by Qiang Gao, updated at May 11, 2017
...
Look up the
We can verify their equality by following Python
code.
In [1]: import numpy as np
In [2]: from scipy.stats import t # the t-distribution
In [3]: from scipy.stats import f # the F-distribution
In [4]: sz = [0.05, 0.01, 0.005, 0.001] # sizes
In [5]: df = [20, 40, 60, 80, 100, 200, 500, 1000] # degrees of freedom
In [6]: SZ, DF = np.meshgrid(sz, df) # generate meshgrid table
In [7]: f.isf(SZ, 1, DF) # isf = inverse survival function = 1 - cdf
Out[7]:
array([[ 4.3512435 , 8.09595806, 9.94393492, 14.81877555],
[ 4.08474573, 7.31409993, 8.82785886, 12.60935783],
[ 4.00119138, 7.07710579, 8.49461671, 11.97298729],
[ 3.96035242, 6.96268806, 8.33460762, 11.67136163],
[ 3.93614299, 6.89530103, 8.24064017, 11.49543133],
[ 3.88837472, 6.76329947, 8.05715996, 11.15450054],
[ 3.86012404, 6.68583329, 7.94984966, 10.95670343],
[ 3.85077467, 6.66029481, 7.91453232, 10.89186556]])
In [8]: t.isf(SZ/2, DF)**2 # isf = inverse survival function = 1 - cdf
Out[8]:
array([[ 4.3512435 , 8.09595806, 9.94393492, 14.81877554],
[ 4.0847457 , 7.31409993, 8.82785886, 12.60935783],
[ 4.00119137, 7.07710581, 8.49461671, 11.97298729],
[ 3.96035242, 6.96268805, 8.33460759, 11.67136163],
[ 3.93614299, 6.89530103, 8.24064016, 11.49543139],
[ 3.88837472, 6.76329947, 8.05715996, 11.15450054],
[ 3.86012404, 6.68583329, 7.94984966, 10.95670343],
[ 3.85077467, 6.66029481, 7.91453232, 10.89186556]])
Copyright ©2017 by Qiang Gao