How do I do a F-test in python

Question

How do I do an F-test to check if the variance is equivalent in two vectors in Python?

For example if I have

a = [1,2,1,2,1,2,1,2,1,2]
b = [1,3,-1,2         


        

Answer 1

if you need a two-tailed test, you can proceed as follow, i choosed alpha =0.05:

a = [1,2,1,2,1,2,1,2,1,2]
b = [1,3,-1,2,1,5,-1,6,-1,2]
print('Variance a={0:.3f}, Variance b={1:.3f}'.format(np.var(a, ddof=1), np.var(b, ddof=1)))
fstatistics = np.var(a, ddof=1)/np.var(b, ddof=1) # because we estimate mean from data
fdistribution = stats.f(len(a)-1,len(b)-1) # build an F-distribution object
p_value = 2*min(fdistribution.cdf(f_critical), 1-fdistribution.cdf(f_critical))
f_critical1 = fdistribution.ppf(0.025)
f_critical2 = fdistribution.ppf(0.975)
print(fstatistics,f_critical1, f_critical2 )
if (p_value<0.05):
    print('Reject H0', p_value)
else:
    print('Cant Reject H0', p_value)

if you want to proceed to an ANOVA like test where only large values can cause rejection, you can proceed to right-tail test, you need to pay attention to the order of variances (fstatistics = var1/var2 or var2/var1):

a = [1,2,1,2,1,2,1,2,1,2]
b = [1,3,-1,2,1,5,-1,6,-1,2]
print('Variance a={0:.3f}, Variance b={1:.3f}'.format(np.var(a, ddof=1), np.var(b, ddof=1)))
fstatistics = max(np.var(a, ddof=1), np.var(b, ddof=1))/min(np.var(a, ddof=1), np.var(b, ddof=1)) # because we estimate mean from data
fdistribution = stats.f(len(a)-1,len(b)-1) # build an F-distribution object 
p_value = 1-fdistribution.cdf(fstatistics)
f_critical = fd.ppf(0.95)
print(fstatistics, f_critical)
if (p_value<0.05):
    print('Reject H0', p_value)
else:
    print('Cant Reject H0', p_value)

The left-tailed can be done as follow :

a = [1,2,1,2,1,2,1,2,1,2]
b = [1,3,-1,2,1,5,-1,6,-1,2]
print('Variance a={0:.3f}, Variance b={1:.3f}'.format(np.var(a, ddof=1), np.var(b, ddof=1)))
fstatistics = min(np.var(a, ddof=1), np.var(b, ddof=1))/max(np.var(a, ddof=1), np.var(b, ddof=1)) # because we estimate mean from data
fdistribution = stats.f(len(a)-1,len(b)-1) # build an F-distribution object
p_value = fdistribution.cdf(fstatistics)
f_critical = fd.ppf(0.05)
print(fstatistics, f_critical)
if (p_value<0.05):
    print('Reject H0', p_value)
else:
    print('Cant Reject H0', p_value)

Answer 2

The test statistic F test for equal variances is simply:

F = Var(X) / Var(Y)

Where F is distributed as df1 = len(X) - 1, df2 = len(Y) - 1

scipy.stats.f which you mentioned in your question has a CDF method. This means you can generate a p-value for the given statistic and test whether that p-value is greater than your chosen alpha level.

Thus:

alpha = 0.05 #Or whatever you want your alpha to be.
p_value = scipy.stats.f.cdf(F, df1, df2)
if p_value > alpha:
    # Reject the null hypothesis that Var(X) == Var(Y)

Note that the F-test is extremely sensitive to non-normality of X and Y, so you're probably better off doing a more robust test such as Levene's test or Bartlett's test unless you're reasonably sure that X and Y are distributed normally. These tests can be found in the scipy api:

• Bartlett's test
• Levene's test

Answer 3

To do a one way anova you can use

import scipy.stats as stats

stats.f_oneway(a,b)

One way Anova checks if the variance between the groups is greater then the variance within groups, and computes the probability of observing this variance ratio using F-distribution. A good tutorial can be found here:

https://www.khanacademy.org/math/probability/statistics-inferential/anova/v/anova-1-calculating-sst-total-sum-of-squares

Answer 4

For anyone who came here searching for an ANOVA F-test or to compare between models for feature selection

• sklearn.feature_selection.f_classif does ANOVA tests, and
• sklearn.feature_selection.f_regression does sequential testing of regressions