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The critical region in hypothesis testing is the set of all values of the test statistic that leads to the rejection of the null hypothesis. It is determined by the significance level, which defines the probability of committing a Type I error, or rejecting a true null hypothesis.
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The rejection region in hypothesis testing is the range of values for which the null hypothesis is not probable, leading to its rejection. It is determined by the significance level and the critical value, and it helps in deciding whether to accept or reject the null hypothesis based on sample data.
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The Kolmogorov-Smirnov Test is a non-parametric test used to determine if a sample comes from a specified distribution or to compare two samples to assess if they come from the same distribution. It is based on the maximum distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution or between the empirical distribution functions of two samples.
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The Likelihood Ratio Test is a statistical method used to compare the goodness of fit between two competing models, typically a null model and an alternative model, by evaluating the ratio of their likelihoods. It is a powerful tool for hypothesis testing, especially in the context of nested models, where one model is a special case of the other.
Statistical hypothesis testing is a method used to make inferences or draw conclusions about a population based on sample data, by determining whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis. It involves calculating a test statistic and comparing it to a critical value or using a p-value to decide whether the observed data is statistically significant under the assumed null hypothesis.
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Statistical testing is a method used to make inferences about a population based on sample data, determining the likelihood that observed differences or relationships are due to chance. It involves setting up a null hypothesis, which is tested against an alternative hypothesis, using a significance level to decide whether to reject the null hypothesis.
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The Anderson-Darling Test is a statistical test used to assess if a given sample comes from a specified continuous probability distribution, focusing on the tails of the distribution for a more sensitive evaluation than other goodness-of-fit tests like the Kolmogorov-Smirnov test. The test calculates a statistic from the sorted observed data and their cumulative distribution function, with larger values indicating a poorer fit to the theoretical distribution.
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