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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 29 Nov 2009 10:58:33 -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/2009/Nov/29/t1259517560h8zeptzn9omb1n3.htm/, Retrieved Sat, 27 Apr 2024 02:16:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61672, Retrieved Sat, 27 Apr 2024 02:16:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190

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] [WS4a] [2009-11-29 17:58:33] [b406b824746c89e17d2637b66f6fb2ee] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.89
105.15
105.24
105.57
105.62
106.17
106.27
106.41
106.94
107.16
107.32
107.32
107.35
107.55
107.87
108.37
108.38
107.92
108.03
108.14
108.3
108.64
108.66
109.04
109.03
109.03
109.54
109.75
109.83
109.65
109.82
109.95
110.12
110.15
110.21
109.99
110.14
110.14
110.81
110.97
110.99
109.73
109.81
110.02
110.18
110.21
110.25
110.36
110.51
110.6
110.95
111.18
111.19
111.69
111.7
111.83
111.77
111.73
112.01
111.86
112.04

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61672&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61672&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61672&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1106.1716666666670.878623234315362.42999999999999
2108.18750.4810051029780361.69000000000001
3109.7558333333330.3940341086605041.17999999999999
4110.3008333333330.4165105768237581.25999999999999
5111.4183333333330.5144782588097181.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.171666666667 & 0.87862323431536 & 2.42999999999999 \tabularnewline
2 & 108.1875 & 0.481005102978036 & 1.69000000000001 \tabularnewline
3 & 109.755833333333 & 0.394034108660504 & 1.17999999999999 \tabularnewline
4 & 110.300833333333 & 0.416510576823758 & 1.25999999999999 \tabularnewline
5 & 111.418333333333 & 0.514478258809718 & 1.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61672&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]106.171666666667[/C][C]0.87862323431536[/C][C]2.42999999999999[/C][/ROW]
[ROW][C]2[/C][C]108.1875[/C][C]0.481005102978036[/C][C]1.69000000000001[/C][/ROW]
[ROW][C]3[/C][C]109.755833333333[/C][C]0.394034108660504[/C][C]1.17999999999999[/C][/ROW]
[ROW][C]4[/C][C]110.300833333333[/C][C]0.416510576823758[/C][C]1.25999999999999[/C][/ROW]
[ROW][C]5[/C][C]111.418333333333[/C][C]0.514478258809718[/C][C]1.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61672&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61672&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
1106.1716666666670.878623234315362.42999999999999
2108.18750.4810051029780361.69000000000001
3109.7558333333330.3940341086605041.17999999999999
4110.3008333333330.4165105768237581.25999999999999
5111.4183333333330.5144782588097181.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.67529472662082
beta-0.0745497897282906
S.D.0.0354963565085791
T-STAT-2.10020962884663
p-value0.126539947104462

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.67529472662082 \tabularnewline
beta & -0.0745497897282906 \tabularnewline
S.D. & 0.0354963565085791 \tabularnewline
T-STAT & -2.10020962884663 \tabularnewline
p-value & 0.126539947104462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61672&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.67529472662082[/C][/ROW]
[ROW][C]beta[/C][C]-0.0745497897282906[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0354963565085791[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.10020962884663[/C][/ROW]
[ROW][C]p-value[/C][C]0.126539947104462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61672&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61672&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)
alpha8.67529472662082
beta-0.0745497897282906
S.D.0.0354963565085791
T-STAT-2.10020962884663
p-value0.126539947104462






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha59.0198333949405
beta-12.7188977655091
S.D.6.51086161292678
T-STAT-1.95348918801418
p-value0.145775913249646
Lambda13.7188977655091

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 59.0198333949405 \tabularnewline
beta & -12.7188977655091 \tabularnewline
S.D. & 6.51086161292678 \tabularnewline
T-STAT & -1.95348918801418 \tabularnewline
p-value & 0.145775913249646 \tabularnewline
Lambda & 13.7188977655091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61672&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]59.0198333949405[/C][/ROW]
[ROW][C]beta[/C][C]-12.7188977655091[/C][/ROW]
[ROW][C]S.D.[/C][C]6.51086161292678[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.95348918801418[/C][/ROW]
[ROW][C]p-value[/C][C]0.145775913249646[/C][/ROW]
[ROW][C]Lambda[/C][C]13.7188977655091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61672&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61672&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)
alpha59.0198333949405
beta-12.7188977655091
S.D.6.51086161292678
T-STAT-1.95348918801418
p-value0.145775913249646
Lambda13.7188977655091


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')