Demo 32 -- some tests of sc v 1.63
[ Obtained using a 450 MHz Pentium II running Linux and gcc-compiled sc ]
[ the form /p/q/ for significance tests below gives the
left (p) and right (q) tail probabilities for the observed result ]
__________Mean and variance of 1,2,..,9 with 10^i added
i mean - 10^i variance
1 5 7.5
2 5 7.5
3 5 7.5
4 5 7.5
5 5 7.5
6 5 7.5
7 5 7.5
8 5 7.5
9 5 7.5
10 5 7.5
11 5 7.5
12 5 7.5
13 5 7.5
14 5 7.5
15 5 7.5
__________Ackermann function, testing recursion
time (secs)
ack( 1 , 1 )= 3 0
ack( 1 , 2 )= 4 0
ack( 1 , 3 )= 5 0
ack( 2 , 1 )= 5 0
ack( 2 , 2 )= 7 0
ack( 2 , 3 )= 9 0
__________small Wampler regression example using lsqs() (Givens)
Solution: 100000, 100000, 100000
100000 100000.01124944 99999.9887505597
__________same, using svdlsqs() (Singular Value Decomposition)
100000 99999.9999999999 100000
__________Testing Singular Value Decomposition routines
Data from Nash(1979), Example 3.2. Using svdlsqs()
Singular Values:
5298.56 345.511 0.0513828 36.1125 21.4209
All SVs in:
207.783 -0.0461924 1.01939 -0.159823 -0.290376
SVs <1 out:
0.0043336 -0.0585322 1.17569 -0.25229 0.699622
SVs <22 out:
0.0051426 0.0434834 0.392027 -0.0693359 1.0115
SVs <40 out:
0.0025459 -0.152991 0.300128 0.469295 0.528882
__________Longley (1967) regressions (JASA 62 819-841)
using lsqsregr() (Givens)
-3482258.6346 15.061872271 -0.035819179293
-2.0202298038 -1.0332268672 -0.051104105654
1829.1514646
-216183.11263 -59.348299379 -0.00023189170167
-0.094308284346 -0.31654691658 -0.09950747005
123.69160185
163482.24472 27.946704408 -0.00048918763524
0.043878613518 -0.24220940258 0.04335594633
-84.249501569
-186189.16704 5.8577810403 -0.0038417353173
-0.074452728762 -0.070583168664 0.0030939004368
96.009934126
134876.74572 -27.792935556 0.018027309611
0.19994872421 -0.063304307904 -0.14356789922
-61.646195843
-4030309.3837 39.424275592 -0.065996259704
-2.3196678654 -0.34243923231 0.049486671856
2096.2885735
384349.16874 3.392522056 0.010703514023
0.12647553773 0.20303490823 -0.0258688355
-196.76061019
267714.86965 25.581824111 0.0060090714316
0.097896199194 -0.20117874736 0.12190358049
-144.18233726
Average (user) time per regression, excluding I/O: 0 secs
__________same, using svdlsqs() (Singular Value Decomposition)
-3482258.6346 15.061872271 -0.035819179292
-2.0202298039 -1.0332268674 -0.051104105661
1829.1514646
-216183.11263 -59.348299379 -0.00023189170159
-0.094308284353 -0.31654691659 -0.099507470051
123.69160185
163482.24472 27.946704408 -0.00048918763529
0.043878613524 -0.24220940257 0.043355946331
-84.249501569
-186189.16704 5.8577810403 -0.0038417353173
-0.074452728769 -0.070583168674 0.0030939004364
