Goodness-of-fit test checks whether the empirical (sample) distribution agrees with some expected probability distribution. This can be a one-tailed or two-tailed test. In this case, the test statistic has the П‡ВІ-distribution with n - 1 degrees of freedom, where n is the sample size. Testing whether the variance of normally distributed data has some pre-determined value. The most popular tests which lead to a П‡ВІ-score are the following:

Two-tailed test: p-value = 2 * min we denote the smaller of the numbers a and b.)

Right-tailed test: p-value = Pr(S в‰Ґ x | H 0) Left-tailed test: p-value = Pr(S в‰¤ x | H 0) In formulas below, S stands for a test statistic, x for the value it produced for a given sample, and Pr(event | H 0) is the probability of an event, calculated under the assumption that H 0 is true: It is the alternative hypothesis which determines what 'extreme' actually means, so the p-value depends on the alternative hypothesis that you state: left-tailed, right-tailed, or two-tailed. More intuitively, p-value answers the question: Assuming that I live in a world where the null hypothesis holds, how probable is it that, for another sample, the test I'm performing will generate a value at least as extreme as the one I observed for the sample I already have? It is crucial to remember that this probability is calculated under the assumption that the null hypothesis is true! Formally, the p-value is the probability that the test statistic will produce values at least as extreme as the value it produced for your sample.

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