Shapiro-Wilk Exponential Test

The Shapiro-Wilk Test for Exponentiality, with origin parameter unknown, employes the following statistic:

WE-Calc

Where

  • s is the sample standard deviation,
  • Xmin is the minimum value in the data set, and
  • n is the sample size.

Use the table below to find the critical values for the Shapiro-Wilk Test for Exponentiality. Two critical values are required. Accept the hypothesis that the distribution can be modeled with an Exponential Distribution if test statistic W(E) falls within the two values.

Note that the critical values are single-tailed values, use alpha/2 and (1-alpha)/2 to obtain the appropriate critical values since this is a two-sided test. For example, with alpha = 0.05, select the critical values corresponding to 0.025 and 0.975.

Critical Values For W(E) Test Statistics For Exponentiality

WE-Dist

Alpha (single-tailed values)
n0.0050.0100.0250.0500.1000.5000.9000.9500.9750.9900.995
30.25190.25380.25960.26970.29150.57140.97090.99260.99810.99970.9999
40.12410.13020.14340.16040.18910.37680.75140.85810.92360.96800.9837
50.08450.09050.10480.11870.14420.28750.55470.66820.75900.86000.9192
60.06100.06650.08020.09560.11730.22760.42920.50890.58420.67750.7501
70.05140.05910.07000.08100.09860.18740.34740.41620.48520.57060.6426
80.04540.05120.06140.07100.08520.16250.29340.34970.40330.48480.5428
90.04040.04420.05370.06330.07510.14150.25530.30050.34540.40150.4433
100.03690.04040.04870.05680.06780.12250.21780.25250.28790.33910.3701
110.03390.03800.04470.05280.06160.11120.19340.22650.26190.30390.3314
120.03110.03580.04100.04940.05670.10090.17230.20190.23640.27160.2978
130.02870.03370.03820.04600.05280.09250.15630.18290.21130.24220.2642
140.02650.03170.03620.04280.04960.08470.14170.16470.18620.21310.2315
150.02470.02980.03440.03980.04660.07780.12850.14850.16690.19260.2123
160.02330.02800.03260.03740.04380.07280.11870.13550.15420.17700.1931
170.02220.02640.03100.03520.04120.06840.10990.12570.14230.16140.1794
180.02120.02500.02940.03320.03880.06400.10150.11640.13110.14830.1668
190.02030.02380.02780.03140.03680.06000.09350.10710.11990.13740.1452
200.01960.02270.02640.03020.03530.05700.08840.10020.11210.12860.1369
210.01900.02170.02500.02900.03370.05400.08390.09480.10540.11980.1288
220.01850.02080.02380.02780.03230.05160.07940.08940.09880.11180.1212
230.01810.02010.02300.02660.03100.04920.07490.08360.09330.10430.1142
240.01770.01940.02240.02560.02980.04680.07040.07880.08820.09840.1071
250.01730.01880.02180.02480.02860.04470.06680.07490.08360.09270.1000
260.01690.01820.02130.02400.02740.04260.06360.07120.07910.08850.0948
270.01650.01770.02080.02320.02640.04070.06060.06780.07470.08430.0896
280.01610.01720.02030.02250.02560.03910.05760.06490.07060.08010.0859
290.01570.01680.01980.02190.02490.03770.05550.06210.06710.07590.0822
300.01530.01640.01930.02130.02420.03640.05360.05930.06430.07190.0786
310.01490.01600.01880.02070.02350.03520.05180.05690.06150.07190.0753
320.01450.01560.01830.02010.02290.03400.04910.05470.05910.06860.0722
330.01410.01520.01780.01950.02230.03290.04750.05270.05730.06610.0691
340.01370.01480.01730.01900.02170.03190.04590.05070.05550.06360.0660
350.01330.01440.01680.01850.02110.03090.04440.04880.05370.06110.0639
360.01290.01410.01640.01800.02050.03000.04290.04700.05190.05880.0608
370.01250.01380.01600.01760.02000.02910.04140.04540.05010.05670.0578
380.01220.01350.01560.01720.01950.02830.04000.04400.04830.05460.0553
390.01200.01330.01520.01680.01900.02750.03860.04260.04650.05250.0531
400.01180.01310.01480.01640.01860.02670.03750.04140.04470.05120.0510
410.01160.01290.01440.01610.01820.02600.03640.04020.04300.04990.0493
420.01140.01270.01400.01580.01780.02530.03550.03890.04170.04760.0482
430.01120.01250.01370.01550.01740.02480.03460.03790.04050.04640.0471
440.01100.01230.01340.01520.01700.02430.03380.03690.03940.04520.0460
