
power = 0.9
significance = 0.02

# convert to what were the function arguments
stdev = np.sqrt(0.5 / n)
effect_size = r
threshold = t
title='Area under the tails give you significance and (1-power)'
subtitle = 'Significance: control right tail; (1-Power): treatment left tail'
eps=1e-6
control_color='#d95f02'
treatment_color='#1b9e77'

# define the wide plotting data
x = set(np.arange(-5 * stdev, 5 * stdev + effect_size, step=stdev / 100))
x.update([threshold, threshold-eps, threshold+eps])
x = sorted(x)

pframe = pd.DataFrame({
    'x': x,
    'control': norm.pdf(x, loc=0, scale=stdev),
    'treatment': norm.pdf(x, loc=effect_size, scale=stdev),
})
# control's right tail
pframe['control_tail'] = np.where(pframe['x'] > threshold, pframe['control'], 0)
# treatment's left tail
pframe['treatment_tail'] = np.where(pframe['x'] <= threshold, pframe['treatment'], 0)

pframe

<style scoped> .dataframe tbody tr th:only-of-type { vertical-align: middle; }

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</style>

	x	control	treatment	control_tail	treatment_tail
0	-0.149805	4.962170e-05	1.069071e-14	0.000000e+00	1.069071e-14
1	-0.149506	5.216325e-05	1.161969e-14	0.000000e+00	1.161969e-14
2	-0.149206	5.482949e-05	1.262815e-14	0.000000e+00	1.262815e-14
3	-0.148907	5.762625e-05	1.372275e-14	0.000000e+00	1.372275e-14
4	-0.148607	6.055961e-05	1.491073e-14	0.000000e+00	1.491073e-14
...	...	...	...	...	...
1332	0.248377	1.588927e-14	6.290411e-05	1.588927e-14	0.000000e+00
1333	0.248677	1.462444e-14	5.986178e-05	1.462444e-14	0.000000e+00
1334	0.248977	1.345895e-14	5.696089e-05	1.345895e-14	0.000000e+00
1335	0.249276	1.238510e-14	5.419515e-05	1.238510e-14	0.000000e+00
1336	0.249576	1.139579e-14	5.155855e-05	1.139579e-14	0.000000e+00

1337 rows × 5 columns

# convert from to long for for plotting using the data algebra

# specify the cdata record transform
record_transform = RecordSpecification(
    pd.DataFrame({
        'group': ['treatment', 'control'],
        'y': ['treatment', 'control'],
        'tail': ['treatment_tail', 'control_tail'],
    }),
    record_keys=['x'],
    control_table_keys=['group'],
).map_from_rows()


record_transform

RecordMap: transforming records of the form:

<style type="text/css"> #T_2e174_row0_col0 { background-color: #FFE4C4; } </style>

	record id	value
	x	treatment	control	treatment_tail	control_tail
0	x record key	treatment value	control value	treatment_tail value	control_tail value

to records of the form:
<style type="text/css"> #T_9fd51_row0_col0, #T_9fd51_row1_col0 { background-color: #FFE4C4; } #T_9fd51_row0_col1, #T_9fd51_row1_col1 { background-color: #7FFFD4; } </style>

	record id	record structure	value
	x	group	y	tail
0	x record key	control	control value	control_tail value
1	x record key	treatment	treatment value	treatment_tail value

For details on the record transform please see here.

# apply the record transform
pframelong = record_transform(pframe)

pframelong

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	x	group	y	tail
0	-0.149805	control	4.962170e-05	0.000000e+00
1	-0.149805	treatment	1.069071e-14	1.069071e-14
2	-0.149506	control	5.216325e-05	0.000000e+00
3	-0.149506	treatment	1.161969e-14	1.161969e-14
4	-0.149206	control	5.482949e-05	0.000000e+00
...	...	...	...	...
2669	0.248977	treatment	5.696089e-05	0.000000e+00
2670	0.249276	control	1.238510e-14	1.238510e-14
2671	0.249276	treatment	5.419515e-05	0.000000e+00
2672	0.249576	control	1.139579e-14	1.139579e-14
2673	0.249576	treatment	5.155855e-05	0.000000e+00

2674 rows × 4 columns

# make the plot using the plotnine implementation 
# of Leland Wilkinson's Grammar of Graphics
# (nearly call equiv to Hadley Wickham ggplot2 realization)
palette = {'control': control_color, 'treatment': treatment_color}
p = (
    ggplot(pframelong, aes(x='x', y='y'))
        + geom_line(aes(color='group'))
        + geom_vline(xintercept=threshold, 
                     color='#7f7f7f', 
                     # linewidth=1,
                     )
        + geom_ribbon(aes(ymin=0, ymax='tail', fill='group'), alpha = 0.5)
        + scale_color_manual(values=palette)
        + scale_fill_manual(values=palette)
        + theme(legend_position='none')
        + ylab('density')
        + xlab('observed difference')
        + ggtitle(
            title 
            + "\n" + subtitle,
            )
    )

p

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