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8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
1/24
NATALIA KOCZKO 3IB
ANALYSING THE CORELATIONS BETWEEN THE LEAVES FROM
SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
DATA COLLECTIONTable 1 . Dimensions of the leaves on the sun-exposed side of the tree
No. Width [cm] 0.1 Length [cm] 0.1
1 96 1042 85 1003 100 1114 95 1255 92 1056 91 110
7 89 978 115 120
9 92 11810 80 95
11 119 12312 91 115
13 94 10914 110 13515 105 10816 95 11217 83 9918 100 121
19 103 1082 90 100
021 84 11222 110 14523 90 11624 85 11025 96 11426 107 12027 110 12328 105 140
29 106 12830 105 117
31 90 12732 118 13533 60 9034 84 10635 98 13036 99 11037 102 132
38 92 11339 85 12040 117 135
41 75 9642 110 132
43 80 11044 98 12145 112 13546 90 11247 83 13048 105 114
49 85 97
50 107 122
Table 2. Dimensions of the leaves on the shadowed side of the tree
1
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
2/24
No. Width [cm] 0.1 Length [cm] 0.11 50 732 72 933 67 1004 70 1045 100 130
6 100 1237 42 56
8 52 110
9 60 8010 91 11611 70 9312 65 9213 68 9714 100 12415 43 60
16 92 13717 54 73
18 83 11619 61 83
20 58 78
21 31 4222 86 11623 45 6224 57 8825 75 102
26 62 9627 47 53
28 94 13029 82 115
30 91 12231 75 10332 74 93
33 55 8834 65 9435 57 7536 77 10537 54 64
38 73 8439 72 80
40 80 10041 81 8742 76 9143 77 10244 94 101
45 83 9046 67 8347 75 102
48 73 8749 53 65
50 86 90
2
DATA PROCESSING
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
3/24
H0: there is no significant difference between the width of the leaves on the sun-exposed and shadowed side of the tree
H1: The dimensions of the leaves on the sun-exposed side are greater than thoseof the shadowed side
Table 3 . Checking for normal distribution for width of the leaves on the sun-exposed side of the tree
Class Frequency
60 69 I
70 79 I
80 89 IIIIIIIIIII
90 99 IIIIIIIIIIIIIIIIII
100 109 IIIIIIIIIII
110 119 IIIII
3
Student t-testIs a statistical test that allows determination of marginal differences between theexamined sets of data. Test can be applied is the test statistic follow a normaldistribution. In this particular case it will be used to check if there is a significantdifference between the width or the length of the leaves on the sun-exposed andshadowed side.
The distribution is slightly skewed but can be still referred to as tonormal
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
4/24
26.9650
4813
samplesofnumber
xx
1
1 ===
Table 4. Calculating standarddeviation for the leaves on the sun-exposed side of the tree
No.Width [cm]
0.1 (X1)Width [cm]
0.1 (X1 )
1 96 9216
2 85 7225
3 100 10000
4 95 9025
5 92 8464
6 91 82817 89 7921
8 115 13225
9 92 8464
10 80 6400
11 119 14161
12 91 8281
13 94 8836
14 110 12100
15 105 11025
16 95 9025
17 83 688918 100 10000
19 103 10609
20 90 8100
21 84 7056
22 110 12100
23 90 8100
24 85 7225
25 96 9216
26 107 11449
27 110 12100
28 105 1102529 106 11236
30 105 11025
31 90 8100
32 118 13924
33 60 3600
34 84 7056
35 98 9604
36 99 9801
37 102 10404
38 92 8464
39 85 7225
40 117 13689
41 75 5625
42 110 12100
43 80 6400
44 98 9604
45 112 12544
46 90 8100
47 83 6889
48 105 11025
49 85 7225
50 107 11449
Sum: 4813 470607
4
( )[ ]1n
nxxS
22
=
Calculations
49
504813470607S
2
=
21.12S=
S = 12.21 constitutes less than 33% of
