In this paper I argue how we can impart deep understanding of inferential statistics by the early introduction of two approaches that students normally encounter only late in their studies, if at all. These are non-parametric methods and ANOVA. As illustration, we imagine a marathon race where firstly there are just two teams with two runners each, and secondly where there is a third team with two or more runners. We consider various statistics we could use to decide the result, thus discovering the concept of statistical tests in general, and why the chi-square statistic in particular is so important. Following the path of this discovery requires only elementary arithmetic. This is in accordance with the author’s belief that students weak in mathematics can learn the fundamentals of inferential statistics at least as readily as a Euclid or a Newton.