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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationTue, 11 Dec 2012 13:28:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/11/t1355250538vseitpu7nj5ys7r.htm/, Retrieved Fri, 29 Mar 2024 06:48:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198617, Retrieved Fri, 29 Mar 2024 06:48:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variability] [Paper 2012: varia...] [2012-12-11 18:28:12] [7a9100b3135ff0dae36397155af309d9] [Current]
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Dataseries X:
87.28
87.28
87.09
86.92
87.59
90.72
90.69
90.3
89.55
88.94
88.41
87.82
87.07
86.82
86.4
86.02
85.66
85.32
85
84.67
83.94
82.83
81.95
81.19
80.48
78.86
69.47
68.77
70.06
73.95
75.8
77.79
81.57
83.07
84.34
85.1
85.25
84.26
83.63
86.44
85.3
84.1
83.36
82.48
81.58
80.47
79.34
82.13
81.69
80.7
79.88
79.16
78.38
77.42
76.47
75.46
74.48
78.27
80.7
79.91
78.75
77.78
81.14
81.08
80.03
78.91
78.01
76.9
75.97
81.93
80.27
78.67
77.42
76.16
74.7
76.39
76.04
74.65
73.29
71.79
74.39
74.91
74.54
73.08
72.75
71.32
70.38
70.35
70.01
69.36
67.77
69.26
69.8
68.38
67.62
68.39
66.95
65.21
66.64
63.45
60.66
62.34
60.32
58.64
60.46
58.59
61.87
61.85
67.44
77.06
91.74
93.15
94.15
93.11
91.51
89.96
88.16
86.98
88.03
86.24
84.65
83.23
81.7
80.25
78.8
77.51
76.2
75.04
74
75.49
77.14
76.15
76.27
78.19
76.49
77.31
76.65
74.99
73.51
72.07
70.59
71.96
76.29
74.86
74.93
71.9
71.01
77.47
75.78
76.6
76.07
74.57
73.02
72.65
73.16
71.53
69.78
67.98
69.96
72.16
70.47
68.86
67.37
65.87
72.16
71.34
69.93
68.44
67.16
66.01
67.25
70.91
69.75
68.59
67.48
66.31
64.81
66.58
65.97
64.7
64.7
60.94
59.08
58.42
57.77
57.11
53.31
49.96
49.4
48.84
48.3
47.74
47.24
46.76
46.29
48.9
49.23
48.53
48.03
54.34
53.79
53.24
52.96
52.17
51.7
58.55
78.2
77.03
76.19
77.15
75.87
95.47
109.67
112.28
112.01
107.93
105.96
105.06
102.98
102.2
105.23
101.85
99.89
96.23
94.76
91.51
91.63
91.54
85.23
87.83
87.38
84.44
85.19
84.03
86.73
102.52
104.45
106.98
107.02
99.26
94.45
113.44
157.33
147.38
171.89
171.95
132.71
126.02
121.18
115.45
110.48
117.85
117.63
124.65
109.59
111.27
99.78
98.21
99.2
97.97
89.55
87.91
93.34
94.42
93.2
90.29
91.46
89.98
88.35
88.41
82.44
79.89
75.69
75.66
84.5
96.73
87.48
82.39
83.48
79.31
78.16
72.77
72.45
68.46
67.62
68.76
70.07
68.55
65.3
58.96
59.17
62.37
66.28
55.62
55.23
55.85
56.75
50.89
53.88
52.95
55.08
53.61
58.78
61.85
55.91
53.32
46.41
44.57
50
50
53.36
46.23
50.45
49.07
45.85
48.45
49.96
46.53
50.51
47.58
48.05
46.84
47.67
49.16
55.54
55.82
58.22
56.19
57.77
63.19
54.76
55.74
62.54
61.39
69.6
79.23
80
93.68
107.63
100.18
97.3
90.45
80.64
80.58
75.82
85.59
89.35
89.42
104.73
95.32
89.27
90.44
86.97
79.98
81.22
87.35
83.64
82.22
94.4
102.18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198617&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198617&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Variability - Ungrouped Data
Absolute range127.38
Relative range (unbiased)6.75702407880874
Relative range (biased)6.76642843141661
Variance (unbiased)355.378832284123
Variance (biased)354.391668861111
Standard Deviation (unbiased)18.8514941658247
Standard Deviation (biased)18.8252933273591
Coefficient of Variation (unbiased)0.243125353309764
Coefficient of Variation (biased)0.242787444385786
Mean Squared Error (MSE versus 0)6366.55895888889
Mean Squared Error (MSE versus Mean)354.391668861111
Mean Absolute Deviation from Mean (MAD Mean)13.7198981481481
Mean Absolute Deviation from Median (MAD Median)13.7033888888889
Median Absolute Deviation from Mean9.93
Median Absolute Deviation from Median10.195
Mean Squared Deviation from Mean354.391668861111
Mean Squared Deviation from Median354.974092222222
Interquartile Difference (Weighted Average at Xnp)20.34
Interquartile Difference (Weighted Average at X(n+1)p)20.33
Interquartile Difference (Empirical Distribution Function)20.34
Interquartile Difference (Empirical Distribution Function - Averaging)20.23
Interquartile Difference (Empirical Distribution Function - Interpolation)20.13
Interquartile Difference (Closest Observation)20.34
Interquartile Difference (True Basic - Statistics Graphics Toolkit)20.13
Interquartile Difference (MS Excel (old versions))20.43
Semi Interquartile Difference (Weighted Average at Xnp)10.17
Semi Interquartile Difference (Weighted Average at X(n+1)p)10.165
Semi Interquartile Difference (Empirical Distribution Function)10.17
Semi Interquartile Difference (Empirical Distribution Function - Averaging)10.115
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)10.065
Semi Interquartile Difference (Closest Observation)10.17
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)10.065
Semi Interquartile Difference (MS Excel (old versions))10.215
Coefficient of Quartile Variation (Weighted Average at Xnp)0.132404634813175
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.132214743277079
Coefficient of Quartile Variation (Empirical Distribution Function)0.132404634813175
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.131517357950852
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.130820471161657
Coefficient of Quartile Variation (Closest Observation)0.132404634813175
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.130820471161657
Coefficient of Quartile Variation (MS Excel (old versions))0.132912627675493
Number of all Pairs of Observations64620
Squared Differences between all Pairs of Observations710.757664568245
Mean Absolute Differences between all Pairs of Observations20.1244617765396
Gini Mean Difference20.1244617765397
Leik Measure of Dispersion0.505359217140801
Index of Diversity0.997058484046802
Index of Qualitative Variation0.999835805729383
Coefficient of Dispersion0.178702678582197
Observations360

