Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_spearman.wasp
Title produced by softwareSpearman Rank Correlation
Date of computationFri, 21 Apr 2023 19:15:44 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2023/Apr/21/t1682097417wbwype49uvbyh55.htm/, Retrieved Thu, 20 Aug 2026 09:47:14 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 20 Aug 2026 09:47:14 +0200
QR Codes:

Original text written by user:
IsPrivate?This computation is private
User-defined keywords
Estimated Impact0
Dataseries X:
21
53
56
65
68
34
83
66
66
42
58
24
78
45
93
34
23
27
36
40
44
51
65
64
55
57
27
35
66
62
56
67
49
43
59
80
36
71
80
60
44
69
65
62
40
30
19
51
88
68
82
45
64
60
47
60
53
51
34
34
38
44
20
21
75
42
68
62
62
Refused
78
54
55
61
58
41
53
28
34
82
46
94
63
50
68
24
26
57
64
53
71
71
89
57
64
80
80
79
67
57
45
27
86
57
62
80
71
44
46
72
48
68
40
72
50
59
36
72
30
63
58
64
58
33
66
62
54
39
78
47
42
19
31
61
81
39
40
51
73
72
55
52
78
66
53
64
46
51
62
52
37
23
64
62
56
52
37
41
20
51
24
68
75
34
75
52
72
51
52
56
32
52
44
53
41
43
35
68
62
62
43
69
20
74
44
77
87
69
34
56
83
53
60
34
86
63
65
68
65
74
61
59
66
86
74
29
32
24
63
53
87
48
53
29
73
41
64
31
83
46
50
29
51
57
42
42
18
50
78
52
33
34
33
66
54
81
24
66
69
55
37
53
37
74
61
58
57
47
64
22
35
30
67
80
22
62
56
70
73
82
21
47
42
67
55
60
63
50
85
78
57
76
67
44
28
47
19
62
74
38
81
61
63
64
60
85
71
23
83
52
41
29
78
24
24
45
18
34
80
38
33
81
39
23
80
25
43
44
75
63
41
30
35
67
32
42
50
46
69
31
39
48
18
69
96
36
56
50
79
46
63
59
49
65
24
45
62
48
59
67
75
82
60
42
60
69
42
82
66
57
60
31
56
57
41
84
90
72
65
66
59
55
82
32
88
72
29
59
30
51
38
43
42
33
44
74
52
48
74
72
58
70
19
41
68
28
30
35
86
44
35
28
66
54
51
23
32
64
82
54
82
32
31
47
35
Refused
Refused
58
20
30
71
33
51
70
32
46
37
50
82
57
59
28
77
70
19
37
60
59
67
40
83
62
24
36
58
Refused
33
57
32
43
65
36
Refused
75
55
89
89
20
74
23
61
78
29
80
43
21
70
20
64
80
32
33
57
31
47
19
31
27
33
40
53
31
29
71
40
23
Refused
51
80
73
61
64
34
28
80
57
18
58
36
34
39
19
40
41
54
62
85
25
52
36
48
33
34
30
26
48
59
87
33
76
32
46
59
75
80
42
37
27
45
78
29
70
60
38
Refused
26
66
Refused
45
33
65
73
25
36
41
63
47
35
37
54
41
40
39
40
Refused
21
74
27
39
41
29
52
37
31
38
40
44
53
50
87
61
36
Refused
62
29
69
47
23
33
59
47
29
22
33
54
47
37
63
38
48
28
26
71
24
59
26
21
71
28
38
71
49
40
26
67
68
57
50
75
58
83
85
57
24
84
66
40
70
20
75
33
22
69
36
49
69
85
84
48
34
62
70
43
72
30
55
76
69
70
54
30
20
90
