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Some studies suggest that likelihood-ratio tests outperform traditional tests like Shapiro-Wilk and Anderson-Darling in terms of power, while other studies highlight the Shapiro-Wilk test as the most powerful for asymmetric distributions and the Kolmogorov-Smirnov test as the most accurate and reliable.
Normality tests are statistical procedures used to determine if a data set is well-modeled by a normal distribution. These tests are crucial in many statistical analyses because many statistical methods assume normality. Various normality tests have been developed, each with its strengths and weaknesses, and their effectiveness can vary depending on the sample size and the specific characteristics of the data.
Likelihood-Ratio Tests for Normality:
Omnibus Tests for Large Samples:
Comparative Power of Normality Tests:
Transformations and Multivariate Tests:
Specialized Tests and Cautionary Notes:
Normality tests are essential tools in statistical analysis, with various tests available to suit different data characteristics and sample sizes. Likelihood-ratio tests and omnibus tests are particularly powerful for large samples. Shapiro-Wilk and D'Agostino tests are generally effective across different types of distributions, while transformations can help address non-normality. Researchers should choose the appropriate test based on their specific needs and be cautious of the underlying assumptions.
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