the mean (96.22) what means that itis a is a small standard deviation
70 % off the data (35 leaves) fallswithin one standard deviation and98% of the data (49 leaves) fallswithin two standard deviations
Calculating the mean
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
5/24
Table 5 . Sorting the widths of the leaves on the sun-exposed side of the
tree
No. Width [cm] 0.1 (X1) Sorted value
1 96 60
2 85 75
3 100 80
4 95 80
5 92 83
6 91 83
7 89 84
8 115 84
9 92 85
10 80 85
11 119 85
12 91 85
13 94 8914 110 90
15 105 90
16 95 90
17 83 90
18 100 91
19 103 91
20 90 92
21 84 92
22 110 92
23 90 94
24 85 9525 96 95
26 107 96
27 110 96
28 105 98
29 106 98
30 105 99
31 90 100
32 118 100
33 60 102
34 84 103
35 98 105
36 99 105
37 102 105
38 92 105
39 85 106
40 117 107
41 75 107
42 110 110
43 80 110
44 98 110
45 112 110
46 90 112
47 83 115
48 105 117
49 85 118
5
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
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50 107 119
Table 6. Checking for normal distribution for width of the leaves on theshadowed side of the tree
Class Frequency
30 39 I
40 49 IIII
50 59 IIIIIIIII
60 69 IIIIIIII
70 79 IIIIIIIIIIIII
80 89 IIIIIII
90 99 IIIII
100 109 III
6
There is a good normal distribution
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
7/24
3.7050
3515
samplesofnumber
x
x
2
2 ===
Table 7 . Calculating standard deviation for the leaves on the shadowed
side of the tree
Table 8 . Sorting the widths of the leaves on the shadowed side of the tree
No.Width [cm] (X2) 0.1
X2 0.1
1 50 2500
2 72 51843 67 4489
4 70 4900
5 100 100006 100 100007 42 17648 52 27049 60 3600
10 91 828111 70 4900
12 65 422513 68 4624
14 100 1000015 43 184916 92 8464
17 54 291618 83 688919 61 372120 58 336421 31 961
22 86 739623 45 2025
24 57 324925 75 562526 62 384427 47 220928 94 8836
29 82 672430 91 828131 75 5625
32 74 547633 55 3025
34 65 422535 57 324936 77 592937 54 291638 73 532939 72 518440 80 640041 81 6561
42 76 577643 77 5929
44 94 883645 83 6889
46 67 448947 75 562548 73 532949 53 280950 86 7396
Sum:
3515 260521
No. Width [cm] (X2) 0.1 Sorted value1 50 31
2 72 423 67 43
4 70 455 100 47
6 100 50
7 42 528 52 53
9 60 5410 91 54
11 70 5512 65 57
13 68 5714 100 58
15 43 6016 92 61
17 54 6218 83 65
19 61 6520 58 67
21 31 6722 86 68
23 45 70
24 57 7025 75 72
26 62 7227 47 73
28 94 7329 82 74
30 91 75
31 75 7532 74 7533 55 76
34 65 77
35 57 77
36 77 8037 54 81
38 73 82
39 72 83
40 80 8341 81 86
42 76 86
43 77 91
44 94 91
45 83 92
46 67 94
47 75 94
48 73 100
49 53 100
50 86 100
7
Calculations
( )[ ]
1n
nxxS
22
=
49
503515260521S
2
=
55.16S=
Calculating the mean
S = 16.55 constitutes less than 33% othe mean (70.03) what means that iis a is a small standard deviation
68 % off the data (34 leaves) falls
within one standard deviation and98% of the data (49 leaves) fallswithin two standard deviations
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
8/24
26.9650
4813
samplesofnumber
xx
1
1 ===
3.7050
3515
samplesofnumber
xx
2
2 ===
14.149150
)50/23164969(470607
1n
)n/)x((xs
1
1
2
1
2
12
1=
=
=
81.273150
)50/12355225(260521
1n
)n/)x((xs
2
2
2
2
2
22
2=
=
=
Table 9 . Calculating mean and varianceMean formula and calculations:
Variance formula and calculations:
Variance for X1 =
Variance for X2 =
No.
