We rarely heard of nonparametric tests while reading standard statistical books. However there are some scenarios where they should be used instead of parametric tests.  has beautiful blog about it, I am putting just a summary from that.
Table below displays various tests, I have verified that all of these tests are available in python stats package.
When to Use Parametric Tests
- Parametric tests can perform well with skewed and nonnormal distributions
- It is important to follow guidance in the sample size of data as shown in table below
- Parametric tests can perform well when the spread/variance of each group is different
- It has Statistical power
Reasons to Use Nonparametric Tests
- Your area of study is better represented by the median
- Income distribution is skewed and median is more useful than mean
- Few billionaires can boost up the mean significantly
- You have a very small sample size
- Even less than what is mentioned in table above
- You have ordinal data, ranked data, or outliers that you can’t remove
 : http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test