Describing the credibility of the null hypothesis

In the previous page, a diagram with scales illustrated how the evidence against H0 was 'weighed' for different data sets. A p-value is a numerical description of this evidence that can give a scale to this diagram.

A p-value is a numerical summary statistic that describes the evidence against H0


Effect of pheromone on rabbits

An experiment is conducted to assess whether rabbits are influenced by a particular pheromone, either positively or negatively. A large cage is constructed whose features (water, food, etc.) are duplicated symmetrically on both sides of a centre line. A rabbit is placed in the centre of the cage and a small quantity of the pheromone is added to one side. During the next 5 hours, a technician records the number of minutes that the rabbit spends in each half of the cage. This experiment is repeated with 16 rabbits.

Do the rabbits tend to spend half their time in each side of the cage (indicating that they are unaffected by the pheromone) or do they tend to spend more time in one or other half (indicating attraction or repulsion)? We examine this question using the difference between the times in the two sides of the cage, pheromone minus non-pheromone. This question is equivalent to asking whether there is evidence that the underlying population mean of these differences could be zero.

The diagram below weighs the evidence using the p-value from a t-test of whether µ = 0.


The p-value is an index of credibility for the null hypothesis, µ = 0.


P-values have the same interpretation for all hypothesis tests.