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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, 26 Apr 2013 14:56:53 -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/2013/Apr/26/t1367002829l7srmgv9x37b4za.htm/, Retrieved Sat, 27 Apr 2024 09:27:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208405, Retrieved Sat, 27 Apr 2024 09:27:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

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] [de spreidings- en...] [2013-04-26 18:56:53] [8907525eeb8291a8059cdce9cf2ca306] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.27
8.25
8.22
8.21
8.12
8.16
8.15
8.1
8.09
8.02
8.03
7.98
7.95
7.92
7.96
7.96
7.94
7.83
7.77
7.8
7.78
7.78
7.8
7.81
7.95
8.02
7.99
8.01
8.03
8.05
8.05
8.06
8.07
7.99
8
8.01
8
8.09
8.1
8.12
8.29
8.32
8.36
8.38
8.48
8.45
8.41
8.38
8.38
8.34
8.41
8.34
8.22
8.27
8.18
8.19
8.19
8.13
8.06
7.99
8
7.98
7.92
7.93
7.9
7.86
7.88
7.88
7.93
7.91
7.89
7.93

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208405&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208405&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208405&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.133333333333330.09384061277538970.289999999999999
27.858333333333330.07952510562232810.19
38.019166666666670.03476108935769050.12
48.281666666666670.161348484137080.48
58.2250.1288762620077530.42
67.91750.04092676385936230.14

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.13333333333333 & 0.0938406127753897 & 0.289999999999999 \tabularnewline
2 & 7.85833333333333 & 0.0795251056223281 & 0.19 \tabularnewline
3 & 8.01916666666667 & 0.0347610893576905 & 0.12 \tabularnewline
4 & 8.28166666666667 & 0.16134848413708 & 0.48 \tabularnewline
5 & 8.225 & 0.128876262007753 & 0.42 \tabularnewline
6 & 7.9175 & 0.0409267638593623 & 0.14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208405&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]8.13333333333333[/C][C]0.0938406127753897[/C][C]0.289999999999999[/C][/ROW]
[ROW][C]2[/C][C]7.85833333333333[/C][C]0.0795251056223281[/C][C]0.19[/C][/ROW]
[ROW][C]3[/C][C]8.01916666666667[/C][C]0.0347610893576905[/C][C]0.12[/C][/ROW]
[ROW][C]4[/C][C]8.28166666666667[/C][C]0.16134848413708[/C][C]0.48[/C][/ROW]
[ROW][C]5[/C][C]8.225[/C][C]0.128876262007753[/C][C]0.42[/C][/ROW]
[ROW][C]6[/C][C]7.9175[/C][C]0.0409267638593623[/C][C]0.14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208405&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208405&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
18.133333333333330.09384061277538970.289999999999999
27.858333333333330.07952510562232810.19
38.019166666666670.03476108935769050.12
48.281666666666670.161348484137080.48
58.2250.1288762620077530.42
67.91750.04092676385936230.14






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.81685682925609
beta0.236201492583795
S.D.0.0853825867491301
T-STAT2.76638951309591
p-value0.0505175407213127

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.81685682925609 \tabularnewline
beta & 0.236201492583795 \tabularnewline
S.D. & 0.0853825867491301 \tabularnewline
T-STAT & 2.76638951309591 \tabularnewline
p-value & 0.0505175407213127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208405&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.81685682925609[/C][/ROW]
[ROW][C]beta[/C][C]0.236201492583795[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0853825867491301[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.76638951309591[/C][/ROW]
[ROW][C]p-value[/C][C]0.0505175407213127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208405&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208405&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-1.81685682925609
beta0.236201492583795
S.D.0.0853825867491301
T-STAT2.76638951309591
p-value0.0505175407213127






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-46.8251716239431
beta21.1996567085292
S.D.10.0693955827947
T-STAT2.10535543411885
p-value0.103028739665824
Lambda-20.1996567085292

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -46.8251716239431 \tabularnewline
beta & 21.1996567085292 \tabularnewline
S.D. & 10.0693955827947 \tabularnewline
T-STAT & 2.10535543411885 \tabularnewline
p-value & 0.103028739665824 \tabularnewline
Lambda & -20.1996567085292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208405&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-46.8251716239431[/C][/ROW]
[ROW][C]beta[/C][C]21.1996567085292[/C][/ROW]
[ROW][C]S.D.[/C][C]10.0693955827947[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.10535543411885[/C][/ROW]
[ROW][C]p-value[/C][C]0.103028739665824[/C][/ROW]
[ROW][C]Lambda[/C][C]-20.1996567085292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208405&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208405&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-46.8251716239431
beta21.1996567085292
S.D.10.0693955827947
T-STAT2.10535543411885
p-value0.103028739665824
Lambda-20.1996567085292


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')