96.009934126
134876.74572 -27.792935556 0.018027309611
0.19994872422 -0.063304307897 -0.14356789922
-61.646195843
-4030309.3837 39.424275592 -0.065996259703
-2.3196678655 -0.34243923253 0.049486671847
2096.2885735
384349.16874 3.392522056 0.010703514023
0.12647553774 0.20303490825 -0.0258688355
-196.76061019
267714.86965 25.581824111 0.0060090714315
0.097896199203 -0.20117874735 0.12190358049
-144.18233726
Average (user) time per regression, excluding I/O: 0.00125 secs
__________Wampler (1970) JASA 65 p549-565 : problem Y1
Solution: 1, 1, 1, 1, 1, 1
Using lsqs() (Givens):
1.00000000005599 ( 10.252 )
0.999999999990997 ( 11.046 )
1.0000000000094 ( 11.027 )
0.999999999998721 ( 11.893 )
1.00000000000006 ( 13.232 )
0.999999999999999 ( 15.051 )
....average # correct digits= 12.084
Using svdlsqs() (Singular Value Decomposition):
1.00000000040327 ( 9.3944 )
0.999999999778143 ( 9.6539 )
1.00000000006606 ( 10.18 )
0.999999999992418 ( 11.12 )
1.00000000000038 ( 12.425 )
0.999999999999993 ( 14.155 )
....average # correct digits= 11.155
__________Wampler (1970) JASA 65 p549-565 : problem Y2
Solution: 1, .1, .01, .001, .0001, .00001
Using lsqs() (Givens):
0.999999999999999 ( 15.256 )
0.0999999999999994 ( 14.245 )
0.0100000000000005 ( 13.342 )
0.000999999999999922 ( 13.108 )
0.000100000000000005 ( 13.3 )
9.99999999999989e-06 ( 13.965 )
....average # correct digits= 13.869
Using svdlsqs() (Singular Value Decomposition):
1.00000000000406 ( 11.392 )
0.0999999999999941 ( 13.23 )
0.010000000000002 ( 12.701 )
0.000999999999999778 ( 12.654 )
0.000100000000000014 ( 12.858 )
9.99999999999446e-06 ( 12.256 )
....average # correct digits= 12.515
__________Do then undo a fast Fourier transform, length 512
.. forward transform .. reverse transform (time: 0 secs)
Biggest change was 3.33066907387547e-16
__________Invert then re-invert a matrix
Matrix is: A(i,i)= N+1, A(i,j)= N, i<>j; N is 15
.. inverting .. re-inverting (time: 0 secs)
Biggest change was 7.46069872548105e-14
__________Solve the equations:
x + 3y - 4z = 8
x + y - 2z = 2
-x - 2y + 5z = -1
x= 1 y= 5 z= 2
Time: 0 secs
__________Minimize x-squared, x in (-1,1), using minimize1
Minimum is 0 at x= 0
Time: 0 secs
__________Minimize Rosenbrock's parabolic valley function
y= 100(b-a^2)^2 + (1-a)^2
Starting point: a= -1.2, b= 1
Solution: minimum of 0 at 1,1
Minimum is 6.07447639246426e-19 at:
0.99999999953864 0.999999999601456
Time: 0 secs
__________Minimize Powell's quartic function
y= (a+10b)^2 + 5(c-d)^2 + (b-2c)^4 + 10(a-d)^4
Starting point: a= 3, b= -1, c= 0, d= 1
Solution: minimum of 0 at 0,0,0,0
Minimum is 2.08825171663833e-17 at:
