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
Hi Robert, On Tue, 13 Jun 2006, Robert Powell wrote:> 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.Well, I can't answer all of your questions, but I did try your sample and at least your installation does the same thing as mine. That is, for your sample data, I got the same results. Each test is slightly different and looks for different characteristics. So, it is not unusual for one test to indicate normality, but another one doesn't. Granted, the difference in p-value is quite large... I plotted the histogram of your data and to me, it doesn't "look" very normal...not very scientific, I know... If you can locate it, I suggest finding the book "Testing for Normality" which the Nortest package cites. It is quite good and might explain something to you...unfortunately, neither it nor any source I've found gives a simple table that says: Use test X if you want to see if the Y property of the distribution is normal. (Various tests seems to place different emphasis on different things...) Ray