Width [cm]0.1
Sun-exposed
side(X1)
Width [cm]0.1
Darkened
side(X2)
1 96 502 85 72
3 100 674 95 705 92 1006 91 1007 89 428 115 529 92 6010 80 91
11 119 7012 91 65
13 94 6814 110 10015 105 4316 95 9217 83 5418 100 8319 103 6120 90 58
21 84 3122 110 86
23 90 45
24 85 5725 96 7526 107 6227 110 4728 105 9429 106 8230 105 91
31 90 7532 118 74
33 60 5534 84 65
35 98 57
36 99 7737 102 5438 92 7339 85 7240 117 80
41 75 8142 110 76
43 80 7744 98 94
45 112 8346 90 6747 83 75
48 105 7349 85 5350 107 86
mean 96.26 70.3variabl
e149.14 273.81
8
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
9/24
Graph 1. Widths of the leaves on the sun-exposed and shadowed side
Calculating value oft:
The formula for t:
Calculating degree of freedom
T value of 8. 95 for 98 degrees of freedom is less than 1%, therefore thedifference between the two sets is highly significant. This implies that widtha ofthe leaves are not random and that the null hypothesis can be rejected. Widths ofthe leaves on the sun-exposed side are grater than those of the leaves placed onthe shadowed side.
9
95.890.2
96.25
48.598.2
96.25
50
81.273
50
14.149
30.7026.96
n
s
n
s
xxt
2
2
2
1
2
1
21==
+
=
+
=
+
=
982)nn(df 21 =+=
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
shadowed side
sun-exposed side
Sample number
Size[cm]
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
10/24
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
11/24
14.11650
5807
samplesofnumber
xx
1
1 ===
Table 11 . Calculating standard deviation for the leaves on the shadowed sideof the tree
Table 12. Sorting the lengths of the
leaves on the sun-exposed side of the tree
No.Length
[cm] (X1) 0.1
X1 0.1
1 104 108162 100 100003 111 12321
4 125 156255 105 11025
6 110 121007 97 9409
8 120 144009 118 1392410 95 902511 123 1512912 115 1322513 109 1188114 135 1822515 108 11664
16 112 1254417 99 9801
18 121 1464119 108 11664
20 100 1000021 112 1254422 145 2102523 116 1345624 110 1210025 114 12996
26 120 1440027 123 15129
28 140 1960029 128 1638430 117 1368931 127 16129
32 135 1822533 90 810034 106 1123635 130 16900
36 110 1210037 132 17424
38 113 1276939 120 14400
40 135 1822541 96 921642 132 1742443 110 12100
44 121 1464145 135 1822546 112 1254447 130 16900
48 114 1299649 97 9409
50 122 14884Sum: 5807 682589
11
Calculations
( )[ ]1n
nxxS
22
=
49
505807682589S
2
=
91.12S=
Calculating the mean
S = 12.91 constitutes less than 33% ofthe mean (116.14) what means that itis a is a small standard deviation
62 % off the data (34 leaves) fallswithin one standard deviation and
98% of the data (49 leaves) fallswithin two standard deviations
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
12/24
Table 13 . Checking for normal distribution for length of the leaves on the sun-exposed side of the tree
No. Length [cm] (X1) 0.1 Sorted value
1 104 90
2 100 95
3 111 96
4 125 97
5 105 97
6 110 997 97 100
8 120 100
9 118 104
10 95 105
11 123 106
12 115 108
13 109 108
14 135 109
15 108 110
16 112 110
17 99 110
18 121 11019 108 111
20 100 112
21 112 112
22 145 112
23 116 113
24 110 114
25 114 114
26 120 115
27 123 116
28 140 117
29 128 118
30 117 120
31 127 120
32 135 120
33 90 121
34 106 121
35 130 122
36 110 123
37 132 123
38 113 125
39 120 127
40 135 128
41 96 13042 132 130
43 110 132
44 121 132
45 135 135
46 112 135
47 130 135
48 114 135
49 97 140
50 122 145
12
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
13/24
Table 14. Calculating standard deviation forthe leaves on the shadowed side of the tree
Class Frequency
40 49 I
50 59 II60 69 IIII
70 79 IIII80 89 IIIIIIIII
90 99 IIIIIIIIII
