1. The ‘!’ symbol in Equations (1) and (2) not only expresses surprise (‘Wow! These equations look very similar), but it also denotes the factorial.

2. This definition does not provide a unique range. The one we show has a probability of 16% on either side of the selected region, which is then known as a central interval. An alternative would be to have the whole of the 32% on the left hand side of the confidence interval; this would be useful for producing upper limits on .

3. If is a discrete variable, such as a number of events, then ‘above' is replaced by ‘greater than or equal to', and correspondingly for ‘below’.

4. This stands for ‘confidence level of signal', but it is a poor notation, as CLs is in fact a ratio of p-values, which is itself not even a p-value, let alone a confidence level.

5. For the purpose of model comparison, any parameters are considered as nuisance parameters, even if they are physically meaningful, e.g. the parameters of a straight line fit, the mass of the Higgs boson, etc.

6. This is an example of Occam’s Razor, whereby a simpler hypothesis may be favoured over a more complex one.