Il test di ipotesi : hypothesis testing

When we do research, we start with a hypothesis that is usually in narrative form: “Preliminary results of studies on a new antihypertensive drug (B) indicate that it can obtain a better pressure control than standard treatment (A)”. The null hypothesis is what is known or assumed from theory or previous research. When we test hypotheses, we always test the null hypothesis (A = B) against an alternative/research hypothesis (A ­ B). Using a counterintuitive logic, we want to reject the null hypothesis in favor of the alternative. After generating a representative sample of the study population, we randomise the subjects to either treatment A or B. We calculate the proportion of people with adequate pressure control in both treatment arms and the chi-square statistic (with its associated P value). The formula for the test statistics is different for each type of test and data, but the basic concept is the same. We calculate how different the outcomes are in our groups, then decide whether to reject or fail to reject the null hypotesis of no difference between treatments. We can make two errors: we can say that treatments are different when they are not (type I error or a), or we can say that they are not different, when they really are (type II error or b). Protection of test (1-a) is the probability of correctly fail to reject the null hypothesis when it is true. Statistical power (1-b) is the probability of rejecting a false null hypothesis. The logic of hypothesis testing is counterintuitive (or backwards). We test whether there is no difference (the study treatment is equivalent to the standard treatment) in order to conclude that difference exists. When we fail to reject the null hypothesis, we need to provide the statistical power, because we could not have enough statistical power in our study.