-9.40391835889073e-06 -9.40597467942905e-07 2.33335224006967e-05 2.3333600784477e-05
Time: 0.01 secs
__________Stem-and-leaf of a standard normal sample (n=80)
#80 stem unit: 1
2 -2* 43 8
5 -1. 80 69 51
13 -1* 43 39 38 34 32 23 8 7
23 -0. 93 91 90 88 87 85 68 58 53 51
(19)-0* 48 48 46 46 44 41 38 37 36 35 33 27 24 21 19 16 12 12 6
38 0* 4 5 8 9 12 13 13 14 17 21 32 32 33 33 41
23 0. 52 55 59 59 60 61 63 79 91 95 96 99
11 1* 6 13 16 17 24 24 34
4 1. 52 52 66
1 2* 45
__________Critically large Chisquare
df 0.05 0.01 0.001 0.0001
1 3.8414 6.6349 10.8276 15.1367
2 5.9914 9.2103 13.8155 18.4207
3 7.8147 11.3449 16.2662 21.1075
4 9.4877 13.2767 18.4668 23.5127
5 11.0705 15.0863 20.515 25.7448
6 12.5916 16.8119 22.4577 27.8563
7 14.0671 18.4753 24.3219 29.8775
8 15.5073 20.0902 26.1245 31.8276
9 16.919 21.666 27.8772 33.7199
10 18.307 23.2093 29.5883 35.564
11 19.6751 24.725 31.2641 37.367
12 21.0261 26.217 32.9095 39.1344
13 22.362 27.6882 34.5282 40.8707
14 23.6848 29.1412 36.1233 42.5793
15 24.9958 30.5779 37.6973 44.2632
16 26.2962 31.9999 39.2524 45.9249
17 27.5871 33.4087 40.7902 47.5664
18 28.8693 34.8053 42.3124 49.1894
19 30.1435 36.1909 43.8202 50.7955
20 31.4104 37.5662 45.3147 52.386
21 32.6706 38.9322 46.797 53.962
22 33.9244 40.2894 48.2679 55.5246
23 35.1725 41.6384 49.7282 57.0746
24 36.415 42.9798 51.1786 58.613
25 37.6525 44.3141 52.6197 60.1403
26 38.8851 45.6417 54.052 61.6573
27 40.1133 46.9629 55.476 63.1645
28 41.3371 48.2782 56.8923 64.6624
29 42.557 49.5879 58.3012 66.1517
30 43.773 50.8922 59.7031 67.6326
31 44.9853 52.1914 61.0983 69.1057
32 46.1943 53.4858 62.4872 70.5712
33 47.3999 54.7755 63.8701 72.0296
34 48.6024 56.0609 65.2472 73.4812
35 49.8018 57.3421 66.6188 74.9262
36 50.9985 58.6192 67.9852 76.365
37 52.1923 59.8925 69.3465 77.7977
38 53.3835 61.1621 70.7029 79.2247
39 54.5722 62.4281 72.0547 80.6462
40 55.7585 63.6907 73.402 82.0623
Average time per value, including I/O: 6.25e-05 secs
__________Critically large Student t
df 0.05 0.01 0.001 0.0001
1 6.3137 31.8205 318.309 3183.1
2 2.9199 6.9645 22.3271 70.7001
3 2.3533 4.5407 10.2145 22.2037
4 2.1318 3.7469 7.1731 13.0337
5 2.0150 3.3649 5.8934 9.6775
6 1.9431 3.1426 5.2076 8.0247
7 1.8945 2.9979 4.7852 7.0634
8 1.8595 2.8964 4.5007 6.4420
9 1.8331 2.8214 4.2968 6.0101
10 1.8124 2.7637 4.1437 5.6938
11 1.7958 2.7180 4.0247 5.4527
12 1.7822 2.681 3.9296 5.2632
13 1.7709 2.6503 3.8519 5.1105
14 1.7613 2.6244 3.7873 4.9850
15 1.7530 2.6024 3.7328 4.88
16 1.7458 2.5834 3.6861 4.7909
17 1.7396 2.5669 3.6457 4.7144
18 1.7340 2.5523 3.6104 4.6480
19 1.7291 2.5394 3.5794 4.5898
20 1.7247 2.5279 3.5518 4.5385
21 1.7207 2.5176 3.5271 4.4928
