[Principles of tests of hypotheses in statistics: alpha, beta and P]

Modern clinical research requires control of statistical methods. We reviewed 120 original manuscripts which were submitted to the Annales françaises d'anesthésie et de reanimation and analyzed their statistical methodology. Most of them contained errors (inappropriate numerical expression of the data, uncontrolled alpha risk, lack of power, use of inadequate statistical tests) and only 9 (7%) were considered as adequate. Therefore it is useful to come back to the methodology of hypothesis testing. An hypothesis test helps to decide between two hypothesis, the null hypothesis (H0) and the alternative hypotheses (H1) that we intend to demonstrate. The decision of the choice between H0 and H1 is associated with two probabilities: the alpha risk which is the probability to reject H0 whereas H0 is true, and the beta risk which is the probability not to reject H0 whereas H1 is true. Because the alpha risk is considered to be very important, it should be verified that the actual risk corresponds to the risk initially retained. The P value is the probability to observe a difference as great as that noted. The P value should be assessed according to its environment: the clinical relevance of a result should be assessed according to the amplitude of the difference and its confidence interval. When the null hypothesis is not rejected, the power of the test is essential. Power calculation is essential in clinical research trials. The number of patients included depends on four elements: the response to the control treatment, the expected response to the new treatment, the level of significance, and the power. The following items should be checked to choose the appropriate test: assess the kind of variable, verify the requirements for application of the test (type of the variable distribution, sample size, particular conditions such as equality of variance, dependence or independence of the variables), determine if data come from paired samples or if multiple comparisons are performed. Statistical analysis has become more easy with computers, however a precise knowledge of statistics remains essential. Advice from a statistician is often useful especially when obtained a priori and not a posteriori.