# [Solved] How do I do a F-test in python

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,-1,2,1,5,-1,6,-1,2]
```

is there something similar to

```
scipy.stats.ttest_ind(a, b)
```

I found

```
sp.stats.f(a, b)
```

But it appears to be something different to an F-test

##
Solution #1:

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:

##
Solution #2:

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

##
Solution #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:

##
Solution #4:

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)
```