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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 computationTue, 26 May 2015 18:15:54 +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/2015/May/26/t1432660571toc03ydg2c7iv46.htm/, Retrieved Tue, 30 Apr 2024 10:25:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279412, Retrieved Tue, 30 Apr 2024 10:25:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Mean Plot luchtva...] [2015-02-26 15:46:06] [77cae2e8655af67d2d17f40c5b6aa8cb]
- RMPD    [Standard Deviation-Mean Plot] [] [2015-05-26 17:15:54] [1689e0541609f8eb663ad6752b966f5b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
498.10
498.76
498.88
498.88
498.88
498.88
499.48
501.21
502.05
502.05
502.05
504.10
506.81
516.88
520.43
520.68
520.68
520.68
521.03
521.25
521.25
521.25
521.65
521.65
522.77
518.72
519.27
519.38
521.29
521.29
521.29
523.47
523.86
524.14
524.14
524.14
534.60
534.99
535.39
535.39
535.39
535.39
535.39
535.64
536.08
537.80
537.80
537.80
537.85
544.39
545.15
544.65
544.65
544.65
545.73
548.94
550.94
551.22
551.22
551.22
553.12
565.37
566.73
566.73
566.78
566.78
566.78
566.78
566.93
566.93
566.93
566.93
574.38
574.40
574.40
574.40
574.40
574.40
574.50
574.50
574.67
574.66
574.66
574.94
576.10
583.38
584.15
584.15
584.15
584.15
585.14
585.14
585.67
586.49
586.81
586.85

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279412&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279412&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1500.2766666666671.916404461643236
2519.524.1964400497217914.84
3521.982.056815720741875.41999999999996
4535.9716666666671.155499367320793.19999999999993
5546.71754.0887008939270813.37
6565.5658333333333.9426374613341113.8099999999999
7574.5258333333330.1732291353477740.560000000000059
8584.3483333333332.8450142461165310.75

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 500.276666666667 & 1.91640446164323 & 6 \tabularnewline
2 & 519.52 & 4.19644004972179 & 14.84 \tabularnewline
3 & 521.98 & 2.05681572074187 & 5.41999999999996 \tabularnewline
4 & 535.971666666667 & 1.15549936732079 & 3.19999999999993 \tabularnewline
5 & 546.7175 & 4.08870089392708 & 13.37 \tabularnewline
6 & 565.565833333333 & 3.94263746133411 & 13.8099999999999 \tabularnewline
7 & 574.525833333333 & 0.173229135347774 & 0.560000000000059 \tabularnewline
8 & 584.348333333333 & 2.84501424611653 & 10.75 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279412&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]500.276666666667[/C][C]1.91640446164323[/C][C]6[/C][/ROW]
[ROW][C]2[/C][C]519.52[/C][C]4.19644004972179[/C][C]14.84[/C][/ROW]
[ROW][C]3[/C][C]521.98[/C][C]2.05681572074187[/C][C]5.41999999999996[/C][/ROW]
[ROW][C]4[/C][C]535.971666666667[/C][C]1.15549936732079[/C][C]3.19999999999993[/C][/ROW]
[ROW][C]5[/C][C]546.7175[/C][C]4.08870089392708[/C][C]13.37[/C][/ROW]
[ROW][C]6[/C][C]565.565833333333[/C][C]3.94263746133411[/C][C]13.8099999999999[/C][/ROW]
[ROW][C]7[/C][C]574.525833333333[/C][C]0.173229135347774[/C][C]0.560000000000059[/C][/ROW]
[ROW][C]8[/C][C]584.348333333333[/C][C]2.84501424611653[/C][C]10.75[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279412&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
1500.2766666666671.916404461643236
2519.524.1964400497217914.84
3521.982.056815720741875.41999999999996
4535.9716666666671.155499367320793.19999999999993
5546.71754.0887008939270813.37
6565.5658333333333.9426374613341113.8099999999999
7574.5258333333330.1732291353477740.560000000000059
8584.3483333333332.8450142461165310.75






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.06316493019381
beta-0.0027893402548336
S.D.0.0204573714958047
T-STAT-0.136348907551766
p-value0.896005328165499

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.06316493019381 \tabularnewline
beta & -0.0027893402548336 \tabularnewline
S.D. & 0.0204573714958047 \tabularnewline
T-STAT & -0.136348907551766 \tabularnewline
p-value & 0.896005328165499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279412&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.06316493019381[/C][/ROW]
[ROW][C]beta[/C][C]-0.0027893402548336[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0204573714958047[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.136348907551766[/C][/ROW]
[ROW][C]p-value[/C][C]0.896005328165499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279412&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)
alpha4.06316493019381
beta-0.0027893402548336
S.D.0.0204573714958047
T-STAT-0.136348907551766
p-value0.896005328165499






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha31.996705009472
beta-4.98159552456205
S.D.7.71673044127731
T-STAT-0.645557799701692
p-value0.54244990444926
Lambda5.98159552456205

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 31.996705009472 \tabularnewline
beta & -4.98159552456205 \tabularnewline
S.D. & 7.71673044127731 \tabularnewline
T-STAT & -0.645557799701692 \tabularnewline
p-value & 0.54244990444926 \tabularnewline
Lambda & 5.98159552456205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279412&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]31.996705009472[/C][/ROW]
[ROW][C]beta[/C][C]-4.98159552456205[/C][/ROW]
[ROW][C]S.D.[/C][C]7.71673044127731[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.645557799701692[/C][/ROW]
[ROW][C]p-value[/C][C]0.54244990444926[/C][/ROW]
[ROW][C]Lambda[/C][C]5.98159552456205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279412&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279412&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)
alpha31.996705009472
beta-4.98159552456205
S.D.7.71673044127731
T-STAT-0.645557799701692
p-value0.54244990444926
Lambda5.98159552456205


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')