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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 computationThu, 22 Nov 2007 05:52:11 -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/2007/Nov/22/t1195735450om5v2ssqxsa8ik8.htm/, Retrieved Fri, 03 May 2024 01:16:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5952, Retrieved Fri, 03 May 2024 01:16:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS10 G29 Q1
Estimated Impact196

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] [St Dev Mean Plot] [2007-11-22 12:52:11] [7a600ca82a81f1b71fd92dcbb183f5b4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
174,1
180,4
182,6
207,1
213,7
186,5
179,1
168,3
156,5
144,3
138,9
137,8
136,3
140,3
149,1
149,2
140,4
129
124,7
130,8
130,1
133,2
130,1
126,6
124,8
125,3
126,9
120,1
118,7
117,7
113,4
107,5
107,6
114,3
114,9
111,2
109,9
108,6
109,2
106,4
103,7
103
96,9
104,7
102,2
99
95,8
94,5
102,7
103,2
105,6
103,9
107,2
100,7
92,1
90,3
93,4
98,5
100,8
102,3
104,7
101,1
101,4
99,5
98,4
96,3
100,7
101,2
100,3
97,8
97,4
98,6
99,7
99
98,1
97
98,5
103,8
114,4
124,5
134,2
131,8
125,6
119,9
114,9
115,5
112,5
111,4
115,3
110,8
103,7
111,1
113
111,2
117,6
121,7
127,3
129,8
137,1
141,4
137,4
130,7
117,2
110,8
111,4
108,2
108,8
110,2
109,5
109,5
116
111,2
112,1
114
119,1
114,1
115,1
115,4
110,8
116
119,2
126,5
127,8
131,3
140,3
137,3
143
134,5
139,9
159,3
170,4
175
175,8
180,9
180,3
169,6
172,3
184,8
177,7
184,6
211,4

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5952&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5952&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1172.44166666666724.6853456098712114
2134.9833333333338.2071845835145450.2
3116.8666666666676.5880516271826728.8
4102.8255.3079914023359912.9
5100.0583333333335.432471115822198.8
699.78333333333332.271896817972858.4
7112.20833333333314.402427720437442.1
8113.2254.3940300408622631.4
9122.52512.676400765344948
10113.5666666666672.9714806022750621.3
11142.04166666666717.471246941674579.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 172.441666666667 & 24.6853456098712 & 114 \tabularnewline
2 & 134.983333333333 & 8.20718458351454 & 50.2 \tabularnewline
3 & 116.866666666667 & 6.58805162718267 & 28.8 \tabularnewline
4 & 102.825 & 5.30799140233599 & 12.9 \tabularnewline
5 & 100.058333333333 & 5.43247111582219 & 8.8 \tabularnewline
6 & 99.7833333333333 & 2.27189681797285 & 8.4 \tabularnewline
7 & 112.208333333333 & 14.4024277204374 & 42.1 \tabularnewline
8 & 113.225 & 4.39403004086226 & 31.4 \tabularnewline
9 & 122.525 & 12.6764007653449 & 48 \tabularnewline
10 & 113.566666666667 & 2.97148060227506 & 21.3 \tabularnewline
11 & 142.041666666667 & 17.4712469416745 & 79.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5952&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]172.441666666667[/C][C]24.6853456098712[/C][C]114[/C][/ROW]
[ROW][C]2[/C][C]134.983333333333[/C][C]8.20718458351454[/C][C]50.2[/C][/ROW]
[ROW][C]3[/C][C]116.866666666667[/C][C]6.58805162718267[/C][C]28.8[/C][/ROW]
[ROW][C]4[/C][C]102.825[/C][C]5.30799140233599[/C][C]12.9[/C][/ROW]
[ROW][C]5[/C][C]100.058333333333[/C][C]5.43247111582219[/C][C]8.8[/C][/ROW]
[ROW][C]6[/C][C]99.7833333333333[/C][C]2.27189681797285[/C][C]8.4[/C][/ROW]
[ROW][C]7[/C][C]112.208333333333[/C][C]14.4024277204374[/C][C]42.1[/C][/ROW]
[ROW][C]8[/C][C]113.225[/C][C]4.39403004086226[/C][C]31.4[/C][/ROW]
[ROW][C]9[/C][C]122.525[/C][C]12.6764007653449[/C][C]48[/C][/ROW]
[ROW][C]10[/C][C]113.566666666667[/C][C]2.97148060227506[/C][C]21.3[/C][/ROW]
[ROW][C]11[/C][C]142.041666666667[/C][C]17.4712469416745[/C][C]79.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5952&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
1172.44166666666724.6853456098712114
2134.9833333333338.2071845835145450.2
3116.8666666666676.5880516271826728.8
4102.8255.3079914023359912.9
5100.0583333333335.432471115822198.8
699.78333333333332.271896817972858.4
7112.20833333333314.402427720437442.1
8113.2254.3940300408622631.4
9122.52512.676400765344948
10113.5666666666672.9714806022750621.3
11142.04166666666717.471246941674579.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-24.0446961827912
beta0.277259115941449
S.D.0.0555425344408066
T-STAT4.99183407334306
p-value0.000747253723602543

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -24.0446961827912 \tabularnewline
beta & 0.277259115941449 \tabularnewline
S.D. & 0.0555425344408066 \tabularnewline
T-STAT & 4.99183407334306 \tabularnewline
p-value & 0.000747253723602543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5952&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-24.0446961827912[/C][/ROW]
[ROW][C]beta[/C][C]0.277259115941449[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0555425344408066[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.99183407334306[/C][/ROW]
[ROW][C]p-value[/C][C]0.000747253723602543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5952&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5952&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-24.0446961827912
beta0.277259115941449
S.D.0.0555425344408066
T-STAT4.99183407334306
p-value0.000747253723602543






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-14.7693622934270
beta3.50689357671818
S.D.0.951449526190713
T-STAT3.68584300079334
p-value0.00502969013519181
Lambda-2.50689357671818

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -14.7693622934270 \tabularnewline
beta & 3.50689357671818 \tabularnewline
S.D. & 0.951449526190713 \tabularnewline
T-STAT & 3.68584300079334 \tabularnewline
p-value & 0.00502969013519181 \tabularnewline
Lambda & -2.50689357671818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5952&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.7693622934270[/C][/ROW]
[ROW][C]beta[/C][C]3.50689357671818[/C][/ROW]
[ROW][C]S.D.[/C][C]0.951449526190713[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.68584300079334[/C][/ROW]
[ROW][C]p-value[/C][C]0.00502969013519181[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.50689357671818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5952&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5952&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-14.7693622934270
beta3.50689357671818
S.D.0.951449526190713
T-STAT3.68584300079334
p-value0.00502969013519181
Lambda-2.50689357671818


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
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')