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I have a dataset and I wanted to check if some variables follow a normal distribution. So, I have read about normallity test but it seem to be sensitive when the amout of data is large and, apparantly when I plot the histogram and the QQ-Plot, the variable seem to be normal. Should I only relly on the Histogram plus QQ-Plot or it is the best practice to do a normallity test as well?

I have plotted histograms, QQ-Plot, Kurtosis, Skewness and also a dataframe with 3 normallity tests

1 - Shapiro-Wilk. 2 - Lilliefors. 3 - D'Agostino_K2

My conclusion was that the variable is normal based on QQ-Plot, Histogrm and, Kurtosis and Skewness between (-1, +1).

Caio Sóter
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When assessing whether a variable follows a normal distribution, it is recommended to use a combination of methods to make a more informed decision. Relying solely on the histogram and QQ-plot may not provide a comprehensive analysis of the data's normality. While visual inspections can provide useful insights, they are not definitive tests for normality.

Using additional normality tests, such as the Shapiro-Wilk, Lilliefors, or D'Agostino_K2 tests, can offer statistical evidence to support or refute the assumption of normality.

These tests are specifically designed to evaluate whether a dataset significantly deviates from a normal distribution.

A kurtosis value within the range of -1 to +1 and skewness between -1 and +1 suggest a relatively symmetric and normally distributed dataset.

it is recommended to utilize a combination of methods including visual inspections (histogram and QQ-plot) and statistical tests (Shapiro-Wilk, Lilliefors, D'Agostino_K2) to assess the normality of your variables.

Bhavik Rathod
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  • Ok, but I have also read that all of these tests can be very sensitive when the dataset is large. So, should I really on them even though my dataset is very large? – Caio Sóter Jun 09 '23 at 11:14
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