# Refining Lottery Tests

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.

National Lottery Level 3 showed how the standard $\chi^2$ goodness-of-fit statistic could be adjusted to allow for non-independence induced by the need to have exactly six unique numbers appear at each draw.

This could show the adjustment of the $\chi^2$ statistic to allow for non-independence.

Genest C, Lockhart RA, Stephens MA (2002) $\chi^2$ and the Lottery. The Statistician, 51, 243-257 shows adjustments to the standard $\chi^2$ statistic for single numbers, pairs etc.