Interpreting the p-value

The p in p-value stands for probability and as such it therefore lies between 0 and 1. I am sure we all know that if the p-value falls below 0.05 we declare statistical significance and conclude that the treatments are different, that is pi 7 p2. In contrast if the p-value is above 0.05 then we talk in terms of non-significant differences. We will now explore just how this p-value is defined and later we will see the principles behind its calculation. 

In the context of the comparison of an active treatment (A) with a placebo treatment (B) in lowering diastolic blood pressure assume that we have the following data  

Suppose that the p-value turns out to be 0.042. What does this p-value actually measure We can see of course that it is 0.05 and so would give statistical significance, but what does the probability 0.042 refer to. What is it the probability of Usually people give one of two responses to this question  

One of these definitions is correct and one is incorrect Which way round is it  

the second definition is the correct one. The first definition is not only incorrect, it is also the common mistake that many people make. We will explore later in Section 9.3.1 why this definition causes so many problems and misunderstandings. For the moment, however, we will explore in more detail the correct definition. It is worthwhile expanding on the various components of the definition  

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