Data Handling & Analysis ZO4030 Andrew Jackson

Course structure Lecture in the morning – Mondays – Thursdays Computer labs in the afternoon – Mondays – Thursdays Assessment by examination in your final Mod Exams

Participation Lectures to be more tutorial based Moodle website associated with course – Lectures will be posted – Web-based discussions – Wiki, directed by the class to assist learning of R and analytical techniques

The R statistical computer language Free Highly flexible – With many contributed packages Inevitable for modern science Slower to familiarise Initially more frustrating

Reading Statistics, An introduction using R. Michael J Crawley. Wiley. ISBN

A simple experiment Question: – Does adding weight to a coin make it unfair? – Blu-tac added to head side Need to construct testable hypotheses – The null hypothesis

Weighted coin toss Toss the coin 6 times What is the hypothesis about how you think your system will behave? – More likely to get heads – Less likely to get heads – Either more or less likely to get heads What are the corresponding null hypotheses? – That the coin is fair

Behaviour of a fair coin The model is a fair 50:50 coin How do we generate information about how a fair coin behaves? – Toss an un-weighted coin 6 times and repeat – Do the maths

Behaviour of weighted coin Compare the weighted coin against the expected behaviour of a fair coin Question – How likely is it that our observed coin is fair?

Behaviour of weighted coin MAPS

Alternative hypotheses HA: coin is more likely to produce heads – One-tailed test in right tail HA: coin is less likely to produce heads – One-tailed test in left tail HA: coin is unfair (in either direction) – Two-tailed test including both left and right tails

P-values A p-value is the probability of your observed data or more extreme being generated according to the null hypothesis The less likely your data are, the less likely you would accept the null hypothesis as being true – We generally use a cut-off of p<0.05 to accept the alternative hypothesis One or two tailed tests refer to where you predict your alternative hypotheses to lie before you do your experiment

More practical data Data derived from experiments or observations are often normally distributed The normal (Gaussian) distribution provides the null hypothesis and model from which we can calculate statistics and p-values

Are these samples different?

Summary Science is about constructing experiments or designing observations to test your ideas about how the world works Hypotheses must be falsifiable Generally we construct null hypotheses against which our alternative hypotheses can be tested P-values tell us how likely it is our data came from the null hypothesis and therefore allow us to accept or reject it (H0)

1 st Practical session Question: – Are the brains of mammals different to those of birds? – Collect some data from literature / internet Revise your JS notes – What are the key summary statistics you might first look for in your data? – What plots would you undertake to explore your data?