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 127.38 \tabularnewline
Relative range (unbiased) & 6.75702407880874 \tabularnewline
Relative range (biased) & 6.76642843141661 \tabularnewline
Variance (unbiased) & 355.378832284123 \tabularnewline
Variance (biased) & 354.391668861111 \tabularnewline
Standard Deviation (unbiased) & 18.8514941658247 \tabularnewline
Standard Deviation (biased) & 18.8252933273591 \tabularnewline
Coefficient of Variation (unbiased) & 0.243125353309764 \tabularnewline
Coefficient of Variation (biased) & 0.242787444385786 \tabularnewline
Mean Squared Error (MSE versus 0) & 6366.55895888889 \tabularnewline
Mean Squared Error (MSE versus Mean) & 354.391668861111 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 13.7198981481481 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 13.7033888888889 \tabularnewline
Median Absolute Deviation from Mean & 9.93 \tabularnewline
Median Absolute Deviation from Median & 10.195 \tabularnewline
Mean Squared Deviation from Mean & 354.391668861111 \tabularnewline
Mean Squared Deviation from Median & 354.974092222222 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 20.34 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 20.33 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 20.34 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 20.23 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 20.13 \tabularnewline
Interquartile Difference (Closest Observation) & 20.34 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 20.13 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 20.43 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 10.17 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 10.165 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 10.17 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 10.115 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 10.065 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 10.17 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 10.065 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 10.215 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.132404634813175 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.132214743277079 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.132404634813175 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.131517357950852 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.130820471161657 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.132404634813175 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.130820471161657 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.132912627675493 \tabularnewline
Number of all Pairs of Observations & 64620 \tabularnewline
Squared Differences between all Pairs of Observations & 710.757664568245 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 20.1244617765396 \tabularnewline
Gini Mean Difference & 20.1244617765397 \tabularnewline
Leik Measure of Dispersion & 0.505359217140801 \tabularnewline
Index of Diversity & 0.997058484046802 \tabularnewline
Index of Qualitative Variation & 0.999835805729383 \tabularnewline
Coefficient of Dispersion & 0.178702678582197 \tabularnewline
Observations & 360 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198617&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]127.38[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]6.75702407880874[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]6.76642843141661[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]355.378832284123[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]354.391668861111[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]18.8514941658247[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]18.8252933273591[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.243125353309764[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.242787444385786[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]6366.55895888889[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]354.391668861111[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]13.7198981481481[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]13.7033888888889[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]9.93[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]10.195[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]354.391668861111[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]354.974092222222[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]20.34[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]20.33[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]20.34[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]20.23[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]20.13[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]20.34[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]20.13[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]20.43[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]10.17[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]10.165[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]10.17[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]10.115[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]10.065[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]10.17[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]10.065[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]10.215[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.132404634813175[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.132214743277079[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.132404634813175[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.131517357950852[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.130820471161657[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.132404634813175[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.130820471161657[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.132912627675493[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]64620[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]710.757664568245[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]20.1244617765396[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]20.1244617765397[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.505359217140801[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.997058484046802[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.999835805729383[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.178702678582197[/C][/ROW]
[ROW][C]Observations[/C][C]360[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198617&T=1

