Earlier this month, I gave the Horizon Lecture at the Australian Statistical Conference 2025 in Perth. I am grateful to the Statistical Society of Australia for providing me with this opportunity.

My slides are available online.

In my lecture, I introduced the audience to sequential analysis, a branch of statistics in which we can analyse and draw conclusions ‘as the data come in’ and as often as we like, rather than only a single time once we have collected all of the data. Amongst other benefits, this allows us to be resilient to the problems of ‘peeking’, ‘p-hacking’ and other forms of undisclosed or inadvertent multiple comparisons.

Sequential analysis goes back as far as the 1940s, with the development of the sequential probability ratio test (SPRT) by Abraham Wald. While that was a landmark advance in statistical methodology, it was not widely known amongst the audience at the conference (based on a show of hands at my lecture). For whatever reason, such methods are rarely taught. In my 4 years of undergraduate education, I only had a single lecture on the topic!

Recently there has been substantial new research into statistical methods that are ‘anytime-valid’, especially to give researchers ‘safer’ statistical tools that allow optional stopping or optional continuation (deciding to stop a study early, or collect more data than originally planned, based on looking at the data so far), without compromising the desired significance or confidence levels.

I summarised some of these developments in my lecture, and then described how we used them to design an award-winning method for auditing preferential elections.