I have got the following dataset:
Time Value
2018-08-01 00:00,4.3
2018-08-02 00:00,3.3
2018-08-03 00:00,5.3
2018-08-04 00:00,6.3
2018-08-05 00:00,3.3
2018-08-06 00:00,3.3
2018-08-07 00:00,1.3
2018-08-08 00:00,2.3
2018-08-09 00:00,4.3
2018-08-10 00:00,3.3
2018-08-11 00:00,5.3
2018-08-12 00:00,6.3
2018-08-13 00:00,3.3
2018-08-14 00:00,3.3
2018-08-15 00:00,1.3
2018-08-16 00:00,2.3
2018-08-17 00:00,4.3
2018-08-18 00:00,3.3
2018-08-19 00:00,5.3
2018-08-20 00:00,6.3
2018-08-21 00:00,3.3
2018-08-22 00:00,1.3
2018-08-22 00:00,4.3
2018-08-23 00:00,2.3
2018-08-24 00:00,4.3
2018-08-25 00:00,3.3
2018-08-26 00:00,5.3
2018-08-27 00:00,6.3
2018-08-28 00:00,3.3
2018-08-29 00:00,3.3
2018-08-30 00:00,1.3
2018-08-31 00:00,2.3
2018-09-01 00:00,4.3
2018-09-02 00:00,3.3
2018-09-03 00:00,2.3
2018-09-04 00:00,6.3
2018-09-05 00:00,3.3
2018-09-06 00:00,3.3
2018-09-07 00:00,3.3
2018-09-08 00:00,2.3
2018-09-09 00:00,4.3
2018-09-10 00:00,3.3
2018-09-11 00:00,5.3
2018-09-12 00:00,4.3
2018-09-13 00:00,3.3
2018-09-14 00:00,3.3
2018-09-15 00:00,4.3
2018-09-16 00:00,2.3
2018-09-17 00:00,6.3
2018-09-18 00:00,5.3
2018-09-19 00:00,5.3
2018-09-20 00:00,6.3
2018-09-21 00:00,6.3
2018-09-22 00:00,3.3
2018-09-22 00:00,4.3
2018-09-23 00:00,2.3
2018-09-24 00:00,4.3
2018-09-25 00:00,3.3
2018-09-26 00:00,5.3
2018-09-27 00:00,6.3
2018-09-28 00:00,3.3
2018-09-29 00:00,4.3
2018-09-30 00:00,2.3
2018-10-01 00:00,4.3
2018-10-02 00:00,3.3
2018-10-03 00:00,5.3
2018-10-04 00:00,6.3
2018-10-05 00:00,1.3
2018-10-06 00:00,3.3
2018-10-07 00:00,3.1
2018-10-08 00:00,2.3
2018-10-09 00:00,4.3
2018-10-10 00:00,3.3
2018-10-11 00:00,5.3
2018-10-12 00:00,6.3
2018-10-13 00:00,3.3
2018-10-14 00:00,3.3
2018-10-15 00:00,4.3
2018-10-16 00:00,2.3
2018-10-17 00:00,4.3
2018-10-18 00:00,3.3
2018-10-19 00:00,5.3
2018-10-20 00:00,6.3
2018-10-21 00:00,7.2
2018-10-22 00:00,3.3
2018-10-22 00:00,4.3
2018-10-23 00:00,2.3
2018-10-24 00:00,4.1
2018-10-25 00:00,3.3
2018-10-26 00:00,5.9
2018-10-27 00:00,6.3
2018-10-28 00:00,4.1
2018-10-29 00:00,3.1
2018-10-30 00:00,4.3
2018-10-31 00:00,2.3
I applied the Shapiro_Wilk_Normality_Test
and Kolmogorov_Smirnov_Test
with alpha = 0.05. As result, I got
Shapiro_Wilk_Normality_Test: Statistics=0.933,p=0.000
Kolmogorov_Smirnov_Test:Statistics=0.937, p=0.000
In both cases, the sample does not look Gaussian (reject $H_0$). Then I applied DAgostino_K_2_Test
DAgostino_K_2_Test Statistics=4.230, p=0.121
which would make to think ofSample looks Gaussian (fail to reject H0)
.
Then, I visualized the data with pyplot.hist
and it looked like Gaussian.
My question is: the data seems to have a Gaussian, and D'Agostino test seems to figure it out whereas Shapiro-Wilk and Kolmogorov-Smirnov seem to reject it. Any particular explanation? It would be very useful.