100 109 IIIIIIIII110 119 IIIII120 129 II
130 139 INo. Length
[cm] (X1) 0.1
X1 0.1
1 73 53292 93 8649
3 100 100004 104 108165 130 169006 123 151297 56 31368 110 121009 80 6400
10 116 13456
11 93 864912 92 8464
13 97 940914 124 1537615 60 360016 137 1876917 73 53298 116 13456
19 83 6889
20 78 608421 42 176422 116 13456
23 62 384424 88 774425 102 1040426 96 921627 53 280928 130 1690029 115 1322530 122 14884
31 103 10609
32 93 864933 88 774434 94 8836
35 75 562536 105 1102537 64 409638 84 705639 80 640040 100 10000
41 87 756942 91 8281
43 102 10404
44 101 1020145 90 810046 83 688947 102 1040448 87 756949 65 422550 90 8100Sum:
4648453968
13
Calculations
( )[ ]1n
nxxS
22
=
49
504648453968S
2
=
13.21S=
Calculating the mean
There is a good normal distribution
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
14/24
96.9250
4648
samplesofnumber
xx
2
2 ===
Table 15. Sorting the lengths of the leaves on the shadowed side of the tree
No. Length [cm] (X1) 0.1 Sorted value
1 73 42
2 93 53
3 100 56
4 104 60
5 130 62
6 123 64
7 56 65
8 110 73
9 80 73
10 116 75
11 93 78
12 92 80
13 97 80
14 124 83
15 60 83
16 137 84
17 73 87
18 116 87
19 83 8820 78 88
21 42 90
22 116 90
23 62 91
24 88 92
25 102 93
26 96 93
27 53 93
28 130 94
29 115 96
30 122 97
31 103 100
32 93 100
33 88 101
14
S = 21.13 constitutes less than 33% ofthe mean (92.96) what means that it is ais a small standard deviation
62 % off the data (34 leaves) fallswithin one standard deviation and
96% of the data (48 leaves) falls within two standard deviations
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
15/24
14.11650
5807
samplesofnumber
xx
1
1 ===
96.9250
4648
samplesofnumber
xx
2
2 ===
61.166150
)50/33721249(682589
1n
)n/)x((xs
1
1
2
1
2
12
1 =
=
=
73.446150
)50/21603904(453968
1n
)n/)x((xs
2
2
2
2
2
22
2=
=
=
34 94 102
35 75 102
36 105 102
37 64 103
38 84 104
39 80 105
40 100 110
41 87 115
42 91 11643 102 116
44 101 116
45 90 122
46 83 123
47 102 124
48 87 130
49 65 130
50 90 137
Table 16. Calculating mean andvariance
Mean formula and calculations:
Variance formula and calculations:
Variance for X1 =
Variance for X2 =
No.
Length [cm]0.1Sun-exposed
side(X1)
Length [cm] 0.1Darkened
side(X2)
1 104 73
2 100 933 111 100
4 125 1045 105 1306 110 1237 97 568 120 1109 118 8010 95 11611 123 93
12 115 9213 109 97
14 135 12415 108 6016 112 13717 99 7318 121 11619 108 8320 100 78
21 112 4222 145 11623 116 62
24 110 8825 114 10226 120 9627 123 5328 140 13029 128 11530 117 12231 127 103
32 135 93
33 90 8834 106 9435 130 75
36 110 10537 132 6438 113 8439 120 8040 135 10041 96 87
42 132 9143 110 102
44 121 101
45 135 9046 112 8347 130 10248 114 8749 97 6550 122 90
mean 116.14 92.96variabl
e166.61 446.73
15
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
16/24
Graph 2 . Widths of the leaves on the sun-exposed and shadowed side
Calculating value oft:
The formula for t:
Calculating degree of freedom
16
62.650.3
18.23
93.833.3
18.23
50
73.446
50
61.166
96.9214.116
n
s
n
s
xxt
2
2
2
1
2
1
21==
+
=
+
=
+
=
982)nn(df 21 =+=
0
20
40
60
80
100
120
140
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
shadowed side
sun-exposed side
Sample number
Size
[cm]
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
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T value of 8. 95 for 98 degrees of freedom is less than 1%, therefore thedifference between the two sets is highly significant. This implies that lengths ofthe leaves are not random and that the null hypothesis can be rejected. Lengthsof the leaves on the sun-exposed side are grater than those of the leaves whichare on the shadowed side.
