import numpy as np
import scipy.stats as st

alpha = 0.05
p = 1 - alpha

dof = np.arange(5, 100)
n = dof / 2.

C_1 = 1 - alpha ** (1. / (n - 1))

fval = st.f.ppf(p, 2, dof - 2)
C_2 = fval / (n - 1. + fval)

import matplotlib.pyplot as plt
ax = plt.gca()

ax.plot(dof, C_1, 'k-', lw=10, label=r'$1-alpha^{1/q}$')
ax.plot(dof, C_2, 'r-', lw=5, label=r'$F_{2,2q}(alpha)/(F_{2,2q}(alpha)+q)$')
ax.plot(dof, 6. / dof, 'b-', lw=2, label=r'$6/d$')

ax.set_xlabel('Degrees of Freedom')
ax.set_ylabel('{:0.0f}% Significance Level'.format(100 * p))
ax.legend()
ax.set_title(r"Coherence level for $alpha=0.05$")