26
56
45
45
35
24
61
57
35
56
31
46
44
57
36
56
73
61
86
46
89
34
27
38
69
90
62
88
38
30
71
23
49
Refused
68
22
59
52
36
44
91
38
22
69
64
52
90
23
42
58
68
52
58
24
82
75
54
72
65
81
44
36
69
82
32
31
31
52
29
24
42
79
52
82
80
70
78
76
32
33
47
56
36
30
50
40
66
55
74
55
84
66
33
34
21
22
22
55
35
24
41
61
39
95
32
37
69
50
59
45
43
74
67
39
33
67
43
52
54
65
61
71
47
31
60
60
32
42
27
41
22
32
31
57
67
69
62
53
80
47
42
34
30
48
25
78
39
72
26
67
70
26
37
34
35
46
57
79
76
33
65
34
40
75
28
33
44
43
68
42
75
56
49
55
32
25
42
31
28
63
66
82
35
62
65
64
45
38
67
73
71
42
34
29
22
71
73
31
50
25
37
63
30
54
86
70
45
69
58
76
70
66
75
74
45
46
77
56
23
29
42
42
27
84
63
79
73
38
35
48
45
72
46
21
26
57
22
51
31
42
72
61
37
40
52
78
63
58
26
41
29
44
48
75
65
48
50
34
61
42
41
73
63
63
78
69
71
49
38
50
66
24
48
55
76
61
48
18
37
46
71
53
55
18
70
44
38
44
23
23
73
62
71
49
68
54
59
71
48
57
43
45
68
72
66
37
44
79
90
65
31
71
72
67
71
64
22
74
59
57
73
33
24
63
27
31
55
41
54
72
51
32
61
34
66
58
34
46
66
39
18
41
42
81
82
42
52
22
75
54
73
74
26
47
29
69
48
67
41
59
42
32
44
41
45
57
87
55
51
81
86
52
31
37
28
94
28
32
63
80
62
60
52
65
37
59
63
66
37
59
41
53
36
49
50
35
55
71
38
65
42
82
57
73
91
54
60
56
58
52
83
51
42
58
40
69
35
40
27
57
26
43
40
86
59
37
55
20
48
63
40
97
31
44
36
42
22
53
40
87
27
59
62
69
18
69
42
56
38
32
61
41
36
60
36
49
72
55
22
49
35
38
43
31
56
47
43
28
28
57
27
58
23
55
62
58
93
68
68
70
66
55
46
70
49
55
43
58
48
32
69
65
72
54
36
62
79
42
45
50
52
70
33
61
55
21
34
72
70
51
52
85
72
28
63
78
52
60
56
74
58
66
71
25
69
69
51
74
55
59
56
71
84
87
51
30
60
32
73
28
49
72
23
75
24
22
75
45
46
48
57
50
46
53
50
54
80
32
51
22
36
70
64
55
59
70
89
46
44
54
52
28
61
29
45
83
51
60
62
79
57
82
66
43
67
52
47
33
62
45
52
76
62
84
59
45
60
70
80
31
49
80
53
18
86
62
70
69
32
40
56
36
23
42
70
38
53
47
70
21
41
24
36
48
78
29
46
69
59
36
63
71
35
33
32
70
81
64
62
67
62
67
73
82
63
49
54
44
58
47
39
65
71
47
80
58
50
46
89
35
26
58
51
55
62
35
27
81
29
72
47
70
70
26
46
28
59
34
28
18
43
26
20
64
19
55
23
56
22
52
24
42
23
44
29
46
39
51
51
69
51
64
43
36
55
60
82
72
78
35
59
55
56
47
73
64
18
89
66
64
60
69
20
70
64
63
73
30
45
50
36
35
34
70
52
44
71
51
19
34
22
47
82
31
28
38
29
39
53
46
47
23
26
32
66
61
32
33
68
51
69
60
47
47
42
36
24
31
54
43
45
31
25
46
57
53
49
55
38
41
71
54
74
76
79
76
90
30
33
75
67
31
80
45
87
46
53
76
22
47
52
82
78
55
40
72
82
37
42
34
49
63
75
42
50
58
31
67
91
69