Table 17 . Ranking the dimensions of the leaves from sun-exposed side
17
The Spearman Rank CorrelationIs a statistical test that assesses the correlation between two sets of variables. The measure ofcorrelation lies between +1 and 1, where +1 stands for a perfect positive correlation while -1determinates perfect negative correlation. In this case the test will be used to determinatewhether there is a correlation between the length and the width of the leaves on each side of thetree (the sun-exposed and the shadowed).
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
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Table 18 . Calculating the differences between ranks
No.Length[cm]
0.1Rank R1
Width[cm] 0.1
Rank R2 D=R1 R2 D
1 104 9 96 26.5 -17,5 306,25
2 100 7.5 85 9.25 -17,5 306,253 111 19 100 31.5 -12,5 156,254 125 38 95 24.5 13,5 182,255 105 10 92 20.33 -10,33 106,71
No.
Length[cm] (X1)
0.1
Sortedvalue
Rank
Width[cm] (X1)
0.1
Sortedvalue
Rank
1 104 90 1 96 60 12 100 95 2 85 75 2
3 111 96 3 100 80 3.54 125 97 4.5 95 80 3.5
5 105 97 4.5 92 83 5.5
6 110 99 6 91 83 5.57 97 100 7.5 89 84 7.5
8 120 100 7.5 115 84 7.59 118 104 9 92 85 9.2510 95 105 10 80 85 9.25
11 123 106 11 119 85 9.2512 115 108 12.5 91 85 9.25
13 109 108 12.5 94 89 1314 135 109 14 110 90 14.2515 108 110 15.25 105 90 14.25
16 112 110 15.25 95 90 14.2517 99 110 15.25 83 90 14.2518 121 110 15.25 100 91 18.5
19 108 111 19 103 91 18.520 100 112 20.33 90 92 20.33
21 112 112 20.33 84 92 20.3322 145 112 20.33 110 92 20.3323 116 113 23 90 94 23
24 110 114 24.5 85 95 24.525 114 114 24.5 96 95 24.526 120 115 26 107 96 26.5
27 123 116 27 110 96 26.528 140 117 28 105 98 28.5
29 128 118 29 106 98 28.530 117 120 30.33 105 99 3031 127 120 30.33 90 100 31.5
32 135 120 30.33 118 100 31.5
33 90 121 33.5 60 102 3334 106 121 33.5 84 103 3435 130 122 35 98 105 35.2536 110 123 36.5 99 105 35.25
37 132 123 36.5 102 105 35.2538 113 125 38 92 105 35.2539 120 127 39 85 106 39
40 135 128 40 117 107 40.541 96 130 41.5 75 107 40.5
42 132 130 41.5 110 110 42.2543 110 132 43.5 80 110 42.2544 121 132 43.5 98 110 42.25
45 135 135 45.25 112 110 42.25
46 112 135 45.25 90 112 4647 130 135 45.25 83 115 47
48 114 135 45.25 105 117 4849 97 140 49 85 118 49
50 122 145 50 107 119 50
18
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
19/24
6 110 15.25 91 18.5 -3,25 10,567 97 4.5 89 13 -8,5 72,258 120 30.33 115 47 -16,67 277,899 118 29 92 20.33 8,67 75,17
10 95 2 80 3.5 -1,5 2,2511 123 36.5 119 50 -13,5 182,25
12 115 26 91 18.5 7,5 56,2513 109 14 94 23 -9 81