22 1.7171 2.5083 3.5049 4.4519
23 1.7138 2.4998 3.4849 4.4152
24 1.7108 2.4921 3.4667 4.3819
25 1.7081 2.4851 3.4501 4.3516
26 1.7056 2.4786 3.435 4.3240
27 1.7032 2.4726 3.4210 4.2987
28 1.7011 2.4671 3.4081 4.2754
29 1.6991 2.4620 3.3962 4.2538
30 1.6972 2.4572 3.3851 4.2339
31 1.6955 2.4528 3.3749 4.2155
32 1.6938 2.4486 3.3653 4.1983
33 1.6923 2.4447 3.3563 4.1822
34 1.6909 2.4411 3.3479 4.1672
35 1.6895 2.4377 3.3400 4.1531
36 1.6883 2.4344 3.3326 4.1399
37 1.6870 2.4314 3.3256 4.1274
38 1.6859 2.4285 3.3190 4.1157
39 1.6848 2.4258 3.3127 4.1046
40 1.6838 2.4232 3.3068 4.0942
41 1.6828 2.4208 3.3012 4.0842
42 1.6819 2.4184 3.2959 4.0748
43 1.6810 2.4162 3.2908 4.0659
44 1.6802 2.4141 3.2860 4.0574
45 1.6794 2.4121 3.2814 4.0493
46 1.6786 2.4101 3.2771 4.0416
47 1.6779 2.4083 3.2729 4.0342
48 1.6772 2.4065 3.2689 4.0272
49 1.6765 2.4048 3.2650 4.0204
50 1.6759 2.4032 3.2614 4.0140
51 1.6752 2.4017 3.2578 4.0078
52 1.6746 2.4002 3.2545 4.0019
53 1.6741 2.3987 3.2512 3.9962
54 1.6735 2.3974 3.2481 3.9908
55 1.6730 2.3960 3.2451 3.9855
56 1.6725 2.3948 3.2422 3.9805
57 1.6720 2.3935 3.2394 3.9756
58 1.6715 2.3923 3.2368 3.9709
59 1.6710 2.3912 3.2342 3.9664
60 1.6706 2.3901 3.2317 3.9620
61 1.6702 2.3890 3.2293 3.9578
62 1.6698 2.3880 3.2269 3.9538
63 1.6694 2.3870 3.2247 3.9498
64 1.6690 2.3860 3.2225 3.9460
65 1.6686 2.3851 3.2204 3.9424
66 1.6682 2.3841 3.2183 3.9388
67 1.6679 2.3833 3.2163 3.9354
68 1.6675 2.3824 3.2144 3.9320
69 1.6672 2.3816 3.2126 3.9288
70 1.6669 2.3808 3.2107 3.9256
71 1.6666 2.3800 3.2090 3.9226
72 1.6662 2.3792 3.2073 3.9196
73 1.666 2.3785 3.2056 3.9168
74 1.6657 2.3778 3.2040 3.914
75 1.6654 2.3771 3.2024 3.9112
76 1.6651 2.3764 3.2009 3.9086
77 1.6648 2.3757 3.1994 3.9060
78 1.6646 2.3751 3.1980 3.9035
79 1.6643 2.3744 3.1966 3.9011
80 1.6641 2.3738 3.1952 3.8987
81 1.6638 2.3732 3.1939 3.8964
82 1.6636 2.3726 3.1926 3.8941
83 1.6634 2.3721 3.1913 3.892
84 1.6632 2.3715 3.1901 3.8898
85 1.6629 2.3710 3.1889 3.8877
86 1.6627 2.3704 3.1877 3.8857
87 1.6625 2.3699 3.1865 3.8837
88 1.6623 2.3694 3.1854 3.8817
89 1.6621 2.3689 3.1843 3.8798
90 1.6619 2.3685 3.1832 3.8780
91 1.6617 2.3680 3.1822 3.8762
92 1.6615 2.3675 3.1811 3.8744
93 1.6614 2.3671 3.1801 3.8727
94 1.6612 2.3666 3.1792 3.8710
95 1.6610 2.3662 3.1782 3.8693
96 1.6608 2.3658 3.1773 3.8677
97 1.6607 2.3654 3.1763 3.8661
98 1.6605 2.365 3.1754 3.8646
99 1.6603 2.3646 3.1746 3.8630
100 1.6602 2.3642 3.1737 3.8616
Average time per value, including I/O: 5e-05 secs
__________Kendall S right tail, n=8
0 0.548
2 0.452
4 0.36
6 0.274
8 0.199
10 0.138
12 0.0894
14 0.0543
16 0.0305
18 0.0156
20 0.00707
