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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 05:41:22 -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/t1195735231nn3jhpags0wl0dc.htm/, Retrieved Thu, 02 May 2024 21:17:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5950, Retrieved Thu, 02 May 2024 21:17:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS10 G29 Q1
Estimated Impact233

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...] [2007-11-22 12:41:22] [7a600ca82a81f1b71fd92dcbb183f5b4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
153.4
159.5
157.4
169.1
172.6
161.7
159.2
157.4
153.9
144.8
142.2
140.1
143.4
153.3
166.9
170.6
182.8
170.3
156.6
155.2
154.7
151.6
152.1
153.2
149.5
149.7
144.3
140
137.8
132.2
128.9
123.1
120.4
122.8
126
124.5
120.6
114.7
111.7
109.1
108
107.7
99.9
103.7
103.4
103.4
104.7
105.8
105.3
103
103.8
103.4
105.8
101.4
97
94.3
96.6
97.1
95.7
96.9
97.4
95.3
93.6
91.5
93.1
91.7
94.3
93.9
90.9
88.3
91.3
91.7
92.4
92
95.6
95.8
96.4
99
107
109.7
116.2
115.9
113.8
112.6
113.7
115.9
110.3
111.3
113.4
108.2
104.8
106
110.9
115
118.4
121.4
128.8
131.7
141.7
142.9
139.4
134.7
125
113.6
111.5
108.5
112.3
116.6
115.5
120.1
132.9
128.1
129.3
132.5
131
124.9
120.8
122
122.1
127.4
135.2
137.3
135
136
138.4
134.7
138.4
133.9
133.6
141.2
151.8
155.4
156.6
161.6
160.7
156
159.5
168.7
169.9
169.9
185.9

Tables (Output of Computation)





Summary of compuational 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 compuational 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=5950&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]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=5950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5950&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1155.9416666666679.9356528205094380.2
2159.22511.041419951503390.8
3133.26666666666710.658017326563856.1
4107.7255.7198418604967529.1
5100.0254.1367806982549312.7
692.752.370078633141265.7
7103.8666666666679.538661363423121.9
8112.4416666666674.8888478533631427.5
9125.55833333333312.694484008514352
10125.555.5120529091008644.6
11139.2416666666677.0944867625672964.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 155.941666666667 & 9.93565282050943 & 80.2 \tabularnewline
2 & 159.225 & 11.0414199515033 & 90.8 \tabularnewline
3 & 133.266666666667 & 10.6580173265638 & 56.1 \tabularnewline
4 & 107.725 & 5.71984186049675 & 29.1 \tabularnewline
5 & 100.025 & 4.13678069825493 & 12.7 \tabularnewline
6 & 92.75 & 2.37007863314126 & 5.7 \tabularnewline
7 & 103.866666666667 & 9.5386613634231 & 21.9 \tabularnewline
8 & 112.441666666667 & 4.88884785336314 & 27.5 \tabularnewline
9 & 125.558333333333 & 12.6944840085143 & 52 \tabularnewline
10 & 125.55 & 5.51205290910086 & 44.6 \tabularnewline
11 & 139.241666666667 & 7.09448676256729 & 64.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5950&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]155.941666666667[/C][C]9.93565282050943[/C][C]80.2[/C][/ROW]
[ROW][C]2[/C][C]159.225[/C][C]11.0414199515033[/C][C]90.8[/C][/ROW]
[ROW][C]3[/C][C]133.266666666667[/C][C]10.6580173265638[/C][C]56.1[/C][/ROW]
[ROW][C]4[/C][C]107.725[/C][C]5.71984186049675[/C][C]29.1[/C][/ROW]
[ROW][C]5[/C][C]100.025[/C][C]4.13678069825493[/C][C]12.7[/C][/ROW]
[ROW][C]6[/C][C]92.75[/C][C]2.37007863314126[/C][C]5.7[/C][/ROW]
[ROW][C]7[/C][C]103.866666666667[/C][C]9.5386613634231[/C][C]21.9[/C][/ROW]
[ROW][C]8[/C][C]112.441666666667[/C][C]4.88884785336314[/C][C]27.5[/C][/ROW]
[ROW][C]9[/C][C]125.558333333333[/C][C]12.6944840085143[/C][C]52[/C][/ROW]
[ROW][C]10[/C][C]125.55[/C][C]5.51205290910086[/C][C]44.6[/C][/ROW]
[ROW][C]11[/C][C]139.241666666667[/C][C]7.09448676256729[/C][C]64.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5950&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
1155.9416666666679.9356528205094380.2
2159.22511.041419951503390.8
3133.26666666666710.658017326563856.1
4107.7255.7198418604967529.1
5100.0254.1367806982549312.7
692.752.370078633141265.7
7103.8666666666679.538661363423121.9
8112.4416666666674.8888478533631427.5
9125.55833333333312.694484008514352
10125.555.5120529091008644.6
11139.2416666666677.0944867625672964.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.65555600099506
beta0.0994410363482491
S.D.0.0374996818973802
T-STAT2.65178346366709
p-value0.0263989150176327

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.65555600099506 \tabularnewline
beta & 0.0994410363482491 \tabularnewline
S.D. & 0.0374996818973802 \tabularnewline
T-STAT & 2.65178346366709 \tabularnewline
p-value & 0.0263989150176327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5950&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.65555600099506[/C][/ROW]
[ROW][C]beta[/C][C]0.0994410363482491[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0374996818973802[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.65178346366709[/C][/ROW]
[ROW][C]p-value[/C][C]0.0263989150176327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5950&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-4.65555600099506
beta0.0994410363482491
S.D.0.0374996818973802
T-STAT2.65178346366709
p-value0.0263989150176327






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.98086192861194
beta2.06329304207797
S.D.0.661714431713749
T-STAT3.11810192311255
p-value0.0123563765770049
Lambda-1.06329304207797

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.98086192861194 \tabularnewline
beta & 2.06329304207797 \tabularnewline
S.D. & 0.661714431713749 \tabularnewline
T-STAT & 3.11810192311255 \tabularnewline
p-value & 0.0123563765770049 \tabularnewline
Lambda & -1.06329304207797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5950&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.98086192861194[/C][/ROW]
[ROW][C]beta[/C][C]2.06329304207797[/C][/ROW]
[ROW][C]S.D.[/C][C]0.661714431713749[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.11810192311255[/C][/ROW]
[ROW][C]p-value[/C][C]0.0123563765770049[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.06329304207797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5950&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5950&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-7.98086192861194
beta2.06329304207797
S.D.0.661714431713749
T-STAT3.11810192311255
p-value0.0123563765770049
Lambda-1.06329304207797


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')