I am working on Kaggle's house pricing exercise and I cannot understand something. I watch and read articles on normality tests, and more specifically JB test, but I cannot understand why according to my understanding of that test I need to reject the null hypothesis (which is the normal distribution) and conclude it is a non-normal distribution when the distribution graph shows a very close result to a normal distribution?

Jarque-Bera test = 171.236, with p-value 6.55459e-038

So from that result, if I am correct, I reject null and conclude the data are not normally distributed. But then this is the distribution graph (n=1460):

enter image description here

PS. The Y var is log of price and the x is year. Could the problem be that year is not a continuous variable?

  • 1
    $\begingroup$ Could you explain in what sense you believe this histogram is "close" to a Normal distribution? In effect, you are confronting a formal test with an unexplained intuition; by default, you should believe the test and use its results to modify your intuition. $\endgroup$
    – whuber
    Jul 29 '18 at 15:57
  • $\begingroup$ I was just confused that according to the graph, it seems the data is normally distributed becasue it follows the Bell curve shape, so I became unsure whther I understand the test meaning correctly. However, reading your answer, can I conclude that the test will win over the graph and this is because the graph actually is not perfect Bell shape..? $\endgroup$
    – Georgi
    Jul 29 '18 at 16:10
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    $\begingroup$ That's right. Unfortunately, the Jarque-Bera test is difficult to visualize with a histogram (because it is based on higher moments of the distribution, which no histogram explicitly shows). You can evaluate normality by comparing the bar areas to the areas predicted by the fitted Normal curve, using the principles of a Chi-squared test of goodness of fit. By looking closely, I see that the bar for the interval [-0.1,0.1] is too high while the one for [0.3,0.5] is too low. Given there are 1460 data points, you can estimate that these show significant deviations from normality. $\endgroup$
    – whuber
    Jul 29 '18 at 16:16