22 0.00275
24 0.000868
26 0.000198
28 2.48e-05
Average time per value, including I/O: 0 secs
__________Binomial point probability and right tail, n=20, p=.5
0 9.53674e-07 1
1 1.90735e-05 0.999999
2 0.000181198 0.99998
3 0.00108719 0.999799
4 0.00462055 0.998712
5 0.0147858 0.994091
6 0.0369644 0.979305
7 0.0739288 0.942341
8 0.120134 0.868412
9 0.160179 0.748278
10 0.176197 0.588099
11 0.160179 0.411901
12 0.120134 0.251722
13 0.0739288 0.131588
14 0.0369644 0.0576591
15 0.0147858 0.0206947
16 0.00462055 0.00590897
17 0.00108719 0.00128841
18 0.000181198 0.000201225
19 1.90735e-05 2.00272e-05
20 9.53674e-07 9.53674e-07
Average time per value, including I/O: 0 secs
__________Some robust and nonrobust estimators
SAT data from Hoaglin, Mosteller, & Tukey (1983, Table 12-11)
Rural Urban
mean 803 932
SD+ 120 177
median 812 900
Fspread 85 277
MAD 47 149
biweight(9) 821 931
Sbi(9) 98 179
huber(2) 815 932
tanh645 816 932
midmean 812 900
shortest .6-fraction 125 225
95% CI, SD+ 730 , 876 825 , 1039
95% CI, F-spread 764 , 860 744 , 1056
95% CI, biweight(9) 759 , 883 817 , 1044
Martinez & Iglewicz (1981) shape statistic
Rural: I= 1.51 ( I90= 1.33 , I95= 1.64 )
Urban: I= 1.01 ( I90= 1.33 , I95= 1.64 )
__________Median polish of Infant mortality data (2 iterations)
Data from Hoaglin, Mosteller & Tukey (1983, 6B)
Typical value: 20.6 (time: 0 secs)
Row effects: -1.55 2.95 -0.35 0.35
Col effects: 7.4 5.85 -0.9 0 -3.45
Residuals:
#20 stem unit: 1
1 -5 7
2 -4 6
4 -3 80
4 -2
6 -1 21
10 -0 8400
10 0 003478
4 1 2
3 2
3 3 0
2 4 9
1 hi (111)
__________polish of the same data using trimmed means (2 iterations)
trimming fraction 0.25
Typical value: 22.4 (time: 0 secs)
Row effects: -2.05 2.13 0.797 -0.797
Col effects: 6.21 4.66 -3.07 -1.19 -4.87
Residuals:
M 10.5 0
F 5.5 -1.444 -0.1675 1.109 | 2.552
E 3 -2.71 0.1927 3.095 | 5.805
D 2 -5.21 -0.8355 3.539 | 8.75
C 1.5 -5.782 0.33 6.442 | 12.22
1 -6.355 1.495 9.345 | 15.7
__________Linear fits: Mickey's (1967) First word - Gesell data
See Rousseeuw & Leroy (1987), Robust Regression and
Outlier Detection, p46.
slope intercept
Least squares -1.127 109.9
Tukey -0.5714 103.6
Sen -0.875 108.8
Siegel -0.3333 100
Rousseeuw -1.375 117.6
Least median of squares= 15.02 (Note: smaller than R&L's!)
__________Checking consistency of Normal and inverse Normal
Biggest difference in 100 cases is 4.193e-12 at p= 0.8958
__________Checking consistency of t and inverse t
df random in [1,200]
Biggest difference in 100 cases is 2.206e-07 at df= 4 and p= 0.9848
__________Checking SS- and df- decomposition by avbc
Fox (1984), Linear Statistical Models & Related Methods
Tables 2.6 & 2.8.
