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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 23 Dec 2009 15:07:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/23/t1261606137xnimqozjm2zms3o.htm/, Retrieved Mon, 29 Apr 2024 10:44:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70594, Retrieved Mon, 29 Apr 2024 10:44:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact100

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [OEF 8.3] [2009-12-23 22:07:45] [bad7dbea6bcbbbbea3fc380bb800ab43] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104,65
109,2
103,93
101,93
101,58
102,63
106,83
105,57
105
104,16
106,93
106,5
106,47
112,33
106,81
103,49
104,13
103,2
105,55
102,8
106,68
105,43
109,01
112,24
112,87
110,98
112,85
112,08
110,72
109,69
112,53
112,99
111,74
111,15
114,82
117,38
117,81
122,85
116,96
119,16
117,74
118,84
123,81
120,33
119,2
117,32
128,58
129,2
126,19
132,1
128,12
122,28
122,36
123,13
125,97
126,14
122,7
122,67
129,19
133,01
123,96
128,96
127,32
131,38
125,25
127,91
130,42
128,44
125,86
125,71
130,63
131,78
125,61
131,84
122,14
127,13
124,49
125,48
129,86
126,32
125,56
125,64
128,26
125,47
134,4
134,5
131,22
121,62
124,16
127,5
132,86
127,87
124,07
124,25
131,16
129,24
129,24
135,51
128,97
126,89
127,52
130,31
132,39
132,69
128,73
129,66
127,72
132,63
129,74
138,46
134,31
128,8
129,95
134,15
136,01
135,1
132,27
132,49
130,06
136,11
131,47
140,61
141,65
126,75
133,9
138,75
141,86
141,13
138,76
138,65
138,59
147,09
140,17
152,38
144,02
139,55
141,1
145,85
147,88
145,17

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70594&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70594&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70594&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1104.92753.071984971751437.27
2104.15252.457239304585535.25
3105.64751.291442991386002.77000000000001
4107.2753.685263446032958.84
5103.921.221174298233742.75
6108.342.993470672424676.80999999999999
7112.1950.8895879195822431.89
8111.48251.545345161013123.3
9113.77252.893664055599176.22999999999999
10119.1952.599596122477495.89
11120.182.642511431700286.07000000000001
12123.5756.1902153974370511.88
13127.17254.085742486582669.82
14124.41.937954247825963.78
15126.89255.1025769633261410.3400000000000
16127.9053.114155851377177.42
17128.0052.130766685178525.16999999999999
18128.4953.164853867084556.07000000000001
19126.684.02428461551459.7
20126.53752.337867618151225.37000000000002
21126.23251.353449297166312.78999999999999
22130.4356.0708566117146912.88
23128.09753.586738304736878.70000000000002
24127.183.574959207226487.09
25130.15253.722798006876018.61999999999999
26130.72752.385908282674195.17
27129.6852.117144303064864.91
28132.82754.460055119240869.66
29133.80252.678250361710056.06
30132.73252.504827006668006.05000000000001
31135.127.214808844776614.9
32138.913.594282496781067.96
33140.77254.212254938470218.5
34144.035.9074134215689812.8300000000000
351452.84346033323256.78

