p-values from n-sigma and vice versa¶

In [26]:

import scipy.stats as st

In [36]:

# define p-value
p = 0.0456

In [37]:

# calculate number of standard deviations (n-sigma) from p-value

# one-tailed
n_sigma_one_tailed = st.norm.ppf(1-p)

# two-tailed
n_sigma_two_tailed = st.norm.ppf(1-p/2.)

print(f" p-value = {p}, n_sigma_one_tailed = {n_sigma_one_tailed:.4f}, n_sigma_two_tailed = {n_sigma_two_tailed:.4f}")

 p-value = 0.0456, n_sigma_one_tailed = 1.6891, n_sigma_two_tailed = 1.9991

In [43]:

# p-value from number of standard deviations (n-sigma)
n_sigma = 5

# one-tailed
p_value_one_tailed = 1 - st.norm.cdf(n_sigma)

# two-tailed
p_value_two_tailed = 2. * (1 - st.norm.cdf(n_sigma))

print(f" n-sigma = {n_sigma}, p_value_one_tailed = {p_value_one_tailed:.2g}, p_value_two_tailed = {p_value_two_tailed:.2g}")

 n-sigma = 5, p_value_one_tailed = 2.9e-07, p_value_two_tailed = 5.7e-07

In [48]:

for nsigma in [1, 2, 3, 4, 5]:
    p_value_one_tailed = 1 - st.norm.cdf(nsigma)
    print(f"{nsigma} {p_value_one_tailed:.2g}")

1 0.16
2 0.023
3 0.0013
4 3.2e-05
5 2.9e-07

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