SS df MS F p
A 264.6 2 132.3 4.3409 0.0232
e(A) 822.9 27 30.478
__________Checking a smoothing routine (4253Ht)
Velleman & Hoaglin (1981) Exhibit 6.11
Smooth:
60 60.35938 60.57812 60.9375 62.21094 65.00781
67.84375 69.28125 69.84375 70.05078 69.53125 67.87109
65.5625 63.00781 59.93359 55.79297 51.82812 50.23438
50.20312 52.03516 55.60547 57.375 57.13281 56.40625
55.41406 54.57812 54.1875 54.21484 54.57422 55.20312
Rough:
#30 stem unit: 10
1 -1. 5
2 -1* 4
6 -0. 9765
14 -0* 43322210
(11) 0* 00012233444
5 0. 78
3 1* 03
1 hi (26)
__________same data, using lowess with smoothing parameter .3
Smooth:
60.90904 61.25217 61.73557 62.11469 62.20473 63.53043
65.46928 65.75627 65.54934 66.88866 67.14991 65.84402
64.51605 63.09065 59.96964 56.40658 53.99168 52.70944
52.25653 53.66488 56.03665 56.72425 56.09758 56.02134
55.30584 53.82471 53.82151 54.35527 54.85807 55.3386
Rough:
#30 stem unit: 10
2 -1* 21
6 -0. 9866
14 -0* 44433321
(10) 0* 0223334444
6 0. 5589
2 1* 4
1 hi (29)
__________Bootstrap Standard Error of the product-moment coefficient
10 data points (x,y uncorrelated uniform random numbers)
50 bootstrap samples
SE estimate= 0.3653538 (time: 0 secs)
Bootstrap distribution of r:
#50 stem unit: 0.1
1 -5 3
3 -4 50
6 -3 443
8 -2 55
17 -1 866433221
22 -0 99663
25 0 099
25 1 35
23 2 26
21 3 22246779
13 4 45
11 5 15689
6 6 24
4 7 35
2 8 11
__________Checking bootstrap estimate of the Standard Error of the median
Sample size 20; 50 bootstrap samples; 20 replications
0.136661
0.1888541
0.1246847
0.3315034
0.358397
0.2113347
0.2178936
0.3889224
0.2493274
0.1696146
0.2128325
0.4468742
0.1362512
0.3496875
0.2101892
0.2991698
0.314317
0.2347494
0.3314881
0.2409116
mean 0.2576832 ( theoretical value= 0.2802496 )
__________Finding CI for a Binomial success probability
20 Bernoulli trials, 5 successes (using minimize1)
90%CI: 0.190983 to 0.440983
Time: 0 secs
__________Least squares and robust fits to Brownlee stack loss data
See Hoaglin, Mosteller, & Tukey (1985), 8.3
Least squares estimates: ( 0 secs):
-39.91967 0.7156402 1.295286 -0.1521225
L1 estimates: ( 0 secs):
-39.68986 0.8318841 0.573913 -0.06086957
R-estimates using Wilcoxon score-function ( 0 secs):
-40.04433 0.7916692 0.9075398 -0.111112
tau estimate from Wilcoxon interval (uncorrected for bias)= 2.734748
tau window estimate= 2.537063
Andrews estimates with cutoff 1.5pi ( 0.01 secs):
-37.13247 0.8182858 0.5195245 -0.07254989
Weight Residual
0 6.1
0.918 1.03
0 6.3
0 8.24
0.959 -0.719
0.882 -1.24
0.992 -0.323
0.964 0.677
0.928 -0.965
0.999 0.124
0.953 0.777
0.996 0.224
0.504 -2.73
0.841 -1.45
0.866 1.32
0.999 0.106
0.985 -0.429
1 0.0787
0.969 0.632
0.745 1.87
0 -8.94
__________Generating 100,000 random numbers
random uniform reals in [0,1], using qrand(): 0.01 secs
random uniform reals in [0,1], using randf(): 0.04 secs
