In order to check visually if a sample follows a normal distribution, it is possible to: The Jarque-Bera test This test is more powerful the higher the number of values.The Lilliefors test This test is a modification of the Kolmogorov-Smirnov test and is suited to normal cases where the parameters of the distribution, the mean and the variance are not known and have to be estimated.The Anderson-Darling test This test proposed by Stephens (1974) is a modification of the Kolmogorov-Smirnov test and is suited to several distributions including the normal distribution for cases where the parameters of the distribution are not known and have to be estimated.The Shapiro-Wilk test This test is best suited to samples of less than 5000 observations.XLSTAT offers four tests for testing the normality of a sample: So when the p-value linked to a normality test is lower than the risk alpha, the corresponding distribution is significantly not-normal. Normality tests are associated to the null hypothesis that the population from which a sample is extracted follows a normal distribution. For example, the normality of residuals obtained in linear regression is rarely tested, even though it governs the quality of the confidence intervals surrounding parameters and predictions. But checking that this is actually true is often neglected.

Assuming a sample is normally distributed is common in statistics.

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