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.9275 & 3.07198497175143 & 7.27 \tabularnewline
2 & 104.1525 & 2.45723930458553 & 5.25 \tabularnewline
3 & 105.6475 & 1.29144299138600 & 2.77000000000001 \tabularnewline
4 & 107.275 & 3.68526344603295 & 8.84 \tabularnewline
5 & 103.92 & 1.22117429823374 & 2.75 \tabularnewline
6 & 108.34 & 2.99347067242467 & 6.80999999999999 \tabularnewline
7 & 112.195 & 0.889587919582243 & 1.89 \tabularnewline
8 & 111.4825 & 1.54534516101312 & 3.3 \tabularnewline
9 & 113.7725 & 2.89366405559917 & 6.22999999999999 \tabularnewline
10 & 119.195 & 2.59959612247749 & 5.89 \tabularnewline
11 & 120.18 & 2.64251143170028 & 6.07000000000001 \tabularnewline
12 & 123.575 & 6.19021539743705 & 11.88 \tabularnewline
13 & 127.1725 & 4.08574248658266 & 9.82 \tabularnewline
14 & 124.4 & 1.93795424782596 & 3.78 \tabularnewline
15 & 126.8925 & 5.10257696332614 & 10.3400000000000 \tabularnewline
16 & 127.905 & 3.11415585137717 & 7.42 \tabularnewline
17 & 128.005 & 2.13076668517852 & 5.16999999999999 \tabularnewline
18 & 128.495 & 3.16485386708455 & 6.07000000000001 \tabularnewline
19 & 126.68 & 4.0242846155145 & 9.7 \tabularnewline
20 & 126.5375 & 2.33786761815122 & 5.37000000000002 \tabularnewline
21 & 126.2325 & 1.35344929716631 & 2.78999999999999 \tabularnewline
22 & 130.435 & 6.07085661171469 & 12.88 \tabularnewline
23 & 128.0975 & 3.58673830473687 & 8.70000000000002 \tabularnewline
24 & 127.18 & 3.57495920722648 & 7.09 \tabularnewline
25 & 130.1525 & 3.72279800687601 & 8.61999999999999 \tabularnewline
26 & 130.7275 & 2.38590828267419 & 5.17 \tabularnewline
27 & 129.685 & 2.11714430306486 & 4.91 \tabularnewline
28 & 132.8275 & 4.46005511924086 & 9.66 \tabularnewline
29 & 133.8025 & 2.67825036171005 & 6.06 \tabularnewline
30 & 132.7325 & 2.50482700666800 & 6.05000000000001 \tabularnewline
31 & 135.12 & 7.2148088447766 & 14.9 \tabularnewline
32 & 138.91 & 3.59428249678106 & 7.96 \tabularnewline
33 & 140.7725 & 4.21225493847021 & 8.5 \tabularnewline
34 & 144.03 & 5.90741342156898 & 12.8300000000000 \tabularnewline
35 & 145 & 2.8434603332325 & 6.78 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70594&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]104.9275[/C][C]3.07198497175143[/C][C]7.27[/C][/ROW]
[ROW][C]2[/C][C]104.1525[/C][C]2.45723930458553[/C][C]5.25[/C][/ROW]
[ROW][C]3[/C][C]105.6475[/C][C]1.29144299138600[/C][C]2.77000000000001[/C][/ROW]
[ROW][C]4[/C][C]107.275[/C][C]3.68526344603295[/C][C]8.84[/C][/ROW]
[ROW][C]5[/C][C]103.92[/C][C]1.22117429823374[/C][C]2.75[/C][/ROW]
[ROW][C]6[/C][C]108.34[/C][C]2.99347067242467[/C][C]6.80999999999999[/C][/ROW]
[ROW][C]7[/C][C]112.195[/C][C]0.889587919582243[/C][C]1.89[/C][/ROW]
[ROW][C]8[/C][C]111.4825[/C][C]1.54534516101312[/C][C]3.3[/C][/ROW]
[ROW][C]9[/C][C]113.7725[/C][C]2.89366405559917[/C][C]6.22999999999999[/C][/ROW]
[ROW][C]10[/C][C]119.195[/C][C]2.59959612247749[/C][C]5.89[/C][/ROW]
[ROW][C]11[/C][C]120.18[/C][C]2.64251143170028[/C][C]6.07000000000001[/C][/ROW]
[ROW][C]12[/C][C]123.575[/C][C]6.19021539743705[/C][C]11.88[/C][/ROW]
[ROW][C]13[/C][C]127.1725[/C][C]4.08574248658266[/C][C]9.82[/C][/ROW]
[ROW][C]14[/C][C]124.4[/C][C]1.93795424782596[/C][C]3.78[/C][/ROW]
[ROW][C]15[/C][C]126.8925[/C][C]5.10257696332614[/C][C]10.3400000000000[/C][/ROW]
[ROW][C]16[/C][C]127.905[/C][C]3.11415585137717[/C][C]7.42[/C][/ROW]
[ROW][C]17[/C][C]128.005[/C][C]2.13076668517852[/C][C]5.16999999999999[/C][/ROW]
[ROW][C]18[/C][C]128.495[/C][C]3.16485386708455[/C][C]6.07000000000001[/C][/ROW]
[ROW][C]19[/C][C]126.68[/C][C]4.0242846155145[/C][C]9.7[/C][/ROW]
[ROW][C]20[/C][C]126.5375[/C][C]2.33786761815122[/C][C]5.37000000000002[/C][/ROW]
[ROW][C]21[/C][C]126.2325[/C][C]1.35344929716631[/C][C]2.78999999999999[/C][/ROW]
[ROW][C]22[/C][C]130.435[/C][C]6.07085661171469[/C][C]12.88[/C][/ROW]
[ROW][C]23[/C][C]128.0975[/C][C]3.58673830473687[/C][C]8.70000000000002[/C][/ROW]
[ROW][C]24[/C][C]127.18[/C][C]3.57495920722648[/C][C]7.09[/C][/ROW]
[ROW][C]25[/C][C]130.1525[/C][C]3.72279800687601[/C][C]8.61999999999999[/C][/ROW]
[ROW][C]26[/C][C]130.7275[/C][C]2.38590828267419[/C][C]5.17[/C][/ROW]
[ROW][C]27[/C][C]129.685[/C][C]2.11714430306486[/C][C]4.91[/C][/ROW]
[ROW][C]28[/C][C]132.8275[/C][C]4.46005511924086[/C][C]9.66[/C][/ROW]
[ROW][C]29[/C][C]133.8025[/C][C]2.67825036171005[/C][C]6.06[/C][/ROW]
[ROW][C]30[/C][C]132.7325[/C][C]2.50482700666800[/C][C]6.05000000000001[/C][/ROW]
[ROW][C]31[/C][C]135.12[/C][C]7.2148088447766[/C][C]14.9[/C][/ROW]
[ROW][C]32[/C][C]138.91[/C][C]3.59428249678106[/C][C]7.96[/C][/ROW]
[ROW][C]33[/C][C]140.7725[/C][C]4.21225493847021[/C][C]8.5[/C][/ROW]
[ROW][C]34[/C][C]144.03[/C][C]5.90741342156898[/C][C]12.8300000000000[/C][/ROW]
[ROW][C]35[/C][C]145[/C][C]2.8434603332325[/C][C]6.78[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70594&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70594&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1104.92753.071984971751437.27
2104.15252.457239304585535.25
3105.64751.291442991386002.77000000000001
4107.2753.685263446032958.84
5103.921.221174298233742.75
6108.342.993470672424676.80999999999999
7112.1950.8895879195822431.89
8111.48251.545345161013123.3
9113.77252.893664055599176.22999999999999
10119.1952.599596122477495.89
11120.182.642511431700286.07000000000001
12123.5756.1902153974370511.88
13127.17254.085742486582669.82
14124.41.937954247825963.78
15126.89255.1025769633261410.3400000000000
16127.9053.114155851377177.42
17128.0052.130766685178525.16999999999999
18128.4953.164853867084556.07000000000001
19126.684.02428461551459.7
20126.53752.337867618151225.37000000000002
21126.23251.353449297166312.78999999999999
22130.4356.0708566117146912.88
23128.09753.586738304736878.70000000000002
24127.183.574959207226487.09
25130.15253.722798006876018.61999999999999
26130.72752.385908282674195.17
27129.6852.117144303064864.91
28132.82754.460055119240869.66
29133.80252.678250361710056.06
30132.73252.504827006668006.05000000000001
31135.127.214808844776614.9
32138.913.594282496781067.96
33140.77254.212254938470218.5
34144.035.9074134215689812.8300000000000
351452.84346033323256.78