random N[0,1], using randnorm(): 0.12 secs
random exponential, using randexp(): 0.06 secs
random Binomial [20,.5] using randbinom(): 0.81 secs
random Poisson [l=2] using randpoiss(): 0.07 secs
random Gamma [2] using randgamma(): 0.22 secs
random integers in [1,100] using irand_(): 0.06 secs
__________Sorting & shuffling 100,000 random numbers
sorting: 0.08 secs
shuffling: 0.03 secs
shuffling rows of 1000x100 matrix: 0.0003 secs
__________Some Exact (permutation-based) tests & intervals
_____unordered r-by-k contingency tables: likelihood statistic
2 0 1 2 6
1 3 1 1 1
1 0 3 1 0
1 2 1 2 0
p= 0.09111777 ( 0.03 secs)
2 0 1 2 6 5
1 3 1 1 1 2
1 0 3 1 0 0
1 2 1 2 0 0
p= 0.04537428 ( 0.14 secs)
____exact odds-ratio 95% 2-sided confidence interval:
442 7
915 62
uncond. OR= 4.278532
95 % cond. CI: 1.960842 to 9.544704
( 0 secs
_____exact Kendall tau (S)
n=30: x,y sampled independently from N[0,1]:
p= 0.7263456 ( 0.02 secs)
n= 40: 4 distinct values on each of x,y with occurrences:-
9 2 1 0
0 5 1 1
1 2 8 0
0 0 1 9
p= 3.175455e-11 ( 0.02 secs)
_____exact Spearman rho
x: 88 107 96 77 83 12 12 12 10 7 4 5 13 19 40 30 9 29
y: 114 143 191 115 125 14 10 15 6 9 6 10 16 15 17 40 9 32
p= 5.663287e-09 ( 0.05 secs)
_____exact Smirnov 2-sample test
nx= ny= 40: x,y sampled independently from N[0,1] & N[0,2]:
p= 0.006760732 ( 0 secs)
_____exact Mann-Whitney (Wilcoxon) 2-sample test
data (n= 63,31) in contingency table form:
1 2 3 2 1 3 4 1 9 3 3 3 3 0 3 1 2 0 0 2 1 1 0 0 1 1 0 1 1 1 0 2 1 2 1 1 1 1 1
1 1 0 2 1 2 2 0 0 1 3 1 1 3 1 2 2 1 1 0 1 0 1 2 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0
U= 967 / 0.47047 / 0.5311222 /
sum p(u) | p(u)<=p(U) & u>=U / 0.4705012 /
sum p(u) | p(u)<=p(U) // 0.939379 //
( 0.38 secs)
_____exact complete Mann-Whitney distribution
data (n= 25,25) random integers in [0,5]:
( 0.02 secs)
_____exact Wilcoxon 1-sample test
Sample from N[0,1], n=100:
T= 2117 / 0.08091873 / 0.9195979 /
( 0.01 secs)
_____exact permutation-based 99% interval for mean:
Samples, n=10, from N[0,1] and N[1,1]:
-0.04573049 to 3.574643 ( 0.01 secs)
_____exact multivariate permutation test:
statistic is no. of crossovers in minimum spanning tree
group sizes: 4,14 no. of variables: 4
[ kc[18][4] ]
. 1 2 36.3
.. 2 3 60
. 1 4 64.5
.. 4 5 15.9
. 1 16 96.5
.. 16 15 59.2
... 15 14 36.3
.... 14 13 6.24
..... 13 6 7.55
..... 13 10 15.3
...... 10 17 5.48
....... 17 7 5.48
........ 7 9 4.69
......... 9 11 6.16
.......... 11 12 5.74
....... 17 8 6.78
... 15 18 27.1
crossings= 2 / 0.005553741 / 0.9993466 /
( 0.5 secs)
_____exact multivariate permutation test:
statistic is Boyett & Schuster's
same problem as previously
max scaled difference= 3.982022 / 0.9990196 / 0.0009803922 /
max scaled abs(difference)= 3.982022 / 0.0009803922 /
( 0.3 secs)
..end of demo32