As an alternative you can also use a QR Code:  

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

Variability - Ungrouped Data
Absolute range127.38
Relative range (unbiased)6.75702407880874
Relative range (biased)6.76642843141661
Variance (unbiased)355.378832284123
Variance (biased)354.391668861111
Standard Deviation (unbiased)18.8514941658247
Standard Deviation (biased)18.8252933273591
Coefficient of Variation (unbiased)0.243125353309764
Coefficient of Variation (biased)0.242787444385786
Mean Squared Error (MSE versus 0)6366.55895888889
Mean Squared Error (MSE versus Mean)354.391668861111
Mean Absolute Deviation from Mean (MAD Mean)13.7198981481481
Mean Absolute Deviation from Median (MAD Median)13.7033888888889
Median Absolute Deviation from Mean9.93
Median Absolute Deviation from Median10.195
Mean Squared Deviation from Mean354.391668861111
Mean Squared Deviation from Median354.974092222222
Interquartile Difference (Weighted Average at Xnp)20.34
Interquartile Difference (Weighted Average at X(n+1)p)20.33
Interquartile Difference (Empirical Distribution Function)20.34
Interquartile Difference (Empirical Distribution Function - Averaging)20.23
Interquartile Difference (Empirical Distribution Function - Interpolation)20.13
Interquartile Difference (Closest Observation)20.34
Interquartile Difference (True Basic - Statistics Graphics Toolkit)20.13
Interquartile Difference (MS Excel (old versions))20.43
Semi Interquartile Difference (Weighted Average at Xnp)10.17
Semi Interquartile Difference (Weighted Average at X(n+1)p)10.165
Semi Interquartile Difference (Empirical Distribution Function)10.17
Semi Interquartile Difference (Empirical Distribution Function - Averaging)10.115
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)10.065
Semi Interquartile Difference (Closest Observation)10.17
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)10.065
Semi Interquartile Difference (MS Excel (old versions))10.215
Coefficient of Quartile Variation (Weighted Average at Xnp)0.132404634813175
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.132214743277079
Coefficient of Quartile Variation (Empirical Distribution Function)0.132404634813175
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.131517357950852
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.130820471161657
Coefficient of Quartile Variation (Closest Observation)0.132404634813175
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.130820471161657
Coefficient of Quartile Variation (MS Excel (old versions))0.132912627675493
Number of all Pairs of Observations64620
Squared Differences between all Pairs of Observations710.757664568245
Mean Absolute Differences between all Pairs of Observations20.1244617765396
Gini Mean Difference20.1244617765397
Leik Measure of Dispersion0.505359217140801
Index of Diversity0.997058484046802
Index of Qualitative Variation0.999835805729383
Coefficient of Dispersion0.178702678582197
Observations360



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
num <- 50
res <- array(NA,dim=c(num,3))
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
iqd <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','unbiased.htm', varx)
res[5,] <- c('Variance (biased)','biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'median.htm', msemed)
load(file='createtable')
mylink1 <- hyperlink('difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')