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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 computationSun, 29 Nov 2015 14:21:36 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448806936w5oa2v8i8nxqxz4.htm/, Retrieved Wed, 15 May 2024 06:59:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284450, Retrieved Wed, 15 May 2024 06:59:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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] [Spreidings en gem...] [2015-11-29 14:21:36] [3f1a7081c5450f075552d8bc3f139f2c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26.133
25.979
25.541
25.308
25.663
25.78
25.328
24.806
24.651
24.531
24.633
25.174
24.449
24.277
24.393
24.301
24.381
24.286
24.335
24.273
24.556
24.841
25.464
25.514
25.531
25.042
24.676
24.809
25.313
25.64
25.447
25.021
24.752
24.939
25.365
25.214
25.563
25.475
25.659
25.841
25.888
25.759
25.944
25.818
25.789
25.662
26.927
27.521
27.485
27.444
27.395
27.45
27.437
27.45
27.458
27.816
27.599
27.588
27.667
27.64

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284450&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284450&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284450&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'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
125.29391666666670.5471369212601731.602
224.58916666666670.4496050455340741.241
325.145750.3194213873980150.964000000000002
425.98716666666670.606375196382472.046
527.535750.1260130765220240.420999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 25.2939166666667 & 0.547136921260173 & 1.602 \tabularnewline
2 & 24.5891666666667 & 0.449605045534074 & 1.241 \tabularnewline
3 & 25.14575 & 0.319421387398015 & 0.964000000000002 \tabularnewline
4 & 25.9871666666667 & 0.60637519638247 & 2.046 \tabularnewline
5 & 27.53575 & 0.126013076522024 & 0.420999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284450&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]25.2939166666667[/C][C]0.547136921260173[/C][C]1.602[/C][/ROW]
[ROW][C]2[/C][C]24.5891666666667[/C][C]0.449605045534074[/C][C]1.241[/C][/ROW]
[ROW][C]3[/C][C]25.14575[/C][C]0.319421387398015[/C][C]0.964000000000002[/C][/ROW]
[ROW][C]4[/C][C]25.9871666666667[/C][C]0.60637519638247[/C][C]2.046[/C][/ROW]
[ROW][C]5[/C][C]27.53575[/C][C]0.126013076522024[/C][C]0.420999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284450&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284450&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
125.29391666666670.5471369212601731.602
224.58916666666670.4496050455340741.241
325.145750.3194213873980150.964000000000002
425.98716666666670.606375196382472.046
527.535750.1260130765220240.420999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.97379959612655
beta-0.099729846956856
S.D.0.078966180129151
T-STAT-1.2629437918074
p-value0.295844695487713

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.97379959612655 \tabularnewline
beta & -0.099729846956856 \tabularnewline
S.D. & 0.078966180129151 \tabularnewline
T-STAT & -1.2629437918074 \tabularnewline
p-value & 0.295844695487713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284450&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.97379959612655[/C][/ROW]
[ROW][C]beta[/C][C]-0.099729846956856[/C][/ROW]
[ROW][C]S.D.[/C][C]0.078966180129151[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.2629437918074[/C][/ROW]
[ROW][C]p-value[/C][C]0.295844695487713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284450&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284450&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)
alpha2.97379959612655
beta-0.099729846956856
S.D.0.078966180129151
T-STAT-1.2629437918074
p-value0.295844695487713






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha33.5283092236593
beta-10.6438677746242
S.D.5.77070175068065
T-STAT-1.84446679701801
p-value0.162314993224848
Lambda11.6438677746242

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 33.5283092236593 \tabularnewline
beta & -10.6438677746242 \tabularnewline
S.D. & 5.77070175068065 \tabularnewline
T-STAT & -1.84446679701801 \tabularnewline
p-value & 0.162314993224848 \tabularnewline
Lambda & 11.6438677746242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284450&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]33.5283092236593[/C][/ROW]
[ROW][C]beta[/C][C]-10.6438677746242[/C][/ROW]
[ROW][C]S.D.[/C][C]5.77070175068065[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.84446679701801[/C][/ROW]
[ROW][C]p-value[/C][C]0.162314993224848[/C][/ROW]
[ROW][C]Lambda[/C][C]11.6438677746242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284450&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284450&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)
alpha33.5283092236593
beta-10.6438677746242
S.D.5.77070175068065
T-STAT-1.84446679701801
p-value0.162314993224848
Lambda11.6438677746242


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')