Created
June 20, 2015 19:24
-
-
Save JohannesBuchner/99b75ec80e7cfcf98675 to your computer and use it in GitHub Desktop.
p-value reliability
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
import matplotlib.pyplot as plt | |
import numpy | |
import scipy.stats | |
# http://www.medpagetoday.com/Blogs/TheMethodsMan/52171 | |
def calc_reliability(p, power=0.8, frac_true=0.1): | |
""" | |
Given this p-value, power of the test and fraction of hypotheses that | |
are actually true. | |
If we receive a negative result, how probable is it that the hypothesis | |
is false? | |
If we receive a positive result, how probable is it that the hypothesis | |
is true? | |
""" | |
frac_false = 1 - frac_true | |
frac_false_pos = frac_false * p | |
frac_false_neg = frac_false * (1 - p) # false, and undetected | |
frac_true_pos = power * frac_true | |
frac_true_neg = (1 - power) * frac_true # true, but undetected | |
frac_pos_total = frac_true_pos + frac_false_pos | |
frac_neg_total = frac_true_neg + frac_false_neg | |
reliability_pos = frac_true_pos / frac_pos_total | |
reliability_neg = frac_true_neg / frac_neg_total | |
return reliability_pos, reliability_neg | |
# p = prob to have as extreme data if false | |
p = 0.05 | |
results = [] | |
p = numpy.logspace(-3, 0, 400) | |
power = 0.8 | |
frac_true = 0.1 | |
reliability_pos, reliability_neg = calc_reliability(p, power=power, frac_true=frac_true) | |
plt.plot(p, reliability_pos, '-', label='"significant" detection', color='r') | |
plt.plot(p, reliability_neg, '--', label='no significant detection', color='g') | |
#plt.plot(p, 1-p/frac_true, '--') | |
threesigma, twosigma = scipy.stats.norm().cdf([-3,-2]) | |
for threshold, label in [(threesigma, '$3\sigma$'), (twosigma, '$2\sigma$'), (0.01, 0.01), (0.05, 0.05), (0.1, 0.1)]: | |
pos, neg = calc_reliability(threshold, power=power, frac_true=frac_true) | |
plt.vlines(threshold, 0, pos, linestyles=['dashed'], alpha=0.5) | |
plt.text(threshold, pos, '%.0f%% for p<%s' % (pos * 100, label), va='bottom', ha='left', fontsize=8) | |
plt.ylim(0, 1.06) | |
plt.xlabel('p-value') | |
plt.ylabel('Prob. that test gave the right answer') | |
plt.gca().set_xscale('log') | |
plt.legend(loc='lower left', frameon=True) | |
plt.savefig('pvalue.pdf', bbox_inches='tight') | |
plt.savefig('pvalue.png', bbox_inches='tight') | |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment