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Author's title

Author*Unverified author*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationTue, 03 Dec 2013 07:48:22 -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/2013/Dec/03/t1386075133uj5mk6det3nqktk.htm/, Retrieved Thu, 28 Mar 2024 16:42:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230253, Retrieved Thu, 28 Mar 2024 16:42:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variability] [] [2013-12-03 12:48:22] [a9b531f12fa224c0c22271b290223f8e] [Current]
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Dataseries X:
25
25
25
25
29
30
30
29
35
30
30
30
29
30
30
26
30
30
30
35
30
30
30
50
25
29
30
25
30
30
25
42
29
15
29
30
25
20
10
30
29
30
50
25
30
30
25
50
29
30
30
30
30
30
30
29
35
40
29
26
23
25
30
30
30
30
20
29
25
25
28
30
30
25
30
31
30
29
45
30
30
35
30
30
25
50
40
20
35
22
30
25
30
30
29
50
45
30
26
30
29
35
20
29
25
30
45
35
30
30
40
20
26
29
20
25
30
30
25
30
23
25
30
30
40
30
40
35
40
30
25
33
30
30
30
35
33
35
30
40
29
25
27
30
30
35
20
30
30
25
25
30
30
30
40
40
30
40
20
50
20
30
30
30
30
25
30
30
30
30
30
30
23
30
25
50
20
23
25
29
26
40
30
30
35
20
29
25
30
30
30
50
30
35
30
30
30
35
30
35
15
30
20
35
40
30
30
40
29
30
20
35
50
30
30
40
30
50
18
15
30
23
29
30
35
30
23
30
25
26
25
30
20
25
30
29
40
30
30
30
40
37
20
25
30
32
35
32
30
30
35
30
25
30
24
30
35
30
30
30
30
30
25
30
25
35
30
30
30
30
30
30
35
32
30
20
20
30
35
30
40
29
26
40
25
35
30
23
30
27
35
30
20
30
25
50
30
30
29
35
29
25
30
45
30
25
29
25
40
30
30
40
30
30
29
35
35
30
30
27
30
30
29
50
30
30
20
25
25
30
27
29
50
50
30
30
40
20
30
30
30
25
30
30
30
30
40
25
35
30
30
35
20
20
50
35
29
50
40
30
45
30
40
30
29
25
40
35
25
21
30
30
30
30
15
30
30
30
30
30
25
30
30
30
30
25
25
40
30
33
40
26
30
37
25
29
30
25
29
30
30
30
30
30
22
25
30
40
30
29
25
30
30
29
30
30
30
35
30
35
30
12
15
25
30
30
30
25
20
30
35
35
29
40
30
40
30
25
30
20
29
28
30
25
30
50
30
30
29
30
35
20
30
30
30
30
30
40
30
30
35
25
30
50
30
30
30
30
25
30
30
30
25
30
30
30
25
30
30
26
30
30
30
30
25
20
30
35
30
20
20
25
30
30
30
30
29
35
25
30
30
35
35
30
20
30
30
30
25
30
30
26
30
25
30
50
30
20
29
30
30
30
30
30
40
30
35
27
30
25
29
25
30
25
30
29
25
20
30
25
32
30
29
30
30
30
30
25
25
30
30
60
20
30
35
25
30
25
30
40
25
30
29
29
30
29
26
18
30
40
30
30
30
30
30
29
30
30
30
35
30
30
30
20
29
20
30
30
25
30
40
30
30
25
40
30
30
29
25
30
35
30
20
30
20
25
30
40
25
47
20
20
30
30
25
30
25
40
29
40
29
30
30
30
35
30
20
30
24
30
40
30
30
15
35
18
30
25
30
30
30
15
20
30
25
30
20
30
30
30
25
40
50
30
30
35
30
30
15
30
25
30
30
26
30
25
25
30
30
30
50
30
25
30
25
30
26
25
34
30
25
30
35
30
40
30
30
29
30
29
30
50
30
15
30
25
50
30
30
35
35
25
23
30
30
30
35
25
15
30
29
30
15
30
40
29
30
25
25
50
30
1
30
30
30
35
30
30
35
30
20
20
20
30
35
30
25
29
35
40
30
35
29
30
30
30
29
30
30
30
30
30
30
30
35
30
30
30
25
50
30
30
30
25
25
35
30
35
30
29
30
35
30
30
35
25
25
29
35
50
30
30
29
30
30
30
20
30
30
20
30
25
20
30
50
20
40
40
30
29
35
25
20
20
21
29
35
30
28
30
30
35
26
30
25
25
30
30
30
25
35
30
35
35
30
29
30
26
30
27
30
30
50
25
30
30
30
40
30
32
25
35
30
30
20
30
40
30
26
30
40
30
30
26
35
35
26
50
30
30
25
30
40
25
30
25
30
15
40
30
25
30
30
30
30
30
25
25
30
20
18
25
30
29
13
27
30
30
30
30
25
30
35
29
30
29
30
30
25
45
29
30
30
25
25
29
30
30
30
29
30
23
35
35
10
32
29
45
30
29
30
15
50
35
25
25
30
30
30
30
30
40
29
25
30
25
30
25
25
30
35
30
25
20
30
30
30
15
30
35
50
35
30
30
25
30
30
15
30
25
30
30
25
29
30
30
40
25
30
30
25
35
29
30
25
30
30
25
30
30
30
25
35
25
29
25
30
30
50
30
30

30
30
30
20
25
25
35
25
30
25
50
20
45
25
35
30
40
35
30
30
30
30
23
30
25
30
15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time16 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 16 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=230253&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]16 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=230253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230253&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 time16 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Variability - Ungrouped Data
Absolute range59
Relative range (unbiased)9.30549246513612
Relative range (biased)9.31006631277782
Variance (unbiased)40.199930262164
Variance (biased)40.1604411361698
Standard Deviation (unbiased)6.34034149412822
Standard Deviation (biased)6.33722661234154
Coefficient of Variation (unbiased)0.21210172656247
Coefficient of Variation (biased)0.211997525265804
Mean Squared Error (MSE versus 0)933.747544204322
Mean Squared Error (MSE versus Mean)40.1604411361698
Mean Absolute Deviation from Mean (MAD Mean)3.7741845214431
Mean Absolute Deviation from Median (MAD Median)3.73968565815324
Median Absolute Deviation from Mean0.892927308447938
Median Absolute Deviation from Median1
Mean Squared Deviation from Mean40.1604411361698
Mean Squared Deviation from Median40.171905697446
Interquartile Difference (Weighted Average at Xnp)4
Interquartile Difference (Weighted Average at X(n+1)p)4
Interquartile Difference (Empirical Distribution Function)4
Interquartile Difference (Empirical Distribution Function - Averaging)4
Interquartile Difference (Empirical Distribution Function - Interpolation)4
Interquartile Difference (Closest Observation)4
Interquartile Difference (True Basic - Statistics Graphics Toolkit)4
Interquartile Difference (MS Excel (old versions))4
Semi Interquartile Difference (Weighted Average at Xnp)2
Semi Interquartile Difference (Weighted Average at X(n+1)p)2
Semi Interquartile Difference (Empirical Distribution Function)2
Semi Interquartile Difference (Empirical Distribution Function - Averaging)2
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)2
Semi Interquartile Difference (Closest Observation)2
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)2
Semi Interquartile Difference (MS Excel (old versions))2
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0714285714285714
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0714285714285714
Coefficient of Quartile Variation (Empirical Distribution Function)0.0714285714285714
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.0714285714285714
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0714285714285714
Coefficient of Quartile Variation (Closest Observation)0.0714285714285714
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0714285714285714
Coefficient of Quartile Variation (MS Excel (old versions))0.0714285714285714
Number of all Pairs of Observations517653
Squared Differences between all Pairs of Observations80.3998605243281
Mean Absolute Differences between all Pairs of Observations6.18227847612204
Gini Mean Difference6.18227847612204
Leik Measure of Dispersion0.500901648092319
Index of Diversity0.998973533447231
Index of Qualitative Variation0.999955808308044
Coefficient of Dispersion0.12580615071477
Observations1018

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 59 \tabularnewline
Relative range (unbiased) & 9.30549246513612 \tabularnewline
Relative range (biased) & 9.31006631277782 \tabularnewline
Variance (unbiased) & 40.199930262164 \tabularnewline
Variance (biased) & 40.1604411361698 \tabularnewline
Standard Deviation (unbiased) & 6.34034149412822 \tabularnewline
Standard Deviation (biased) & 6.33722661234154 \tabularnewline
Coefficient of Variation (unbiased) & 0.21210172656247 \tabularnewline
Coefficient of Variation (biased) & 0.211997525265804 \tabularnewline
Mean Squared Error (MSE versus 0) & 933.747544204322 \tabularnewline
Mean Squared Error (MSE versus Mean) & 40.1604411361698 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 3.7741845214431 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 3.73968565815324 \tabularnewline
Median Absolute Deviation from Mean & 0.892927308447938 \tabularnewline
Median Absolute Deviation from Median & 1 \tabularnewline
Mean Squared Deviation from Mean & 40.1604411361698 \tabularnewline
Mean Squared Deviation from Median & 40.171905697446 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 4 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 4 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 4 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 4 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 4 \tabularnewline
Interquartile Difference (Closest Observation) & 4 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 4 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 4 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 2 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 2 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 2 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 2 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 2 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 2 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 2 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 2 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.0714285714285714 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.0714285714285714 \tabularnewline
Number of all Pairs of Observations & 517653 \tabularnewline
Squared Differences between all Pairs of Observations & 80.3998605243281 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 6.18227847612204 \tabularnewline
Gini Mean Difference & 6.18227847612204 \tabularnewline
Leik Measure of Dispersion & 0.500901648092319 \tabularnewline
Index of Diversity & 0.998973533447231 \tabularnewline
Index of Qualitative Variation & 0.999955808308044 \tabularnewline
Coefficient of Dispersion & 0.12580615071477 \tabularnewline
Observations & 1018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230253&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]59[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]9.30549246513612[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]9.31006631277782[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]40.199930262164[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]40.1604411361698[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]6.34034149412822[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]6.33722661234154[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.21210172656247[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.211997525265804[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]933.747544204322[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]40.1604411361698[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]3.7741845214431[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]3.73968565815324[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]0.892927308447938[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]1[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]40.1604411361698[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]40.171905697446[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]4[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]4[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]2[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.0714285714285714[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]517653[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]80.3998605243281[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]6.18227847612204[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]6.18227847612204[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.500901648092319[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.998973533447231[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.999955808308044[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.12580615071477[/C][/ROW]
[ROW][C]Observations[/C][C]1018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230253&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 range59
Relative range (unbiased)9.30549246513612
Relative range (biased)9.31006631277782
Variance (unbiased)40.199930262164
Variance (biased)40.1604411361698
Standard Deviation (unbiased)6.34034149412822
Standard Deviation (biased)6.33722661234154
Coefficient of Variation (unbiased)0.21210172656247
Coefficient of Variation (biased)0.211997525265804
Mean Squared Error (MSE versus 0)933.747544204322
Mean Squared Error (MSE versus Mean)40.1604411361698
Mean Absolute Deviation from Mean (MAD Mean)3.7741845214431
Mean Absolute Deviation from Median (MAD Median)3.73968565815324
Median Absolute Deviation from Mean0.892927308447938
Median Absolute Deviation from Median1
Mean Squared Deviation from Mean40.1604411361698
Mean Squared Deviation from Median40.171905697446
Interquartile Difference (Weighted Average at Xnp)4
Interquartile Difference (Weighted Average at X(n+1)p)4
Interquartile Difference (Empirical Distribution Function)4
Interquartile Difference (Empirical Distribution Function - Averaging)4
Interquartile Difference (Empirical Distribution Function - Interpolation)4
Interquartile Difference (Closest Observation)4
Interquartile Difference (True Basic - Statistics Graphics Toolkit)4
Interquartile Difference (MS Excel (old versions))4
Semi Interquartile Difference (Weighted Average at Xnp)2
Semi Interquartile Difference (Weighted Average at X(n+1)p)2
Semi Interquartile Difference (Empirical Distribution Function)2
Semi Interquartile Difference (Empirical Distribution Function - Averaging)2
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)2
Semi Interquartile Difference (Closest Observation)2
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)2
Semi Interquartile Difference (MS Excel (old versions))2
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0714285714285714
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0714285714285714
Coefficient of Quartile Variation (Empirical Distribution Function)0.0714285714285714
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.0714285714285714
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0714285714285714
Coefficient of Quartile Variation (Closest Observation)0.0714285714285714
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0714285714285714
Coefficient of Quartile Variation (MS Excel (old versions))0.0714285714285714
Number of all Pairs of Observations517653
Squared Differences between all Pairs of Observations80.3998605243281
Mean Absolute Differences between all Pairs of Observations6.18227847612204
Gini Mean Difference6.18227847612204
Leik Measure of Dispersion0.500901648092319
Index of Diversity0.998973533447231
Index of Qualitative Variation0.999955808308044
Coefficient of Dispersion0.12580615071477
Observations1018



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')