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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, 31 May 2008 07:23:36 -0600
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/May/31/t1212240280n19285e1fvecapk.htm/, Retrieved Wed, 15 May 2024 11:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13593, Retrieved Wed, 15 May 2024 11:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

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] [Standard deviatio...] [2008-05-31 13:23:36] [3e68c9212ad297cb41373898449ccda3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
68,4
70,6
83,9
90,1
90,6
87,1
90,8
94,1
99,8
96,8
87
96,3
107,1
115,2
106,1
89,5
91,3
97,6
100,7
104,6
94,7
101,8
102,5
105,3
110,3
109,8
117,3
118,8
131,3
125,9
133,1
147
145,8
164,4
149,8
137,7
151,7
156,8
180
180,4
170,4
191,6
199,5
218,2
217,5
205
194
199,3
219,3
211,1
215,2
240,2
242,2
240,7
255,4
253
218,2
203,7
205,6
215,6
188,5
202,9
214
230,3
230
241
259,6
247,8
270,3
289,7
322,7
315
320,2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13593&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]4 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=13593&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13593&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
187.95833333333339.7575572887082931.4
2101.3666666666677.2316643794474925.7
3132.617.064529932529154.6
4188.721.525798475317966.5
5226.68333333333318.424086671989251.7
6250.98333333333342.3723930993955134.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 87.9583333333333 & 9.75755728870829 & 31.4 \tabularnewline
2 & 101.366666666667 & 7.23166437944749 & 25.7 \tabularnewline
3 & 132.6 & 17.0645299325291 & 54.6 \tabularnewline
4 & 188.7 & 21.5257984753179 & 66.5 \tabularnewline
5 & 226.683333333333 & 18.4240866719892 & 51.7 \tabularnewline
6 & 250.983333333333 & 42.3723930993955 & 134.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13593&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]87.9583333333333[/C][C]9.75755728870829[/C][C]31.4[/C][/ROW]
[ROW][C]2[/C][C]101.366666666667[/C][C]7.23166437944749[/C][C]25.7[/C][/ROW]
[ROW][C]3[/C][C]132.6[/C][C]17.0645299325291[/C][C]54.6[/C][/ROW]
[ROW][C]4[/C][C]188.7[/C][C]21.5257984753179[/C][C]66.5[/C][/ROW]
[ROW][C]5[/C][C]226.683333333333[/C][C]18.4240866719892[/C][C]51.7[/C][/ROW]
[ROW][C]6[/C][C]250.983333333333[/C][C]42.3723930993955[/C][C]134.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13593&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13593&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
187.95833333333339.7575572887082931.4
2101.3666666666677.2316643794474925.7
3132.617.064529932529154.6
4188.721.525798475317966.5
5226.68333333333318.424086671989251.7
6250.98333333333342.3723930993955134.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.31747769212769
beta0.156108668325127
S.D.0.0495913366069839
T-STAT3.14790201285162
p-value0.0345837210149169

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6.31747769212769 \tabularnewline
beta & 0.156108668325127 \tabularnewline
S.D. & 0.0495913366069839 \tabularnewline
T-STAT & 3.14790201285162 \tabularnewline
p-value & 0.0345837210149169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13593&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.31747769212769[/C][/ROW]
[ROW][C]beta[/C][C]0.156108668325127[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0495913366069839[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.14790201285162[/C][/ROW]
[ROW][C]p-value[/C][C]0.0345837210149169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13593&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13593&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-6.31747769212769
beta0.156108668325127
S.D.0.0495913366069839
T-STAT3.14790201285162
p-value0.0345837210149169






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.57114269917458
beta1.26772246743142
S.D.0.333993048640465
T-STAT3.79565524669376
p-value0.0191752349845574
Lambda-0.267722467431423

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.57114269917458 \tabularnewline
beta & 1.26772246743142 \tabularnewline
S.D. & 0.333993048640465 \tabularnewline
T-STAT & 3.79565524669376 \tabularnewline
p-value & 0.0191752349845574 \tabularnewline
Lambda & -0.267722467431423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13593&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.57114269917458[/C][/ROW]
[ROW][C]beta[/C][C]1.26772246743142[/C][/ROW]
[ROW][C]S.D.[/C][C]0.333993048640465[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.79565524669376[/C][/ROW]
[ROW][C]p-value[/C][C]0.0191752349845574[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.267722467431423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13593&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13593&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-3.57114269917458
beta1.26772246743142
S.D.0.333993048640465
T-STAT3.79565524669376
p-value0.0191752349845574
Lambda-0.267722467431423


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')