Shapiro-Wilk Test: Determining Data Normality
Definition and Significance
The Shapiro-Wilk test is a statistical method used to assess whether a set of data is normally distributed. It tests the null hypothesis that the data comes from a normal distribution.
Methodology
The Shapiro-Wilk test calculates a statistic (W) based on the data's residuals, which are the differences between the observed values and the expected values under the assumption of normality. A smaller W value indicates a greater departure from normality.
Significance Levels
Researchers typically set a significance level (α) of 0.05, meaning they are willing to accept a 5% chance of incorrectly rejecting the null hypothesis. If the calculated W value is less than the critical value determined by the significance level and degrees of freedom, the null hypothesis is rejected, suggesting that the data is not normally distributed.
Alternatives to the Shapiro-Wilk Test
Other tests that can be used to assess normality include: * Jarque-Bera test * D'Agostino and Pearson test * Lilliefors test
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