59
34
69
67
62
50
28
68
70
88
53
69
76
74
52
18
26
36
30
44
28
24
42
41
78
77
71
70
71
29
32
66
60
20
69
74
65
80
66
54
75
33
69
70
35
62
44
80
74
22
28
55
25
78
58
99
76
77
75
44
37
49
54
66
45
39
26
71
62
50
74
44
79
40
21
55
61
52
56
68
29
26
43
30
56
68
40
65
66
27
54
19
72
71
77
42
52
45
33
57
22
56
34
46
42
56
80
85
85
95
73
45
62
31
54
26
30
74
21
54
20
30
78
33
50
52
32
65
46
68
57
46
56
36
31
45
19
71
73
53
72
71
63
68
57
83
68
41
61
73
25
29
27
39
35
39
61
80
85
27
65
20
35
36
63
60
68
47
29
62
61
70
50
73
86
75
19
81
87
95
80
61
23
75
62
67
62
59
67
21
48
Refused
64
41
53
59
72
71
26
35
36
45
33
75
47
24
79
56
80
Refused
67
43
24
49
39
34
58
47
47
66
65
29
42
60
36
24
25
26
66
24
20
25
19
23
22
22
22
22
79
18
67
34
78
41
46
54
51
55
46
32
29
87
29
83
45
60
55
79
45
69
88
72
63
78
24
60
89
37
27
46
68
64
61
81
87
59
83
66
73
66
52
78
26
32
51
77
20
31
35
57
26
68
36
36
40
29
34
50
65
64
Refused
79
80
74
69
71
31
25
Refused
83
84
61
52
79
40
21
69
70
53
40
67
62
38
52
72
67
58
63
33
40
31
20
36
54
43
72
42
74
67
72
29
50
60
64
40
65
63
38
24
56
41
23
60
80
42
76
85
35
27
62
43
27
56
59
70
71
73
43
67
19
48
68
66
60
41
52
30
54
71
70
51
61
44
27
53
55
56
28
69
67
65
53
61
30
39
58
25
67
24
19
65
23
64
61
53
58
65
18
73
29
69
61
63
73
56
37
51
60
38
46
68
32
42
23
61
19
77
30
26
24
44
81
45
51
48
50
40
54
58
45
77
30
66
54
79
76
50
80
59
47
26
64
71
73
79
62
72
74
72
42
59
80
53
75
89
72
53
73
61
88
65
50
90
55
69
48
71
67
49
73
32
37
40
65
36
28
42
95
53
30
65
78
58
62
31
75
52
32
55
78
62
75
75
Refused
57
63
49
56
68
64
76
42
62
51
48
27
41
32
76
45
69
50
23
71
21
49
43
57
39
80
93
29
72
26
76
54
53
71
68
61
57
73
61
43
62
84
68
80
35
36
23
30
81
74
66
Refused
24
50
58
77
42
39
52
51
48
45
77
44
67
67
48
45
67
69
20
66
48
75
31
55
56
78
59
67
41
90
42
89
31
51
57
72
32
50
52
57
60
55
45
35
85
63
38
47
20
29
44
36
73
52
59
42
23
45
36
38
89
70
26
53
20
54
31
42
64
37
62
74
54
19
64
58
80
47
71
56
73
71
39
46
69
63
37
56
37
81
26
75
66
67
62
59
52
58
18
22
24
52
74
Refused
58
52
80
52
53
34
72
65
58
63
51
35
66
Refused
31
26
54
30
71
25
62
38
19
63
43
46
51
53
63
44
37
76
22
62
42
39
51
50
90
75
48
81
89
51
29
46
51
74
35
66
46
39
72
73
51
25
82
84
34
54
22
65
64
19
31
44
67
77
75
54
44
55
49
75
53
53
59
46
50
82
86
Dataseries Y:
4
4
3
4
4
3
4
4
4
3
2
2
3
4
3
3
2
3
4
3
4
4
3
4
4
4
4
3
1
4
4
1
2
4
4
2
3
3
3
3
4
4
3
4
4
4
1
2
3
3
4
4
3
3
1
3
2
4
1
2
3
3
4
4
4
3
4
3
2
2
3
3
3
3
4
3
3
4
3
4
3
3
2
1
3
4
4
3
4
3
3
4
1
