Dr Jennifer Rogers – “Yeah. But is it Significant?”
For this year’s Maths off piste we welcomed Dr Rogers from her day job of Director of Statistical Consultancy Services at the University of Oxford for a fascinating and entertaining journey through the proper and improper use of statistics in the modern high tech and journalistic world.
There are some very surprising statistical facts out there: for example, there is a 1 in 2,000,000 chance of death by selfie (Russia has even produced a government leaflet warning of the risks) and that cheerleading is deadlier than playing baseball. Regression to the mean can explain why speed cameras appear to reduce accidents and new managers of football teams appear to do better initially than their sacked forerunner (in fact, statistics show that teams tend to do better who, radically, don’t sack their manager after a bad run of results).
From the world of Medicine, the importance of the difference between relative and absolute increase demonstrated that newspaper headlines getting excited about the apparent 20% increase risk of developing pancreatic cancer as a result of eating a bacon sandwich every day (from 5 in 400 to 6 in 400) is, contrary to the implication, insignificant to the increase from 4 to 96 in 400 chance of developing lung cancer as a result of becoming a 25-a-day smoker.
In clinical testing, understanding the significance of increased survival rates from trial medicines is a key part of Dr Rogers’ work. For example, an increase in survival rate from 60% to 65% is not significant if the sample size is 100, but is significant in a sample of 1000. The mathematics of hypothesis testing behind the analysis showed the probability of this difference in survival rates occurring naturally significantly dropped from 47% to 2.7% between sample sizes. We ended up exploring utility functions and how they can inform decision-making and some correlations which certainly do not imply causation (another all too frequent source of misinformation found in the media). From the website tylervigen.com one “spurious correlation” example was the high correlation between cheese consumption and death from entanglement with one’s bedsheets.
We are very grateful to Dr Rogers for such an enlightening presentation and were delighted to welcome over 100 students and staff from other schools to join us. Huge thanks go to her and to Miss Mather for making the whole event happen.