[R] Cramer-von Mises normality test

[Robert Powell]

Hi, this is my first help request so please bear with me.

I've been running some normality tests using the nortest package. For  
some of my datasets the Cramer-von Mises normality test generates an  
extremely high probability (e.g., 1.637e+31) and indicates normality  
when the other tests do not. Is there something I'm misunderstanding  
or potentially a bug in the code?

Below are the results of the tests and then, below that, I've  
provided that column of the datafile.

Thank you in advance for your help.

Bob Powell

 > shapiro.test(Mn.Total..ug.kg)

	Shapiro-Wilk normality test

data:  Mn.Total..ug.kg
W = 0.5269, p-value < 2.2e-16

 > shapiro.test(ln.Mn.Total..ug/kg)
Error in inherits(x, "factor") : object "ln.Mn.Total..ug" not found
 > shapiro.test(ln.Mn.Total..ug.kg)

	Shapiro-Wilk normality test

data:  ln.Mn.Total..ug.kg
W = 0.943, p-value = 1.301e-06

 > sf.test(Mn.Total..ug.kg)

	Shapiro-Francia normality test

data:  Mn.Total..ug.kg
W = 0.5173, p-value < 2.2e-16

 > sf.test(ln.Mn.Total..ug.kg)

	Shapiro-Francia normality test

data:  ln.Mn.Total..ug.kg
W = 0.9403, p-value = 3.461e-06

 > cvm.test(Mn.Total..ug.kg)

	Cramer-von Mises normality test

data:  Mn.Total..ug.kg
W = 4.024, p-value = 1.637e+31

 > cvm.test(ln.Mn.Total..ug.kg)

	Cramer-von Mises normality test

data:  ln.Mn.Total..ug.kg
W = 0.356, p-value = 7.647e-05

 > lillie.test(Mn.Total..ug.kg)

	Lilliefors (Kolmogorov-Smirnov) normality test

data:  Mn.Total..ug.kg
D = 0.2325, p-value < 2.2e-16

 > lillie.test(ln.Mn.Total..ug.kg)

	Lilliefors (Kolmogorov-Smirnov) normality test

data:  ln.Mn.Total..ug.kg
D = 0.0869, p-value = 0.002011


OK, next the data column:

Mn-Total, ug/kg
460000
400000
510000
600000
770000
180000
210000
1000000
2600000
490000
260000
760000
840000
400000
430000
230000
660000
1200000
370000
230000
290000
320000
400000
660000
620000
1100000
350000
450000
880000
960000
570000
870000
820000
970000
1100000
450000
730000
390000
640000
380000
340000
1400000
870000
260000
430000
290000
290000
550000
540000
240000
470000
650000
390000
380000
410000
220000
400000
380000
500000
1000000
520000
690000
500000
520000
260000
630000
630000
410000
290000
1300000
860000
600000
450000
330000
390000
580000
270000
460000
360000
300000
3600000
540000
370000
460000
150000
560000
630000
810000
1300000
470000
620000
520000
540000
440000
1900000
760000
750000
440000
550000
3300000
780000
3600000
1400000
840000
450000
970000
610000
490000
280000
960000
350000
1100000
770000
510000
460000
590000
760000
610000
550000
460000
470000
650000
370000
170000
630000
530000
720000
850000
570000
860000
6000000
1700000
1400000
470000
1200000
360000
370000
1100000
310000
430000
480000
670000
350000
530000
380000
490000
490000
380000
630000
370000
710000
1500000
380000
550000
560000
560000
350000
340000
250000
390000
670000
720000
440000
380000
240000
340000
350000
310000
250000
320000
360000
360000
490000
490000
490000
710000
670000
1200000
530000
500000
490000