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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, 25 Nov 2007 07:00:32 -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/25/t1195998690jolj7y9v4c4pmok.htm/, Retrieved Sat, 04 May 2024 15:15:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6453, Retrieved Sat, 04 May 2024 15:15:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

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] [WS10Q1-a] [2007-11-25 14:00:32] [f15e5fe6fe718a2cea2c195ef11f432f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.3
7
6.6
6.4
6.3
6.4
6.3
6
5.3
5.2
5.1
5.4
5.8
5.6
5.6
5.4
5.4
5.5
5.5
5.3
5.7
5.6
5.5
5.6
5.9
6
7
6.6
6.6
6.3
6.3
6.3
6.3
6.2
6.2
6.3
6.4
6.4
7.8
7.7
7.7
7.7
7.7
7.6
7.5
7.4
7.4
7.5
7.6
7.6
8.1
7.8
8
7.9
7.9
7.8
6.7
6.6
6.6
7.7
7.9
8
7.7
7.5
7.6
7.8
7.8
7.7
7.4
7.5
7.2
7.5
7.6
7.6
7.8
7.7
7.7
8.2
8.2
8.1
7.8
7.8
7.7
6.7
6.7
6.7
7.2
6.9
6.8
7.2
7.1
6.9
6.9
6.7
6.5
6.6
6.6
6.5
6.3

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6453&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]3 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=6453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6453&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
16.108333333333330.7204270618981161.5
25.541666666666670.1378954368902450.2
36.333333333333330.2902454551623921.4
47.40.4842989309769892.4
57.5250.5577959874688632.7
67.633333333333330.2269694946796852.5
77.741666666666670.3918680977836882.7
86.850.2276360731917981.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.10833333333333 & 0.720427061898116 & 1.5 \tabularnewline
2 & 5.54166666666667 & 0.137895436890245 & 0.2 \tabularnewline
3 & 6.33333333333333 & 0.290245455162392 & 1.4 \tabularnewline
4 & 7.4 & 0.484298930976989 & 2.4 \tabularnewline
5 & 7.525 & 0.557795987468863 & 2.7 \tabularnewline
6 & 7.63333333333333 & 0.226969494679685 & 2.5 \tabularnewline
7 & 7.74166666666667 & 0.391868097783688 & 2.7 \tabularnewline
8 & 6.85 & 0.227636073191798 & 1.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6453&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]6.10833333333333[/C][C]0.720427061898116[/C][C]1.5[/C][/ROW]
[ROW][C]2[/C][C]5.54166666666667[/C][C]0.137895436890245[/C][C]0.2[/C][/ROW]
[ROW][C]3[/C][C]6.33333333333333[/C][C]0.290245455162392[/C][C]1.4[/C][/ROW]
[ROW][C]4[/C][C]7.4[/C][C]0.484298930976989[/C][C]2.4[/C][/ROW]
[ROW][C]5[/C][C]7.525[/C][C]0.557795987468863[/C][C]2.7[/C][/ROW]
[ROW][C]6[/C][C]7.63333333333333[/C][C]0.226969494679685[/C][C]2.5[/C][/ROW]
[ROW][C]7[/C][C]7.74166666666667[/C][C]0.391868097783688[/C][C]2.7[/C][/ROW]
[ROW][C]8[/C][C]6.85[/C][C]0.227636073191798[/C][C]1.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6453&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
16.108333333333330.7204270618981161.5
25.541666666666670.1378954368902450.2
36.333333333333330.2902454551623921.4
47.40.4842989309769892.4
57.5250.5577959874688632.7
67.633333333333330.2269694946796852.5
77.741666666666670.3918680977836882.7
86.850.2276360731917981.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.116368496809804
beta0.0382017272715843
S.D.0.0971270097915914
T-STAT0.393317238464923
p-value0.707680575232963

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.116368496809804 \tabularnewline
beta & 0.0382017272715843 \tabularnewline
S.D. & 0.0971270097915914 \tabularnewline
T-STAT & 0.393317238464923 \tabularnewline
p-value & 0.707680575232963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6453&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.116368496809804[/C][/ROW]
[ROW][C]beta[/C][C]0.0382017272715843[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0971270097915914[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.393317238464923[/C][/ROW]
[ROW][C]p-value[/C][C]0.707680575232963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6453&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)
alpha0.116368496809804
beta0.0382017272715843
S.D.0.0971270097915914
T-STAT0.393317238464923
p-value0.707680575232963






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.09845991979278
beta1.56150222270886
S.D.1.71176467688229
T-STAT0.91221780878952
p-value0.396825252713299
Lambda-0.561502222708862

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.09845991979278 \tabularnewline
beta & 1.56150222270886 \tabularnewline
S.D. & 1.71176467688229 \tabularnewline
T-STAT & 0.91221780878952 \tabularnewline
p-value & 0.396825252713299 \tabularnewline
Lambda & -0.561502222708862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6453&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.09845991979278[/C][/ROW]
[ROW][C]beta[/C][C]1.56150222270886[/C][/ROW]
[ROW][C]S.D.[/C][C]1.71176467688229[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.91221780878952[/C][/ROW]
[ROW][C]p-value[/C][C]0.396825252713299[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.561502222708862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6453&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6453&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-4.09845991979278
beta1.56150222270886
S.D.1.71176467688229
T-STAT0.91221780878952
p-value0.396825252713299
Lambda-0.561502222708862


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')