14 135 45.25 110 42.25 3 9
15 108 12.5 105 35.25 -22,75 517,5616 112 20.33 95 24.5 -4,17 17,3917 99 6 83 5.5 0,5 0,2518 121 33.5 100 31.5 2 4,0019 108 12.5 103 34 -21,5 462,252 100 7.5 90 14.25 -6,75 45,56
21 112 20.33 84 7.5 12,83 164,61
22 145 50 110 42.25 7,75 60,0623 116 27 90 14.25 12,75 162,56
24 110 15.25 85 9.25 6 3625 114 24.5 96 26.5 -2 4
26 120 30.33 107 40.5 -10,17 103,43
27 123 36.5 110 42.25 -5,75 33,0628 140 49 105 35.25 13,75 189,0629 128 40 106 39 1 130 117 28 105 35.25 -7,25 52,5631 127 39 90 14.25 24,75 612,56
32 135 45.25 118 49 -3,75 14,0633 90 1 60 1 0 0,00
34 106 11 84 7.5 3,5 12,2535 130 41.5 98 28.5 13 169,00
36 110 15.25 99 30 -14,75 217,5637 132 43.5 102 33 10,5 110,2538 113 23 92 20.33 2,67 7,13
39 120 30.33 85 9.25 21,08 444,3740 135 45.25 117 48 -2,75 7,5641 96 3 75 2 1 142 132 43.5 110 42.25 1,25 1,5643 110 15.25 80 3.5 11,75 138,06
44 121 33.5 98 28.5 5 2545 135 45.25 112 46 -,75 0,56
46 112 20.33 90 14.25 6,08 36,9747 130 41.5 83 5.5 36 129648 114 24.5 105 35.25 -10,75 115,5649 97 4.5 85 9.25 -4,75 22,5650 122 35 107 40.5 -5,5 30,25
Sum: 6939,94
H0: there is no correlation between the length and the width of the leaves on the sun-exposed side of the tree
H1: There is a positive correlation between the length and width of the leaves on thesun-exposed side of the tree
Calculating the Spearman Rank correlation (rs)
Formula:
19
33.0124950
64.41639
249950
6939,946
)1n(n
D61r
2
2
s ==
=
=
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
20/24
The critical value for 50 sample pairs is 0.28. the calculated value of spearmanrank correlation is 0.33, what indicates that there is positive correlation betweenexamined sets of data. Therefore the null hypothesis can be rejected and H1supported as the greater the length of the leaf the greater its width.
Graph 3. The length and the width of the leaves on the sun-exposed side of thetree
Graph 4. Correlation between the length and the width of the leaves on thesun-exposed side of the tree
20
1 4 710
13
16
19
22
25
28
31
34
37
40
43
46
49
0
20
40
60
80
100
120
140
160 width
lenght
Sample number
Size[cm]
50
60
70
80
90
100
110
120
130
80 90 100 110 120 130 140 150
Widthoftheleaf
[cm]
Length of the leaf [cm]
8/3/2019 ANALYSING CORELATIONS BETWEEN THE LEAVES FROM SUN-EXPOSED AND SHADOWED SIDE OF THE THREE
21/24
Table 19 . Ranking the dimensions of the leaves from the shadowed side
Table 20. Calculating the differences between ranks
No. Length[cm]
Rank R1 Width[cm]
Rank R2 D=R1 R2 D
No.
