PRINCIPLES OF HYPOTHESIS TESTS IN STATISTICS - ALPHA, BETA AND P

Modern clinical research requires control of statistical methods. We r eviewed 120 original manuscripts which were submitted to the Annales f rancaises d'anesthesie et de reanimation and analyzed their statistica l methodology. Most of them contained errors (inappropriate numerical expression of the data, uncontrolled a risk, lack of power, use of ina dequate 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 hypo-thesis, the null hypothesis (H-0) and the alternative hypotheses (H-1) that we intend to demonstrate. The decision of the choice between H-0 and H-1 is associated with two probabilities: the alpha risk which is the pro bability to reject H-0, whereas H-0, is true, and the beta risk which is the probability not to reject H-0 whereas H-1 is true. Because the or risk is considered to be very important, it should be verified that the actual risk corresponds to the risk initially retained. The P val ue is the probability to observe a difference as great as that noted. The P value should be assessed according to its environment: the clini cal relevance of a result should be assessed according to the amplitud e of the difference and its confidence interval. When the null hypothe sis is not rejected, the power of the test is essential. Power calcula tion is essential in clinical research trials. The number of patients included depends on four elements: the response to the control treatme nt, the expected response to the new treatment, the level of significa nce, and the power. The following items should be checked to choose th e appropriate test: assess the kind of variable, verify the requiremen ts for application of the test (type of the variable distribution, sam ple size, particular conditions such as equality of variance, dependen ce or independence of the variables), determine if data come from pair ed samples or if multiple comparisons are performed. Statistical analy sis has become more easy with computers, however a precise knowledge o f statistics remains essential. Advice from a statistician is often us eful, especially when obtained a priori and not a posteriori. (C) 1998 Elsevier, Paris.