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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 computationFri, 25 May 2012 07:34:02 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/25/t1337945828x7j0v63a379aab6.htm/, Retrieved Fri, 03 May 2024 20:39:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167467, Retrieved Fri, 03 May 2024 20:39:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact105

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] [] [2012-05-25 11:34:02] [d94b10b2615af2e11b32dea0ad6a3c7b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
227.81
227.81
227.01
227.26
227.1
227.59
227.59
227.7
227.75
226.33
225.95
226.33
226.33
226.22
224.84
221.88
222.37
221.8
221.8
221.8
221.9
220.2
219.95
220.05
220.05
220.05
220.62
221.53
221.61
221.5
221.5
221.87
222.27
220.86
221.49
221.67
221.67
221.72
221.67
220.29
220.75
219.59
219.59
219.59
219.82
221.59
220.9
221.01
221.01
219.69
221
219.82
218.04
217.97
217.97
217.53
217
217.18
217.68
217.71

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'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167467&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167467&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'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1227.1858333333330.6553619171299481.86000000000001
2222.4283333333332.214570893519616.38000000000002
3221.2516666666670.7019949926437982.22
4220.68250.8784296422387122.13
5218.551.435960242549154.00999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 227.185833333333 & 0.655361917129948 & 1.86000000000001 \tabularnewline
2 & 222.428333333333 & 2.21457089351961 & 6.38000000000002 \tabularnewline
3 & 221.251666666667 & 0.701994992643798 & 2.22 \tabularnewline
4 & 220.6825 & 0.878429642238712 & 2.13 \tabularnewline
5 & 218.55 & 1.43596024254915 & 4.00999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167467&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]227.185833333333[/C][C]0.655361917129948[/C][C]1.86000000000001[/C][/ROW]
[ROW][C]2[/C][C]222.428333333333[/C][C]2.21457089351961[/C][C]6.38000000000002[/C][/ROW]
[ROW][C]3[/C][C]221.251666666667[/C][C]0.701994992643798[/C][C]2.22[/C][/ROW]
[ROW][C]4[/C][C]220.6825[/C][C]0.878429642238712[/C][C]2.13[/C][/ROW]
[ROW][C]5[/C][C]218.55[/C][C]1.43596024254915[/C][C]4.00999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167467&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
1227.1858333333330.6553619171299481.86000000000001
2222.4283333333332.214570893519616.38000000000002
3221.2516666666670.7019949926437982.22
4220.68250.8784296422387122.13
5218.551.435960242549154.00999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha14.116239048947
beta-0.058278510663458
S.D.0.113331214887978
T-STAT-0.514231765017813
p-value0.642572962581166

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 14.116239048947 \tabularnewline
beta & -0.058278510663458 \tabularnewline
S.D. & 0.113331214887978 \tabularnewline
T-STAT & -0.514231765017813 \tabularnewline
p-value & 0.642572962581166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167467&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.116239048947[/C][/ROW]
[ROW][C]beta[/C][C]-0.058278510663458[/C][/ROW]
[ROW][C]S.D.[/C][C]0.113331214887978[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.514231765017813[/C][/ROW]
[ROW][C]p-value[/C][C]0.642572962581166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167467&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)
alpha14.116239048947
beta-0.058278510663458
S.D.0.113331214887978
T-STAT-0.514231765017813
p-value0.642572962581166






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha77.7764448174331
beta-14.3866061744228
S.D.19.0164354556777
T-STAT-0.756535377408359
p-value0.504317106185191
Lambda15.3866061744228

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 77.7764448174331 \tabularnewline
beta & -14.3866061744228 \tabularnewline
S.D. & 19.0164354556777 \tabularnewline
T-STAT & -0.756535377408359 \tabularnewline
p-value & 0.504317106185191 \tabularnewline
Lambda & 15.3866061744228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167467&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]77.7764448174331[/C][/ROW]
[ROW][C]beta[/C][C]-14.3866061744228[/C][/ROW]
[ROW][C]S.D.[/C][C]19.0164354556777[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.756535377408359[/C][/ROW]
[ROW][C]p-value[/C][C]0.504317106185191[/C][/ROW]
[ROW][C]Lambda[/C][C]15.3866061744228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167467&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167467&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)
alpha77.7764448174331
beta-14.3866061744228
S.D.19.0164354556777
T-STAT-0.756535377408359
p-value0.504317106185191
Lambda15.3866061744228


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')