# level 2

As of the 23rd May 2022 this website is archived and will receive no further updates.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

School level maths / simulations

## ESP and the significance of significance

A controversy about experiments in extra-sensory perception throws some light, and maybe some confusion, on the idea of statistical significance. This article discusses a common misinterpretation of the results of significance tests, and investigates some criticisms of significance tests in general.

## The Maths of Paul the “Psychic” Octopus

England’s performance in the World-Cup last summer was thankfully overshadowed by the attention given to Paul the Octopus, who was reported as making an unbroken series of correct predictions of match winners. Here we present a mathematical analysis of Paul’s performance in an attempt to answer the question that (briefly) gripped the world: was Paul psychic?

## Clone of The force of mortality

How long are going to live? showed how the chances of dying each year depend on how old you are and what your health behaviours have been. Here we show how these annual 'hazards', survival curves and life expectancies can all be obtained from data on what proportion of people of each age die each year in the UK.

## Postscript: What happened next

After a couple of days of fairly intensive discussion the news inevitably moved on to other topics, but a fairly clear message had been sent to NICE that the media will rapidly pick up on any divergence from the advice of the Department of Health.

## The force of mortality

How long are going to live? showed how the chances of dying each year depend on how old you are and what your health behaviours have been. Here we show how these annual 'hazards', survival curves and life expectancies can all be obtained from data on what proportion of people of each age die each year in the UK.

## The propensity approach

Some people may find all the other interpretations and definitions of probability are somewhat unintuitive: surely the probability of something happening is not really a "degree of belief", but something objective about the world that would be the same even if there were no human (or alien) beings around to believe it?

## What are the chances?

In Why coincidences happen we saw how the chance of a rare event occurring to someone, somewhere, depended on the number of opportunities for it to occur.

## The development of probability

Probability theory was one of the last major areas of mathematics to be developed; its beginnings are usually dated to correspondence between the mathematicians Fermat and Pascal in the 1650's concerning some interesting problems that arose from gambling.