Python Programming for Biology: Bioinformatics and Beyond

22

Statistics

Contents

Statistical analyses

Samples and significance

Null and alternative hypotheses

Type I and II errors

Statistics in Python

Simple statistical parameters

Mode, median and mean

Variance, standard deviation and skew

Statistical tests

Significance and hypotheses

Tailed tests and p-values

Z-scores and Z-test

T-tests

Probability intervals

Chi-squared and G-tests

Correlation and covariance

Covariance

Correlation coefficient

Simple linear regression

Statistical analyses

In  this  chapter  we  look  at  the  analysis  and  interpretation  of  collections  of  data  in  a

mathematical  way.  In  order  to  understand  the  basics  of  statistics  we  will  assume  some

familiarity with the basics of probability, as discussed in

Chapter 21

.

Generally  when  we  gather  numerical  measurements  we  don’t  get  identical  results,

rather  we  get  a  spread  of  values.  The  underlying  reason  for  this  variation  could  be  a

natural  variation  in  what  we  are  measuring,  an  error  in  the  way  we  make  the

measurements or, as is almost always the case, a combination of both of these. Statistics

helps us to make sense of variations in numerical data and commonly we are asking the

---

question  whether  what  we  measure  is  statistically  significant,  according  to  some  prior

hypothesis. Depending on the result this naturally then drives further investigations, based

on  a  belief  of  a  hypothesis  being  true  or  untrue.  Statistics  is  a  vast  subject,  so  in  this

chapter  we  can  only  cover  a  few  of  the  more  important  aspects  that  we  either  refer  to

elsewhere in this book or that are otherwise commonly used in biology.