Hypothesis testing: proportions.

T he process of drawing conclusions about an entire population on the basis of the information contained in a random sample drawn from that population is known as statistical inference. Methods of statistical inference fall into 2 general categories: estimation and hypothesis testing. With estimation, our goal is to describe or estimate some characteristic of a population of interest, such as the mean pulmonary regurgitation fraction of all patients alive 10 years after repair of tetralogy of Fallot or the proportion of children with acute Kawasaki disease who develop coronary artery abnormalities. With hypothesis testing, we begin by claiming that the population parameter of interest is equal to some postulated value (or, in the situation in which we are comparing 2 populations, that the 2 parameters are equal to each other). This statement about the value of the population parameter is called the null hypothesis (H 0). The alternative hypothesis (H A) is a second statement that contradicts the null. Together, the null and alternative hypotheses account for all possible values of the population parameter; consequently, 1 of the 2 statements must be true. After formulating the hypotheses needed to answer our study question, we draw a random sample from the population of interest and use the information in this sample to calculate a test statistic. The test statistic is compared with the critical values of an appropriate probability distribution. If there is evidence that the sample could not have come from a population with the postulated value of the parameter, as determined by a comparison of the magnitude of the test statistic with the critical values of the probability distribution, we reject the null hypothesis. This occurs when the probability value of the test is sufficiently small, usually Ͻ0.05. The probability value is the probability of observing a test statistic as large as we got, or even larger, given that the null hypothesis is true. In this case we conclude that the data are not compatible with the null hypothesis; they are more supportive of the alternative. Such a test result is said to be statistically significant. If the probability value of the test is large, we fail to reject the null hypothesis. With dichotomous or binary data, values fall into 2 unordered categories or classes that are mutually exclusive; examples of dichotomous variables include gender and survival to hospital discharge after a surgical procedure yes/no. With this type …