Python Programming for Biology: Bioinformatics and Beyond

Figure 22.1.  An example of results from drawing different numbers of random

samples from an underlying probability distribution. The samples illustrated are taken

randomly from a normal distribution with a mean of 0.0 and a standard deviation of 1.0,

where the sampling was done using the Python example.

Null and alternative hypotheses

Instead of trying to show whether something is likely to be true, in statistics we often aim

to show whether something is likely to be false. The basic reason for this is that it is often

easier  to  know  what  the  underlying  probability  distribution  would  be  if  the  observed

measurements  were  generated  by  a  random  process,  rather  than  know  what  the  situation

would  be  in  an  as  yet  unproven,  non-random  situation.  In  essence,  a  random  process  is

often  used  as  a  scientific  control.  In  this  case  we  hypothesise  a  statement  called  a  null

hypothesis  and  we  try  and  demonstrate,  to  a  certain  confidence  level,  whether  it  can  be

rejected.  For  example,  when  analysing  whether  a  new  drug  is  beneficial  for  a  medical

condition the null hypothesis might be that there is no difference in the treatment outcome

compared to a placebo. If we can demonstrate that this hypothesis is likely to be wrong,

then  we  have  evidence  that  the  new  drug  has  a  worthwhile  effect.  The  alternative

hypothesis  is  the  negation  (the  opposite)  of  the  null  hypothesis,  and  thus  if  the  null

hypothesis is rejected then the alternative hypothesis is accepted.