The hypothesis for the Shapiro-Wilk and D’Agostino-Pearson’s K² tests are: Lastly, the implementation of those algorithms in Python (c.f., Section 3). Secondly, a comparison between the tests and a conclusion about which is the optimal method to use (c.f., Section 2). Firstly, a description of each of those tests (c.f., Section 1). Hence, the aim of this article is to describe and compare the three main normality tests: For example, the article mentions 27 different normality tests. However, there are several tests in the literature that can be used to assess this normality, becoming difficult to determine which is the most accurate one for our scenario. It is also necessary to include the results from the normality tests. Otherwise, we might draw inaccurate conclusions and develop incorrect models.īut, to conclude the distribution of the data, statisticians should not rely only on graphical methods such as histograms or distribution plots. For a normal distribution, 68% of the observations are within ± one standard deviation of the mean, 95% are within ± two standard deviations, and 99.7% are within ± three standard deviations.įor many of the most popular statistical tests, testing the normality is necessary to fulfill the assumptions. Normal distribution, also known as the Gaussian distribution, is a probability distribution described with two parameters: the mean and the standard deviation.
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