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.23299713988329
beta0.060085965432694
S.D.0.0201869390681857
T-STAT2.97647727720091
p-value0.00542486000954119

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.23299713988329 \tabularnewline
beta & 0.060085965432694 \tabularnewline
S.D. & 0.0201869390681857 \tabularnewline
T-STAT & 2.97647727720091 \tabularnewline
p-value & 0.00542486000954119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70594&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.23299713988329[/C][/ROW]
[ROW][C]beta[/C][C]0.060085965432694[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0201869390681857[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.97647727720091[/C][/ROW]
[ROW][C]p-value[/C][C]0.00542486000954119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70594&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70594&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.23299713988329
beta0.060085965432694
S.D.0.0201869390681857
T-STAT2.97647727720091
p-value0.00542486000954119






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.1263679533619
beta2.53073947380842
S.D.0.774552825283704
T-STAT3.26735555174233
p-value0.00253727048241806
Lambda-1.53073947380842

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.1263679533619 \tabularnewline
beta & 2.53073947380842 \tabularnewline
S.D. & 0.774552825283704 \tabularnewline
T-STAT & 3.26735555174233 \tabularnewline
p-value & 0.00253727048241806 \tabularnewline
Lambda & -1.53073947380842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70594&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.1263679533619[/C][/ROW]
[ROW][C]beta[/C][C]2.53073947380842[/C][/ROW]
[ROW][C]S.D.[/C][C]0.774552825283704[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.26735555174233[/C][/ROW]
[ROW][C]p-value[/C][C]0.00253727048241806[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.53073947380842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70594&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70594&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.1263679533619
beta2.53073947380842
S.D.0.774552825283704
T-STAT3.26735555174233
p-value0.00253727048241806
Lambda-1.53073947380842


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')