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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 computationSat, 22 Apr 2017 13:00:37 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/22/t1492862474gszvii7oou2en6l.htm/, Retrieved Sun, 12 May 2024 14:53:21 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 12 May 2024 14:53:21 +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 
79.92
80.26
80.69
84.5
85.45
86.19
86.4
85.98
85.87
86.06
86.43
86.43
86.37
86.84
86.73
90.99
92.61
93.83
94.2
94.01
93.47
93.27
94.3
94.53
94.59
94.69
94.67
96.55
97.14
97.32
97.97
98.49
99.11
99.09
98.76
99.2
99.61
99.54
99.68
100.75
100.38
100.79
100.39
100.39
100.12
100
99.17
99.17
99.59
99.96
99.68
101.03
100.99
101.38
101.84
101.52
101.37
101.22
101.45
101.99
104.05
104.61
105.06
105.4
104.71
104.8
104.83
104.81
104.49
104.59
104.5
104.61

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'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
184.5152.607449119175856.51000000000001
291.76253.226374618952088.16
397.29833333333331.802734454974314.61
499.99916666666670.5635513743352521.62
5101.0016666666670.8147150459274732.39999999999999
6104.7050.3293657817409381.35000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 84.515 & 2.60744911917585 & 6.51000000000001 \tabularnewline
2 & 91.7625 & 3.22637461895208 & 8.16 \tabularnewline
3 & 97.2983333333333 & 1.80273445497431 & 4.61 \tabularnewline
4 & 99.9991666666667 & 0.563551374335252 & 1.62 \tabularnewline
5 & 101.001666666667 & 0.814715045927473 & 2.39999999999999 \tabularnewline
6 & 104.705 & 0.329365781740938 & 1.35000000000001 \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]84.515[/C][C]2.60744911917585[/C][C]6.51000000000001[/C][/ROW]
[ROW][C]2[/C][C]91.7625[/C][C]3.22637461895208[/C][C]8.16[/C][/ROW]
[ROW][C]3[/C][C]97.2983333333333[/C][C]1.80273445497431[/C][C]4.61[/C][/ROW]
[ROW][C]4[/C][C]99.9991666666667[/C][C]0.563551374335252[/C][C]1.62[/C][/ROW]
[ROW][C]5[/C][C]101.001666666667[/C][C]0.814715045927473[/C][C]2.39999999999999[/C][/ROW]
[ROW][C]6[/C][C]104.705[/C][C]0.329365781740938[/C][C]1.35000000000001[/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
184.5152.607449119175856.51000000000001
291.76253.226374618952088.16
397.29833333333331.802734454974314.61
499.99916666666670.5635513743352521.62
5101.0016666666670.8147150459274732.39999999999999
6104.7050.3293657817409381.35000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha15.0294557304091
beta-0.139539275345066
S.D.0.0411552231490082
T-STAT-3.39056053322428
p-value0.0275157642078625

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15.0294557304091 \tabularnewline
beta & -0.139539275345066 \tabularnewline
S.D. & 0.0411552231490082 \tabularnewline
T-STAT & -3.39056053322428 \tabularnewline
p-value & 0.0275157642078625 \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]15.0294557304091[/C][/ROW]
[ROW][C]beta[/C][C]-0.139539275345066[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0411552231490082[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.39056053322428[/C][/ROW]
[ROW][C]p-value[/C][C]0.0275157642078625[/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)
alpha15.0294557304091
beta-0.139539275345066
S.D.0.0411552231490082
T-STAT-3.39056053322428
p-value0.0275157642078625






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha45.5476851703922
beta-9.9417074378178
S.D.3.08047272026739
T-STAT-3.22733175736575
p-value0.0320565809589748
Lambda10.9417074378178

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 45.5476851703922 \tabularnewline
beta & -9.9417074378178 \tabularnewline
S.D. & 3.08047272026739 \tabularnewline
T-STAT & -3.22733175736575 \tabularnewline
p-value & 0.0320565809589748 \tabularnewline
Lambda & 10.9417074378178 \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]45.5476851703922[/C][/ROW]
[ROW][C]beta[/C][C]-9.9417074378178[/C][/ROW]
[ROW][C]S.D.[/C][C]3.08047272026739[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.22733175736575[/C][/ROW]
[ROW][C]p-value[/C][C]0.0320565809589748[/C][/ROW]
[ROW][C]Lambda[/C][C]10.9417074378178[/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)
alpha45.5476851703922
beta-9.9417074378178
S.D.3.08047272026739
T-STAT-3.22733175736575
p-value0.0320565809589748
Lambda10.9417074378178


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')