Modern statistics

• motivate by problem solving
• start with visualization and exploring data
• focus on what can be reasonably learned from data, biases in data, concluding causation
• models and algorithms
• assessing uncertainty through re-sampling data (boostrap)
• probability theory as neat way of turning random variation into uncertainty about what is true
• hypothesis testing and its potential problems
• bayesian methods
• PPDAC: problem -> plan -> data -> analysis -> conclusion

What problems do I care about

• housing price
• employability
• …

Looking at data: What was the pattern of Harold Shipman’s murders

• Problem: can more detail tell us more about what Shipman did?
• Plan: compare actual times at which his patients died with the times of deaths recorded by other local GPs
• Data: a huge exercise requiring examination of death certificates
• Analysis: simple plotting

Inference and bias: How many sexual partners have people in Britain had in their lifetime?

• Problem: cannot know this as a fact
• Plan: survey in which people are carefully asked about the sexual activity
• Data: reports of numbers of partners
• Analysis: plotting and summary statistics

Regression, prediction and algorithms: Who was the luckiest person on the titanic?

The mysteries of the P-value

• P-value: a measure of the conflict between the data and a null hypothesis of no effect
• Specifically, P = probability of getting such an extreme result, were the null hypothesis true
• Not the probability of the null hypothesis
• Traditional threshold of 5% to declare statistically significant
• no significant does not mean no effect
• if many tests or crucial decision, use more stringent threshold

Quick analogy

• H0: The defendant is innocent
• Evidence (data): test results, testimony
• p-value: how likely you’d see that evidence if the defendant were actually innocent A very low p-value is like very strong evidence against the defendant being innocent -> convict the defendant (reject H0) If p=0.01 If the defendant is truly innocent, there is only 1% chance of seeing evidence this strong. The evidence is very unlikely under the assumption of innocence, which leads you to reject the assumption of innocence.

Another analogy - Explain to me p-value like I’m 5

• H0: I didn’t eat all the cookies
• T (data): The cookie crumble over their shirt, chocolate over their hands
• Question: If they really didn’t eat the cookies, how likely you will see these evidences? p=0.01 => 1% you will see these => extremely rare
• p = 0.01 < 0.05 => reject H0 null hypothesis you don’t believe them
• p > 0.05 => can’t reject H0 which mean you can’t tell if the defendant didn’t eat all the cookies