Statistical Tests: Verifying Hypotheses
Statistical tests based on hypotheses are used to statistically verify or disprove, at a certain level of significance, models of populations and their probability distributions. The null and alternative hypothesis are the corner-stones of each such verification, and go hand-in-hand with the possibility of inference errors; these are defined first, followed by the exposition of standard parametric tests for normally distributed variables (tests of mean, variance, comparison of means, variances). Pearson’s \(\chi ^2\)-test is introduced as a means to ascertain the quality of regression (goodness of fit) in the case of binned data. The Kolmogorov–Smirnov test with which binned data can be compared to a continuous distribution function or two binned data sets can be compared to each other, is discussed as a distribution-free alternative.
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