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
Computer user-interface test
In an assessment of the user-interface of a computer program, sixteen users are shown a screen containing typical output for 10 seconds. Each user is then asked to indicate the position on the screen of a particular piece of information. The vertical distance between the indicated location and the actual location is recorded from each individual. (These 'errors' are negative if the user indicated too low a position.)
Do the users tend to pick the location of the item correctly, or is there a tendency to point too high or low? This question is equivalent to asking whether there is evidence that the underlying population mean of the 'errors' is different from 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 similar interpretation for all hypothesis tests.