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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 computationThu, 03 Dec 2009 09:26:13 -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/03/t1259857631kzu3nwsp2wy8pou.htm/, Retrieved Fri, 09 May 2025 23:09:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62880, Retrieved Fri, 09 May 2025 23:09:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [standard deviatio...] [2009-11-24 21:20:13] [8b1aef4e7013bd33fbc2a5833375c5f5]
-    D          [Standard Deviation-Mean Plot] [SHw WS8] [2009-11-26 18:11:50] [af2352cd9a951bedd08ebe247d0de1a2]
-    D              [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 16:26:13] [d9efc2d105d810fc0b0ac636e31105d1] [Current]
-    D                [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 17:45:49] [af2352cd9a951bedd08ebe247d0de1a2]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91.2
80.8
72.3
99.7
90.1
83.1
71.9
78.6
87.2
90.6
80
73.1
85.6
73.8
70.6
91.8
81.3
85.2
69.6
83.3
89.8
99.5
78.9
83.8
92
80.9
74.6
97.9
88.3
88.1
66.4
92.3
95.6
99.7
78.9
79.4
87.8
80.5
71.8
89.2
96.4
83.5
64.3
85.9
89.2
81.8
79.5
68.7
76.4
73.6
57.7
78.3
75.5
62.4
55.6
62.9
66.7
66.8
59.9
52
61.2

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62880&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62880&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62880&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
183.21666666666678.740171969738727.8
282.76666666666678.7659810770058329.9
386.17510.182795204747033.3
481.559.3539976869396732.1
565.658.738368892939426.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 83.2166666666667 & 8.7401719697387 & 27.8 \tabularnewline
2 & 82.7666666666667 & 8.76598107700583 & 29.9 \tabularnewline
3 & 86.175 & 10.1827952047470 & 33.3 \tabularnewline
4 & 81.55 & 9.35399768693967 & 32.1 \tabularnewline
5 & 65.65 & 8.7383688929394 & 26.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62880&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]83.2166666666667[/C][C]8.7401719697387[/C][C]27.8[/C][/ROW]
[ROW][C]2[/C][C]82.7666666666667[/C][C]8.76598107700583[/C][C]29.9[/C][/ROW]
[ROW][C]3[/C][C]86.175[/C][C]10.1827952047470[/C][C]33.3[/C][/ROW]
[ROW][C]4[/C][C]81.55[/C][C]9.35399768693967[/C][C]32.1[/C][/ROW]
[ROW][C]5[/C][C]65.65[/C][C]8.7383688929394[/C][C]26.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62880&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62880&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
183.21666666666678.740171969738727.8
282.76666666666678.7659810770058329.9
386.17510.182795204747033.3
481.559.3539976869396732.1
565.658.738368892939426.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.06746517803794
beta0.0386720087002421
S.D.0.0388580470705529
T-STAT0.995212359232233
p-value0.392986635228523

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.06746517803794 \tabularnewline
beta & 0.0386720087002421 \tabularnewline
S.D. & 0.0388580470705529 \tabularnewline
T-STAT & 0.995212359232233 \tabularnewline
p-value & 0.392986635228523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62880&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.06746517803794[/C][/ROW]
[ROW][C]beta[/C][C]0.0386720087002421[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0388580470705529[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.995212359232233[/C][/ROW]
[ROW][C]p-value[/C][C]0.392986635228523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62880&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62880&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)
alpha6.06746517803794
beta0.0386720087002421
S.D.0.0388580470705529
T-STAT0.995212359232233
p-value0.392986635228523






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.906696670922283
beta0.298433674936748
S.D.0.310561808625914
T-STAT0.960947761919515
p-value0.407467486853469
Lambda0.701566325063252

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.906696670922283 \tabularnewline
beta & 0.298433674936748 \tabularnewline
S.D. & 0.310561808625914 \tabularnewline
T-STAT & 0.960947761919515 \tabularnewline
p-value & 0.407467486853469 \tabularnewline
Lambda & 0.701566325063252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62880&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.906696670922283[/C][/ROW]
[ROW][C]beta[/C][C]0.298433674936748[/C][/ROW]
[ROW][C]S.D.[/C][C]0.310561808625914[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.960947761919515[/C][/ROW]
[ROW][C]p-value[/C][C]0.407467486853469[/C][/ROW]
[ROW][C]Lambda[/C][C]0.701566325063252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62880&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62880&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)
alpha0.906696670922283
beta0.298433674936748
S.D.0.310561808625914
T-STAT0.960947761919515
p-value0.407467486853469
Lambda0.701566325063252


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')