2
2
3
1
1
4
2
4
3
3
2
3
4
4
4
3
4
4
4
3
4
4
4
4
4
4
4
3
4
2
3
4
4
3
3
1
3
3
3
2
4
4
3
3
2
3
4
4
2
3
4
1
4
3
4
1
3
4
2
4
4
4
4
4
4
2
4
3
4
4
2
1
4
4
3
3
3
4
3
2
4
4
3
3
4
3
3
3
4
4
4
3
4
4
4
3
4
4
4
4
3
4
4
4
4
3
3
3
3
4
4
3
3
3
1
4
4
3
2
2
4
4
1
4
4
3
4
4
4
3
3
4
2
F
3
4
4
4
4
3
4
4
4
4
4
4
2
2
3
2
4
3
3
4
4
3
3
4
3
3
4
2
3
4
2
4
4
4
4
3
4
3
1
3
1
4
2
4
4
3
3
2
2
4
4
4
4
4
4
4
3
4
4
4
3
4
3
2
3
2
1
3
3
3
1
3
4
2
3
3
4
4
3
2
3
3
4
2
3
3
2
4
2
3
2
3
3
1
3
3
3
1
2
4
4
4
4
3
4
2
4
3
2
3
4
3
3
4
4
4
1
4
4
4
4
3
3
4
4
4
4
2
4
3
4
4
4
4
3
4
4
3
4
2
1
3
2
1
1
4
3
4
4
3
4
4
3
3
2
3
4
4
4
4
4
2
2
3
1
3
3
4
3
2
4
4
2
4
3
4
3
2
2
4
4
2
1
4
3
3
3
3
4
1
4
4
3
2
2
3
4
4
1
4
2
4
4
4
4
3
4
3
2
3
4
2
3
4
4
4
4
3
4
4
1
2
3
4
4
4
4
4
4
4
4
3
3
1
4
4
4
2
4
4
4
4
4
2
3
4
4
4
4
3
4
4
4
3
4
2
4
4
4
2
3
3
3
4
2
4
3
3
3
3
2
3
2
4
3
1
3
2
2
4
2
4
4
4
4
4
4
3
2
3
1
4
3
4
2
4
2
3
3
2
3
2
3
4
4
3
4
3
4
2
2
3
4
2
3
4
4
3
3
4
3
4
4
4
4
4
3
4
4
3
4
3
4
4
2
1
3
1
4
1
4
3
4
4
3
4
4
4
3
4
3
3
4
4
1
4
4
2
2
2
4
2
1
4
4
3
2
4
4
3
1
4
2
2
4
4
1
1
4
1
3
1
3
3
3
2
2
2
4
4
3
1
4
4
4
1
3
3
2
4
4
4
3
3
4
4
2
3
3
2
2
3
4
2
1
4
2
4
3
4
3
4
4
2
3
3
4
1
3
4
3
2
4
4
1
1
1
2
2
3
3
2
1
3
3
2
1
2
3
4
4
4
2
1
2
3
4
3
4
4
4
1
3
3
3
2
4
1
3
4
1
3
4
3
2
2
3
2
4
4
2
3
4
4
4
4
4
4
3
1
1
4
2
4
4
4
3
4
4
4
4
4
3
3
2
4
4
4
4
3
3
3
3
2
3
2
2
3
2
3
4
2
3
3
4
3
2
3
3
3
3
3
2
2
2
3
3
2
3
2
4
3
2
4
4
3
4
4
1
4
2
2
2
4
2
1
4
1
2
4
4
4
2
4
3
4
4
1
3
4
2
3
4
3
3
4
4
4
4
3
4
1
4
4
4
4
4
1
3
4
3
3
1
3
3
3
2
3
4
4
4
1
1
1
4
4
2
4
4
4
4
4
4
3
4
4
4
3
4
3
2
1
2
3
3
1
4
3
1
3
4
2
4
3
2
4
2
2
4
2
3
2
4
3
2
4
4
3
2
4
2
4
3
4
4
4
3
4
3
4
3
2
1
2
4
4
2
4
3
1
4
2
3
4
3
4
3
4
4
4
1
3
3
2
4
3
4
4
3
2
4
2
2
4
4
3
4
2
3
4
4
2
3
3
3
1
4
2
4
4
3
4
4
4
3
2
4
4
3
4
4
4
4
4
4
3
2
4
3
3
2
2
1
4
4
4
4
1
4
4
4
3
4
4
3
4
4
4
3
4
4
2
4
4
4
4
3
3
2
2
2
2
2
4
3
2
1
4
2
4
3
3
3
4
3
3
2
1
4
4
3
4
2
1
3
2
3
4
3
4
2
3
2
3
2
2
3
4
3
3
2
4
3
3
3
4
3
3
4
3
2
2
4
4
3
1
4
4
1
3
3
4
4
2
2
3
4
2
3
4
4
3
4
4
3
1
4
3
3
4
1
2
2
2
3
2
2
2
4
3
1
2
3
2
2
2
3
1
2
3
2
4
4
3
3
4
4
4
3
4
4
3
3
3
3
3
1
2
3
3
1
2
3
4
4
2
2
3
3
3
3
3
2
4
3
2
4
4
3
4
3
4
4
3
4
4
3
4
2
4
2
2
2
3
3
3
4
3
2
2
3
3
3
4
2
3
1
4
3
3
4
3
4
2
4
4
3
3
3
2
3
2
1
3
1
3
3
4
2
4
1
2
3
4
4
2
4
2
4
3
1
2
4
2
1
2
2
4
4
1
3
4
4
2
3
4
4
3
4
4
3
4
4
3
4
4
2
3
3
3
4
4
4
4
4
4
4
4
4
3
3
4
4
4
4
4
4
3
4
1
2
4
4
2
4
3
4
3
4
4
3
3
4
2
4
1
1
3
4
4
4
4
3
3
4
4
4
2
4
3
2
2
4
4
3
4
4
3
4
3
1
3
4
4
3
3
4
4
4
1
4
1
3
2
3
3
4
4
3
4
4
2
4
2
2
2
4
4
4
4
2
4
3
4
2
1
4
3
2
4
3
2
4
4
4
4
1
3