450.01080.01210.01310.01490.01660.02380.03290.03590.03850.04400.0449
460.01060.01190.01290.01460.01620.02330.03200.03490.03760.04230.0438
470.01040.01170.01270.01430.01580.02280.03110.03400.03670.04160.0427
480.01030.01150.01250.01430.01580.02280.03110.03400.03670.03940.0426
490.01020.01130.01230.01410.01550.02230.03030.03320.03580.03820.0416
500.01010.01110.01220.01370.01490.02130.02880.03170.03400.03600.0394
510.01000.01090.01200.01350.01470.02090.02820.03100.03310.03490.0383
520.00990.01070.01190.01330.01450.02050.02760.03030.03230.03410.0373
530.00970.01060.01180.01310.01430.02010.02700.02960.03150.03320.0363
540.00950.01040.01160.01290.01410.01970.02640.02890.03070.03290.0353
550.00940.01030.01150.01270.01390.01930.02580.02820.02990.03210.0343
560.00930.01020.01130.01250.01370.01890.02520.02750.02920.03130.0333
570.00920.01010.01120.01230.01350.01850.02470.02680.02850.03060.0324
580.00910.01000.01100.01210.01330.01820.02420.02620.02790.03010.0318
590.00900.00980.01090.01190.01310.01790.02380.02570.02740.02960.0312
600.00890.00950.01080.01170.01290.01760.02340.02520.02700.02910.0306
610.00880.00930.01070.01150.01270.01730.02300.02470.02660.02860.0301
620.00870.00920.01050.01130.01250.01700.02260.02420.02620.02810.0296
630.00860.00910.01040.01120.01230.01670.02220.02380.02570.02760.0291
640.00850.00900.01020.01110.01210.01640.02180.02340.02520.02710.0286
650.00840.00890.01010.01090.01190.01610.02150.02300.02470.02660.0281
660.00820.00880.00990.01080.01170.01590.02110.02250.02420.02610.0276
670.00810.00870.00980.01070.01150.01570.02070.02210.02370.02560.0271
680.00800.00860.00960.01050.01140.01550.02040.02170.02320.02510.0266
690.00790.00850.00950.01040.01130.01520.01980.02130.02270.02460.0261
700.00780.00840.00940.01030.01110.01500.01940.02090.02220.02410.0256
710.00770.00830.00930.01020.01090.01470.01910.02050.02180.02370.0251
720.00760.00820.00920.01010.01080.01450.01880.02010.02140.02320.0246
730.00750.00810.00910.01000.01070.01430.01850.01980.02110.02280.0241
740.00740.00800.00900.00980.01060.01410.01820.01950.02080.02240.0236
750.00730.00790.00890.00970.01050.01390.01790.01920.02050.02200.0231
760.00730.00780.00880.00960.01040.01370.01760.01890.02020.02170.0227
770.00720.00770.00870.00950.01030.01350.01730.01860.01990.02140.0223
780.00710.00770.00860.00930.01010.01340.01700.01830.01960.02110.0219
790.00700.00760.00850.00920.01000.01320.01680.01800.01930.02080.0215
800.00700.00750.00840.00910.00990.01310.01660.01770.01900.02050.0211
810.00690.00740.00830.00900.00980.01290.01640.01750.01870.02020.0207
820.00680.00740.00820.00880.00970.01280.01620.01730.01840.01990.0203
830.00670.00730.00810.00870.00960.01260.01600.01700.01810.01960.0199
840.00670.00730.00800.00860.00950.01250.01580.01680.01780.01930.0196
850.00650.00720.00790.00850.00940.01230.01560.01660.01740.01900.0193
860.00660.00710.00780.00850.00930.01220.01540.01640.01720.01870.0190
870.00650.00710.00770.00840.00920.01200.01520.01620.01700.01840.0187
880.00650.00700.00770.00840.00910.01190.01500.01600.01680.01810.0185
890.00640.00700.00760.00830.00900.01170.01480.01580.01660.01790.0183
900.00640.00690.00750.00820.00890.01160.01470.01560.01640.01760.0181
910.00630.00680.00750.00820.00880.01140.01450.01540.01620.01730.0179
920.00630.00680.00740.00810.00870.01130.01430.01530.01600.01710.0177
930.00620.00670.00730.00810.00860.01120.01410.01510.01580.01680.0175
940.00620.00670.00730.00800.00850.01100.01390.01490.01560.01650.0173
950.00610.00660.00720.00790.00840.01090.01380.01470.01540.01630.0171
960.00610.00650.00720.00780.00830.01080.01360.01450.01530.01610.0169
970.00600.00650.00710.00770.00820.01070.01340.01430.01520.01590.0167
980.00600.00640.00700.00760.00810.01050.01330.01420.01510.01570.0165
990.00590.00640.00700.00750.00800.01040.01320.01400.01500.01550.0163
1000.00590.00630.00690.00740.00790.01030.01310.01390.01490.01530.0161