Length[cm] (X1)
0.1
Sortedvalue
Rank
Width[cm] (X1)
0.1
Sortedvalue
Rank
1 73 42 1 50 31 12 93 53 2 72 42 23 100 56 3 67 43 3.5
4 104 60 4 70 45 3.55 130 62 5 100 47 5.5
6 123 64 6 100 50 5.57 56 65 7 42 52 7.58 110 73 8.5 52 53 7.59 80 73 8.5 60 54 9.510 116 75 10 91 54 9.511 93 78 11 70 55 1112 92 80 12.5 65 57 12.513 97 80 12.5 68 57 12.5
14 124 83 14.5 100 58 1415 60 83 14.5 43 60 15
16 137 84 16 92 61 1617 73 87 17.5 54 62 17
18 116 87 17.5 83 65 18.519 83 88 19.5 61 65 18.520 78 88 19.5 58 67 20.521 42 90 21.5 31 67 20.522 116 90 21.5 86 68 2223 62 91 23 45 70 23.5
24 88 92 24.5 57 70 23.525 102 93 25.33 75 72 25.5
26 96 93 25.33 62 72 25.527 53 93 25.33 47 73 27.5
28 130 94 28 94 73 27.529 115 96 29 82 74 2930 122 97 30 91 75 30.3331 103 100 31.5 75 75 30.3332 93 100 31.5 74 75 30.3333 88 101 33 55 76 3334 94 102 34.33 65 77 34.535 75 102 34.33 57 77 34.5
36 105 102 34.33 77 80 3637 64 103 37 54 81 37
38 84 104 38 73 82 3839 80 105 39 72 83 39.5
40 100 110 40 80 83 39.541 87 115 41.5 81 86 41.542 91 116 42.33 76 86 41.543 102 116 42.33 77 91 43.544 101 116 42.33 94 91 43.545 90 122 45 83 92 45
46 83 123 46 67 94 46.547 102 124 47 75 94 46.5
48 87 130 48.5 73 100 47.3349 65 130 48.5 53 100 47.3350 90 137 50 86 100 47.33
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0.1 0.11 73 8,5 96 26,5 -18 3242 93 25,33 85 9.25 16,08 258,56643 100 31,5 100 31,5 0 04 104 38 95 24.5 13,5 182,255 130 48,5 92 20,33 28,17 793,5489
6 123 46 91 18,5 27,5 756,257 56 3 89 13 -10 100
8 110 40 115 47 -7 49
9 80 12,5 92 20,33 -7,83 61,308910 116 42,33 80 3,5 38,83 1507,76911 93 25,33 119 50 -24,67 608,608912 92 24 91 18,5 5,5 30,2513 97 30 94 23 7 4914 124 47 110 42,25 4,75 22,562515 60 4 105 35,25 -31,25 976,5625
16 137 50 95 24,5 25,5 650,2517 73 8,5 83 5,5 3 9
18 116 42,33 100 31,5 10,83 117,288919 83 14,5 103 34 -19,5 380,25
2 78 11 90 14,25 -3,25 10,5625
21 42 1 84 7,5 -6,5 42,2522 116 42,33 110 42,25 0,08 0,006423 62 5 90 14,25 -9,25 85,562524 88 19,5 85 9,25 10,25 105,062525 102 34,33 96 26,5 7,83 61,3089
26 96 29 107 40,5 -11,5 132,2527 53 2 110 42,25 -40,25 1620,063
28 130 48,5 105 35,25 13,25 175,562529 115 41 106 39 2 4
30 122 45 105 35,25 9,75 95,062531 103 37 90 14,25 22,75 517,562532 93 25,33 118 49 -23,67 560,2689
33 88 19,5 60 1 18,5 342,2534 94 28 84 7,5 20,5 420,2535 75 10 98 28,5 -18,5 342,2536 105 39 99 30 9 8137 64 6 102 33 -27 729
38 84 16 92 20,33 -4,33 18,748939 80 12,5 85 9,25 3,25 10,5625
40 100 31,5 117 48 -16,5 272,2541 87 17,5 75 2 15,5 240,2542 91 23 110 42,25 -19,25 370,562543 102 34,33 80 3,5 30,83 950,488944 101 33 98 28,5 4,5 20,25
45 90 21,5 112 46 -24,5 600,2546 83 14,5 90 14,25 0,25 0,062547 102 34,33 83 5,5 28,83 831,1689
48 87 15,5 105 35,25 -19,75 390,062549 65 7 85 9,25 -2,25 5,0625
50 90 21,5 107 40,5 -19 361Sum: 16271,46
H0: there is no correlation between the length and the width of the leaves on theshadowed side of the tree
H1: There is a positive correlation between the length and width of the leaves on theshadowed side of the tree
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results of Spearman Rank Correlation statistical tests it can be observed thatthere is a strong positive correlation (the greater the length of the leaf, thegreater its width) between the leaves on both the sun-exposed and theshadowed side of the tree. However the gradient of correlation appears to bemuch grater on the shadowed side as the value of rs there is 0.78 which is graterthan 0.33 on the sun-exposed side.