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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 computationMon, 21 Mar 2016 22:38:21 +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/Mar/21/t1458599940xuryrmah32u3x2j.htm/, Retrieved Sun, 05 May 2024 14:11:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294397, Retrieved Sun, 05 May 2024 14:11:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

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] [] [2016-03-21 22:38:21] [0b2c3ebb4286059f748822350b46c363] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.95
108.55
110.81
111.54
110.38
106.67
106.45
105.44
105.37
103.72
106.57
108.54
110.36
106.64
103.45
101.36
101.9
100.86
100.37
100.16
99.5
99.52
99.2
99.35
99.37
99.85
99.76
100.07
99.77
99.93
99.16
99.4
99.81
99.67
99.37
99.49
99.28
99.33
99.19
98.11
99.12
99.06
97.41
98.45
100.33
103.18
103.06
103.48
102.8
103.92
103.9
103.96
103.62
103.83
104.09
104.07
103.22
104.01
104.01
104.24
102.93
104.73
106.48
119.5
122.45
125.29
126.56
126.38
127.95
128.23
128.7
127.86

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=294397&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=294397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294397&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
1107.4991666666672.447334202141127.82000000000001
2101.8891666666673.4165225764147311.16
399.63750.2747602260484240.909999999999997
41002.081507320975056.07000000000001
5103.8058333333330.4109956499069361.44
6120.5883333333339.9524970218381325.77

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 107.499166666667 & 2.44733420214112 & 7.82000000000001 \tabularnewline
2 & 101.889166666667 & 3.41652257641473 & 11.16 \tabularnewline
3 & 99.6375 & 0.274760226048424 & 0.909999999999997 \tabularnewline
4 & 100 & 2.08150732097505 & 6.07000000000001 \tabularnewline
5 & 103.805833333333 & 0.410995649906936 & 1.44 \tabularnewline
6 & 120.588333333333 & 9.95249702183813 & 25.77 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294397&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]107.499166666667[/C][C]2.44733420214112[/C][C]7.82000000000001[/C][/ROW]
[ROW][C]2[/C][C]101.889166666667[/C][C]3.41652257641473[/C][C]11.16[/C][/ROW]
[ROW][C]3[/C][C]99.6375[/C][C]0.274760226048424[/C][C]0.909999999999997[/C][/ROW]
[ROW][C]4[/C][C]100[/C][C]2.08150732097505[/C][C]6.07000000000001[/C][/ROW]
[ROW][C]5[/C][C]103.805833333333[/C][C]0.410995649906936[/C][C]1.44[/C][/ROW]
[ROW][C]6[/C][C]120.588333333333[/C][C]9.95249702183813[/C][C]25.77[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294397&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
1107.4991666666672.447334202141127.82000000000001
2101.8891666666673.4165225764147311.16
399.63750.2747602260484240.909999999999997
41002.081507320975056.07000000000001
5103.8058333333330.4109956499069361.44
6120.5883333333339.9524970218381325.77






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-40.0795817929177
beta0.408987887586168
S.D.0.0960485584013974
T-STAT4.25813665913613
p-value0.0130729940232814

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -40.0795817929177 \tabularnewline
beta & 0.408987887586168 \tabularnewline
S.D. & 0.0960485584013974 \tabularnewline
T-STAT & 4.25813665913613 \tabularnewline
p-value & 0.0130729940232814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294397&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-40.0795817929177[/C][/ROW]
[ROW][C]beta[/C][C]0.408987887586168[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0960485584013974[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.25813665913613[/C][/ROW]
[ROW][C]p-value[/C][C]0.0130729940232814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294397&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-40.0795817929177
beta0.408987887586168
S.D.0.0960485584013974
T-STAT4.25813665913613
p-value0.0130729940232814






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-59.8958771810127
beta12.9674338127454
S.D.6.79839548657466
T-STAT1.90742563276191
p-value0.129128473113135
Lambda-11.9674338127454

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -59.8958771810127 \tabularnewline
beta & 12.9674338127454 \tabularnewline
S.D. & 6.79839548657466 \tabularnewline
T-STAT & 1.90742563276191 \tabularnewline
p-value & 0.129128473113135 \tabularnewline
Lambda & -11.9674338127454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294397&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-59.8958771810127[/C][/ROW]
[ROW][C]beta[/C][C]12.9674338127454[/C][/ROW]
[ROW][C]S.D.[/C][C]6.79839548657466[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.90742563276191[/C][/ROW]
[ROW][C]p-value[/C][C]0.129128473113135[/C][/ROW]
[ROW][C]Lambda[/C][C]-11.9674338127454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294397&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-59.8958771810127
beta12.9674338127454
S.D.6.79839548657466
T-STAT1.90742563276191
p-value0.129128473113135
Lambda-11.9674338127454


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')