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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 14 Dec 2008 05:23:38 -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/2008/Dec/14/t122925762134l7kv3b326gr4c.htm/, Retrieved Wed, 15 May 2024 22:22:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33320, Retrieved Wed, 15 May 2024 22:22:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

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] [VAC Standard Devi...] [2008-12-14 12:23:38] [490fee4f334e2e025c95681783e3fd0b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
124,1
124,4
115,7
108,3
102,3
104,6
104
103,5
96
96,6
95,4
92,1
93
90,4
93,3
97,1
111
114,1
113,3
111
107,2
118,3
134,1
139
116,7
112,5
122,8
130
125,6
123,8
135,8
136,4
135,3
149,5
159,6
161,4
175,2
199,5
245
257,8

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33320&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33320&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1118.1257.6917163234222316.1
2103.60.9763879010584532.30000000000000
395.0252.010596926288314.5
493.452.759830912694956.69999999999999
5112.351.592691642053373.09999999999999
6124.6514.606505399992231.8
7120.57.6153354051764117.5
8130.46.6272166103123612.6
9151.4511.972886034703626.1
10219.37538.641805944684782.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 118.125 & 7.69171632342223 & 16.1 \tabularnewline
2 & 103.6 & 0.976387901058453 & 2.30000000000000 \tabularnewline
3 & 95.025 & 2.01059692628831 & 4.5 \tabularnewline
4 & 93.45 & 2.75983091269495 & 6.69999999999999 \tabularnewline
5 & 112.35 & 1.59269164205337 & 3.09999999999999 \tabularnewline
6 & 124.65 & 14.6065053999922 & 31.8 \tabularnewline
7 & 120.5 & 7.61533540517641 & 17.5 \tabularnewline
8 & 130.4 & 6.62721661031236 & 12.6 \tabularnewline
9 & 151.45 & 11.9728860347036 & 26.1 \tabularnewline
10 & 219.375 & 38.6418059446847 & 82.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33320&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]118.125[/C][C]7.69171632342223[/C][C]16.1[/C][/ROW]
[ROW][C]2[/C][C]103.6[/C][C]0.976387901058453[/C][C]2.30000000000000[/C][/ROW]
[ROW][C]3[/C][C]95.025[/C][C]2.01059692628831[/C][C]4.5[/C][/ROW]
[ROW][C]4[/C][C]93.45[/C][C]2.75983091269495[/C][C]6.69999999999999[/C][/ROW]
[ROW][C]5[/C][C]112.35[/C][C]1.59269164205337[/C][C]3.09999999999999[/C][/ROW]
[ROW][C]6[/C][C]124.65[/C][C]14.6065053999922[/C][C]31.8[/C][/ROW]
[ROW][C]7[/C][C]120.5[/C][C]7.61533540517641[/C][C]17.5[/C][/ROW]
[ROW][C]8[/C][C]130.4[/C][C]6.62721661031236[/C][C]12.6[/C][/ROW]
[ROW][C]9[/C][C]151.45[/C][C]11.9728860347036[/C][C]26.1[/C][/ROW]
[ROW][C]10[/C][C]219.375[/C][C]38.6418059446847[/C][C]82.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33320&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
1118.1257.6917163234222316.1
2103.60.9763879010584532.30000000000000
395.0252.010596926288314.5
493.452.759830912694956.69999999999999
5112.351.592691642053373.09999999999999
6124.6514.606505399992231.8
7120.57.6153354051764117.5
8130.46.6272166103123612.6
9151.4511.972886034703626.1
10219.37538.641805944684782.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-27.4313432099107
beta0.290646338593292
S.D.0.0327260636407792
T-STAT8.8811884552814
p-value2.04309112537430e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -27.4313432099107 \tabularnewline
beta & 0.290646338593292 \tabularnewline
S.D. & 0.0327260636407792 \tabularnewline
T-STAT & 8.8811884552814 \tabularnewline
p-value & 2.04309112537430e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33320&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-27.4313432099107[/C][/ROW]
[ROW][C]beta[/C][C]0.290646338593292[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0327260636407792[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.8811884552814[/C][/ROW]
[ROW][C]p-value[/C][C]2.04309112537430e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33320&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-27.4313432099107
beta0.290646338593292
S.D.0.0327260636407792
T-STAT8.8811884552814
p-value2.04309112537430e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-16.6835830885389
beta3.81867400733671
S.D.0.869463763402118
T-STAT4.39198753079099
p-value0.00231139143953474
Lambda-2.81867400733671

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -16.6835830885389 \tabularnewline
beta & 3.81867400733671 \tabularnewline
S.D. & 0.869463763402118 \tabularnewline
T-STAT & 4.39198753079099 \tabularnewline
p-value & 0.00231139143953474 \tabularnewline
Lambda & -2.81867400733671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33320&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-16.6835830885389[/C][/ROW]
[ROW][C]beta[/C][C]3.81867400733671[/C][/ROW]
[ROW][C]S.D.[/C][C]0.869463763402118[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.39198753079099[/C][/ROW]
[ROW][C]p-value[/C][C]0.00231139143953474[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.81867400733671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33320&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-16.6835830885389
beta3.81867400733671
S.D.0.869463763402118
T-STAT4.39198753079099
p-value0.00231139143953474
Lambda-2.81867400733671


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')