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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, 18 Nov 2016 19:21:07 +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/2016/Nov/18/t1479497194u6zeud89cguhb03.htm/, Retrieved Fri, 03 May 2024 03:01:48 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 03:01:48 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
75.8
75.7
112.3
110.9
99.6
107.5
90
88.8
129.7
120.4
93.3
96
81.1
78
111.9
117.6
101
98.3
91
86.8
108.8
110.1
93.8
100.6
75.7
69
116
94.5
105.1
95.3
79.7
76.1
111.1
106.3
89.5
96.8
67.8
62.5
90.1
93.6
94.2
93.2
81
73.7
97.7
97.5
82.7
88.8
68.5
61.1
89.6
87.6
90.8
84.3
75
78.4
83.5
93
79.3
83.9
65
60.3
80.6
86.5
78.7
80.7
70.6
67.2
88
89.1
69
84.1

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
110016.752801665284654
298.2512.552471687064139.6
392.92515.231135873597947
485.233333333333311.810036820305435.2
581.259.4400982275320931.9
676.659.8166370838675528.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100 & 16.7528016652846 & 54 \tabularnewline
2 & 98.25 & 12.5524716870641 & 39.6 \tabularnewline
3 & 92.925 & 15.2311358735979 & 47 \tabularnewline
4 & 85.2333333333333 & 11.8100368203054 & 35.2 \tabularnewline
5 & 81.25 & 9.44009822753209 & 31.9 \tabularnewline
6 & 76.65 & 9.81663708386755 & 28.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100[/C][C]16.7528016652846[/C][C]54[/C][/ROW]
[ROW][C]2[/C][C]98.25[/C][C]12.5524716870641[/C][C]39.6[/C][/ROW]
[ROW][C]3[/C][C]92.925[/C][C]15.2311358735979[/C][C]47[/C][/ROW]
[ROW][C]4[/C][C]85.2333333333333[/C][C]11.8100368203054[/C][C]35.2[/C][/ROW]
[ROW][C]5[/C][C]81.25[/C][C]9.44009822753209[/C][C]31.9[/C][/ROW]
[ROW][C]6[/C][C]76.65[/C][C]9.81663708386755[/C][C]28.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
110016.752801665284654
298.2512.552471687064139.6
392.92515.231135873597947
485.233333333333311.810036820305435.2
581.259.4400982275320931.9
676.659.8166370838675528.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-10.6994905349524
beta0.261646910305908
S.D.0.0811078076200196
T-STAT3.22591521067482
p-value0.0320997030115234

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -10.6994905349524 \tabularnewline
beta & 0.261646910305908 \tabularnewline
S.D. & 0.0811078076200196 \tabularnewline
T-STAT & 3.22591521067482 \tabularnewline
p-value & 0.0320997030115234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.6994905349524[/C][/ROW]
[ROW][C]beta[/C][C]0.261646910305908[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0811078076200196[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.22591521067482[/C][/ROW]
[ROW][C]p-value[/C][C]0.0320997030115234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-10.6994905349524
beta0.261646910305908
S.D.0.0811078076200196
T-STAT3.22591521067482
p-value0.0320997030115234






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.80680947246406
beta1.85495683211625
S.D.0.534728432949353
T-STAT3.46896988792055
p-value0.0256076206588444
Lambda-0.854956832116248

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.80680947246406 \tabularnewline
beta & 1.85495683211625 \tabularnewline
S.D. & 0.534728432949353 \tabularnewline
T-STAT & 3.46896988792055 \tabularnewline
p-value & 0.0256076206588444 \tabularnewline
Lambda & -0.854956832116248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.80680947246406[/C][/ROW]
[ROW][C]beta[/C][C]1.85495683211625[/C][/ROW]
[ROW][C]S.D.[/C][C]0.534728432949353[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.46896988792055[/C][/ROW]
[ROW][C]p-value[/C][C]0.0256076206588444[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.854956832116248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-5.80680947246406
beta1.85495683211625
S.D.0.534728432949353
T-STAT3.46896988792055
p-value0.0256076206588444
Lambda-0.854956832116248


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')