1
4
4
3
1
3
4
4
1
3
3
4
4
4
2
1
4
4
4
4
2
4
4
4
4
2
4
3
4
4
1
4
4
4
4
3
3
4
4
3
4
1
4
3
1
2
3
3
3
4
3
3
4
4
4
3
4
2
2
3
4
3
4
2
4
4
2
4
4
4
4
3
4
4
3
3
4
3
3
1
1
3
4
4
2
3
1
4
4
2
3
4
4
4
3
4
4
4
4
2
4
4
1
2
3
4
3
4
4
3
3
3
4
1
4
4
2
4
4
4
2
4
4
4
4
3
4
4
4
4
4
4
3
4
3
4
4
4
3
4
2
4
3
3
4
4
4
3
3
2
4
4
3
2
4
3
4
3
3
3
4
3
3
4
3
4
4
4
4
4
1
4
4
4
2
2
4
3
2
3
2
3
4
4
3
3
4
4
3
3
3
3
3
3
4
4
3
4
4
4
4
4
4
2
4
1
3
4
3
4
4
1
3
3
3
2
4
3
4
3
4
2
3
4
2
2
2
4
3
3
3
2
4
4
4
4
3
4
1
3
4
3
4
4
2
4
3
3
3
4
4
4
4
3
3
4
4
1
4
4
4
2
4
4
2
4
4
3
3
4
3
4
3
4
4
4
4
2
4
4
1
4
4
4
4
4
4
4
4
4
3
3
3
3
3
3
2
4
4
4
4
4
3
4
3
4
3
2
4
4
3
3
4
3
3
2
3
3
1
3
4
4
4
4
3
3
4
4
3
3
1
1
2
4
3
4
4
4
2
4
3
2
1
3
1
1
1
4
2
3
4
4
3
1
3
3
3
4
3
3
3
4
4
4
3
2
3
3
3
3
2
4
4
4
4
4
4
3
4
4
1
4
3
4
4
3
4
3
4
4
3
4
4
4
3
3
3
1
2
4
3
4
4
4
4
1
3
3
4
3
3
2
3
3
4
4
3
4
3
4
3
3
2
2
4
4
4
4
1
4
4
4
4
4
4
1
4
4
4
3
3
4
3
3
4
3
3
4
3
4
4
4
4
4
4
3
4
3
4
4
4
4
4
4
3
4
4
4
4
4
4
4
3
1
2
4
2
4
4
3
4
3
2
2
3
4
3
4
4
3
3
2
3
3
4
4
2
3
3
3
3
4
2
1
4
3
3
4
3
4
3
3
3
4
3
3
2
4
3
4
3
4
3
4
3
3
4
3
4
2
4
4
2
4
4
4
4
3
3
4
3
4
4
3
2
1
3
3
4
4
2
4
3
4
4
2
3
3
3
4
4
3
4
4
4
2
4
4
4
3
4
2
4
4
2
4
3
4
3
1
4
3
4
4
4
1
4
4
3
2
4
4
3
4
4
4
4
4
4
3
2
4
2
3
1
4
3
4
4
4
4
1
3
2
4
1
4
2
3
4
3
4
2
4
4
4
2
3
4
4
3
1
3
3
4
1
4
4
1
4
4
4
3
3
2
2
3
4
4
3
1
4
4
3
3
3
3
4
2
4
4
3
3
3
2
4
4
2
1
4
3
4
4
4
2
3
4
3
4
4
4
3
3
4
4
4
4
4
2
2
2
2
3
4
1
4
4
4
2
1
4
3
3
4
3
4
3
4
2
3
4
2
4
4
4
4
3
4
3
3
3
4
2
4
4
3
2
2
3
3
3
1
2
4
1
4
3
4
2
2
1
3
3
4
3
4
3
2
2
4
4
3
4
4
4
4
4
4
4
3
4
1
1
3
2
2
3
3
3
4
3
2
3
4
3
3
4
4
4
3
4
3
3
3
3
2
4
4
3
1
3
3
4
4
4
3
4
3
4
3
4
2
4
4
4
3
4
4
4
4
4
3
4
3
1
4
4
3
3
4
4
4
4
4
3
4
2
4
1
3
3
2
2
2
3
4
4
4
1
4
2
4
2
2
3
4
1
4
3
4
3
3
4
3
3
2
2
3
3
4
2
3
4
4
4
4
2
2
4




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
k <- cor.test(x,y,method='spearman')
bitmap(file='test1.png')
plot(x,y,main='Scatterplot',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='test2.png')
plot(rank(x),rank(y),main='Scatterplot of Ranks',xlab=xlab,ylab=ylab)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Spearman Rank Correlation',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'rho',header=TRUE)
a<-table.element(a,k$estimate)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'2-sided p-value',header=TRUE)
a<-table.element(a,k$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S',header=TRUE)
a<-table.element(a,k$statistic)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')