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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 computationSat, 23 Jul 2016 09:16:55 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jul/23/t1469261832dqomfqkf9lvk03g.htm/, Retrieved Tue, 07 May 2024 14:23:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295934, Retrieved Tue, 07 May 2024 14:23:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

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] [] [2016-07-23 08:16:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
181896,00
181580,00
181234,00
180598,00
187123,00
186807,00
181896,00
178638,00
178954,00
178954,00
179269,00
179936,00
181580,00
179616,00
181580,00
179936,00
185158,00
187469,00
177656,00
175025,00
177305,00
176989,00
175025,00
175345,00
179269,00
178638,00
179269,00
179269,00
183545,00
184176,00
172398,00
172398,00
176989,00
174709,00
170785,00
172398,00
176327,00
174363,00
174047,00
169803,00
176007,00
177305,00
164545,00
164229,00
170785,00
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160967,00
163598,00
166509,00
167176,00
165212,00
161287,00
169456,00
169456,00
155078,00
154101,00
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144283,00
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132190,00
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126301,00
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121043,00
125950,00
120728,00
120412,00
115154,00
123670,00
125319,00
109266,00
105688,00
107968,00
99132,00
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98470,00
91946,00
92928,00
89004,00
97172,00
98150,00
78524,00
77221,00
80799,00
71333,00
62817,00
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57244,00
64462,00
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40244,00
35333,00
43186,00
45813,00
24853,00
23240,00
26502,00
18649,00
12444,00
15040,00

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295934&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295934&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1181407.0833333332851.823992348298485
2179390.3333333334000.7807495613412444
3176986.9166666674470.797294327913391
4169929.3333333335713.65370022216338
5158890.59045.1121556944225840
6136404.91666666710976.241354177333373
7111349.66666666712568.848564702535969
883677.333333333312712.39776634235653
953624.2513031.961863922440244
1030616.7511989.350919765133369

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 181407.083333333 & 2851.82399234829 & 8485 \tabularnewline
2 & 179390.333333333 & 4000.78074956134 & 12444 \tabularnewline
3 & 176986.916666667 & 4470.7972943279 & 13391 \tabularnewline
4 & 169929.333333333 & 5713.653700222 & 16338 \tabularnewline
5 & 158890.5 & 9045.11215569442 & 25840 \tabularnewline
6 & 136404.916666667 & 10976.2413541773 & 33373 \tabularnewline
7 & 111349.666666667 & 12568.8485647025 & 35969 \tabularnewline
8 & 83677.3333333333 & 12712.397766342 & 35653 \tabularnewline
9 & 53624.25 & 13031.9618639224 & 40244 \tabularnewline
10 & 30616.75 & 11989.3509197651 & 33369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295934&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]181407.083333333[/C][C]2851.82399234829[/C][C]8485[/C][/ROW]
[ROW][C]2[/C][C]179390.333333333[/C][C]4000.78074956134[/C][C]12444[/C][/ROW]
[ROW][C]3[/C][C]176986.916666667[/C][C]4470.7972943279[/C][C]13391[/C][/ROW]
[ROW][C]4[/C][C]169929.333333333[/C][C]5713.653700222[/C][C]16338[/C][/ROW]
[ROW][C]5[/C][C]158890.5[/C][C]9045.11215569442[/C][C]25840[/C][/ROW]
[ROW][C]6[/C][C]136404.916666667[/C][C]10976.2413541773[/C][C]33373[/C][/ROW]
[ROW][C]7[/C][C]111349.666666667[/C][C]12568.8485647025[/C][C]35969[/C][/ROW]
[ROW][C]8[/C][C]83677.3333333333[/C][C]12712.397766342[/C][C]35653[/C][/ROW]
[ROW][C]9[/C][C]53624.25[/C][C]13031.9618639224[/C][C]40244[/C][/ROW]
[ROW][C]10[/C][C]30616.75[/C][C]11989.3509197651[/C][C]33369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295934&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
1181407.0833333332851.823992348298485
2179390.3333333334000.7807495613412444
3176986.9166666674470.797294327913391
4169929.3333333335713.65370022216338
5158890.59045.1121556944225840
6136404.91666666710976.241354177333373
7111349.66666666712568.848564702535969
883677.333333333312712.39776634235653
953624.2513031.961863922440244
1030616.7511989.350919765133369






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha16729.7299912442
beta-0.0623393590904556
S.D.0.0134589047107074
T-STAT-4.63183003598061
p-value0.00168403022727226

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 16729.7299912442 \tabularnewline
beta & -0.0623393590904556 \tabularnewline
S.D. & 0.0134589047107074 \tabularnewline
T-STAT & -4.63183003598061 \tabularnewline
p-value & 0.00168403022727226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295934&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]16729.7299912442[/C][/ROW]
[ROW][C]beta[/C][C]-0.0623393590904556[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0134589047107074[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.63183003598061[/C][/ROW]
[ROW][C]p-value[/C][C]0.00168403022727226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295934&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)
alpha16729.7299912442
beta-0.0623393590904556
S.D.0.0134589047107074
T-STAT-4.63183003598061
p-value0.00168403022727226






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha16.4893907265743
beta-0.648445226888153
S.D.0.240031778968446
T-STAT-2.70149740036463
p-value0.0270113309975445
Lambda1.64844522688815

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 16.4893907265743 \tabularnewline
beta & -0.648445226888153 \tabularnewline
S.D. & 0.240031778968446 \tabularnewline
T-STAT & -2.70149740036463 \tabularnewline
p-value & 0.0270113309975445 \tabularnewline
Lambda & 1.64844522688815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295934&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]16.4893907265743[/C][/ROW]
[ROW][C]beta[/C][C]-0.648445226888153[/C][/ROW]
[ROW][C]S.D.[/C][C]0.240031778968446[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.70149740036463[/C][/ROW]
[ROW][C]p-value[/C][C]0.0270113309975445[/C][/ROW]
[ROW][C]Lambda[/C][C]1.64844522688815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295934&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295934&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)
alpha16.4893907265743
beta-0.648445226888153
S.D.0.240031778968446
T-STAT-2.70149740036463
p-value0.0270113309975445
Lambda1.64844522688815


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')