Python Programming for Biology: Bioinformatics and Beyond

Figure 22.2.  A histogram of samples taken from a skewed distribution. The above

data were generated by randomly selecting 100 values using a gamma distribution, which

is asymmetric, as illustrated in the Python sample. The difference between the mean and

median of a distribution compared to the standard deviation can be used as a rough

measure of asymmetry, though the proper skewness is easy to calculate using SciPy.

When  a  statistical  model  has  an  approximating  probability  distribution  then  we  can

calculate probabilities with reference to that distribution. And, as we mentioned above, the

probability distribution could be a null hypothesis, which represents a random expectation.

In  this  case,  our  notion  of  significance  would  be  based  on  the  likelihood  of  the  null

hypothesis  generating  the  observed  data,  though  this  is  often  also  compared  to  the

likelihood  of  the  same  data  being  generated  by  a  competing  hypothesis,  such  as  the

alternative hypothesis.