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edited Jul 14, 2018 at 17:05

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Short Answer: This is a spectacular example of Unfortunately, there's a weaknessbug in the D'Agostino Test of normalityscipy. Even though thestats.normaltest, specifically in scipy.stats.kurtosistest (Scipy 1.1.0). The data are clearly non-normal, the D'Agostino test gives a non-significant p-value because the sample skewness and kurtosis (excess) are approximately 0. Other normalitynumerous tests give p-values much lower thancorrectly indicate that (ps<.05, correctly indicating non-normalitysee examples in R below). I've reported the bug.

library(moments)
library(nortest)
x=c(0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1687, 0.1687, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.2005, 0.2216, 0.2216, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.48, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912)

pList <- list()
pList$DAgostino <- agostino.test(x)$p.value
pList$ShapiroWilk <- shapiro.test(x)$p.value
pList$ShapiroFrancia <- sf.test(x)$p.value
pList$AndersonDarling <- ad.test(x)$p.value
pList$KolmSmirLill <- lillie.test(x)$p.value
pList$PearsonChiSq <- pearson.test(x)$p.value
pList

D'Agostino 0.8180437

Pearson Chi Squared 0***

moment(x,order=3,central=TRUE)

Skewness = - Pearson Chi Squared 0.001708608

moment(x,order=4,central=TRUE)

Kurtosis = 0.03113902

Short Answer: This is a spectacular example of a weakness in the D'Agostino Test of normality. Even though the data are clearly non-normal, the D'Agostino test gives a non-significant p-value because the sample skewness and kurtosis (excess) are approximately 0. Other normality tests give p-values much lower than .05, correctly indicating non-normality.

library(moments)
library(nortest)
x=c(0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1687, 0.1687, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.2005, 0.2216, 0.2216, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.48, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912)

pList <- list()
pList$DAgostino <- agostino.test(x)$p.value
pList$ShapiroWilk <- shapiro.test(x)$p.value
pList$ShapiroFrancia <- sf.test(x)$p.value
pList$AndersonDarling <- ad.test(x)$p.value
pList$KolmSmirLill <- lillie.test(x)$p.value
pList$PearsonChiSq <- pearson.test(x)$p.value
pList

D'Agostino 0.8180437

Pearson Chi Squared 0***

moment(x,order=3,central=TRUE)

Skewness = -0.001708608

moment(x,order=4,central=TRUE)

Kurtosis = 0.03113902

Unfortunately, there's a bug in scipy.stats.normaltest, specifically in scipy.stats.kurtosistest (Scipy 1.1.0). The data are clearly non-normal, and numerous tests correctly indicate that (ps<.05, see examples in R below). I've reported the bug.

library(moments)
library(nortest)
x=c(0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1687, 0.1687, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.2005, 0.2216, 0.2216, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.48, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912)

pList <- list()
pList$ShapiroWilk <- shapiro.test(x)$p.value
pList$ShapiroFrancia <- sf.test(x)$p.value
pList$AndersonDarling <- ad.test(x)$p.value
pList$KolmSmirLill <- lillie.test(x)$p.value
pList$PearsonChiSq <- pearson.test(x)$p.value
pList

Pearson Chi Squared 0

Source Link

created Jul 11, 2018 at 16:12

Anthony

1.7k
15
26

Code and Details:

library(moments)
library(nortest)
x=c(0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1622, 0.1687, 0.1687, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.1729, 0.2005, 0.2216, 0.2216, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.2498, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.3143, 0.48, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.4854, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5078, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.5328, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.6496, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.9119, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912, 0.912)

pList <- list()
pList$DAgostino <- agostino.test(x)$p.value
pList$ShapiroWilk <- shapiro.test(x)$p.value
pList$ShapiroFrancia <- sf.test(x)$p.value
pList$AndersonDarling <- ad.test(x)$p.value
pList$KolmSmirLill <- lillie.test(x)$p.value
pList$PearsonChiSq <- pearson.test(x)$p.value
pList

P-values:

D'Agostino 0.8180437

Shapiro-Wilk 1.572961e-23

Shapiro-Francia 2.64774e-20

Anderson-Darling 3.7e-24

Kolmogorov-Smirnov (Lilliefors version) 9.468351e-83

Pearson Chi Squared 0***

moment(x,order=3,central=TRUE)

Skewness = -0.001708608

moment(x,order=4,central=TRUE)

Kurtosis = 0.03113902