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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 computationSun, 17 Aug 2014 11:02:17 +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/2014/Aug/17/t1408269794n44saxe95mke9z0.htm/, Retrieved Thu, 16 May 2024 23:25:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235605, Retrieved Thu, 16 May 2024 23:25:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

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] [] [2014-08-17 10:02:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
740
730
740
820
820
850
870
930
890
790
840
880
730
730
770
880
820
900
940
1080
920
710
880
910
680
740
740
810
800
900
920
1030
910
720
930
900
680
770
770
810
810
910
820
980
830
760
930
910
640
780
690
820
800
910
850
980
830
820
1010
930
630
760
670
850
780
900
840
1050
810
860
1020
820
670
780
690
800
810
910
870
1010
810
960
990
780
700
810
760
810
840
900
920
1050
860
870
880
860
650
830
730
810
840
940
870
940
770
870
860
760

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=235605&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=235605&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235605&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
182564.5966506308746200
2855.833333333333108.331002305924370
3840106.685604379495350
4831.66666666666785.6879468911716300
5838.333333333333108.781125813871370
6832.5122.186519119523420
7840110.20641789594340
885586.6025403784439350
9822.584.7590166831288290

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 825 & 64.5966506308746 & 200 \tabularnewline
2 & 855.833333333333 & 108.331002305924 & 370 \tabularnewline
3 & 840 & 106.685604379495 & 350 \tabularnewline
4 & 831.666666666667 & 85.6879468911716 & 300 \tabularnewline
5 & 838.333333333333 & 108.781125813871 & 370 \tabularnewline
6 & 832.5 & 122.186519119523 & 420 \tabularnewline
7 & 840 & 110.20641789594 & 340 \tabularnewline
8 & 855 & 86.6025403784439 & 350 \tabularnewline
9 & 822.5 & 84.7590166831288 & 290 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235605&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]825[/C][C]64.5966506308746[/C][C]200[/C][/ROW]
[ROW][C]2[/C][C]855.833333333333[/C][C]108.331002305924[/C][C]370[/C][/ROW]
[ROW][C]3[/C][C]840[/C][C]106.685604379495[/C][C]350[/C][/ROW]
[ROW][C]4[/C][C]831.666666666667[/C][C]85.6879468911716[/C][C]300[/C][/ROW]
[ROW][C]5[/C][C]838.333333333333[/C][C]108.781125813871[/C][C]370[/C][/ROW]
[ROW][C]6[/C][C]832.5[/C][C]122.186519119523[/C][C]420[/C][/ROW]
[ROW][C]7[/C][C]840[/C][C]110.20641789594[/C][C]340[/C][/ROW]
[ROW][C]8[/C][C]855[/C][C]86.6025403784439[/C][C]350[/C][/ROW]
[ROW][C]9[/C][C]822.5[/C][C]84.7590166831288[/C][C]290[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235605&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235605&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
182564.5966506308746200
2855.833333333333108.331002305924370
3840106.685604379495350
4831.66666666666785.6879468911716300
5838.333333333333108.781125813871370
6832.5122.186519119523420
7840110.20641789594340
885586.6025403784439350
9822.584.7590166831288290






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-376.853235567902
beta0.566186223124256
S.D.0.542155127722943
T-STAT1.04432512794307
p-value0.331052139577559

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -376.853235567902 \tabularnewline
beta & 0.566186223124256 \tabularnewline
S.D. & 0.542155127722943 \tabularnewline
T-STAT & 1.04432512794307 \tabularnewline
p-value & 0.331052139577559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235605&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-376.853235567902[/C][/ROW]
[ROW][C]beta[/C][C]0.566186223124256[/C][/ROW]
[ROW][C]S.D.[/C][C]0.542155127722943[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.04432512794307[/C][/ROW]
[ROW][C]p-value[/C][C]0.331052139577559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235605&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235605&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-376.853235567902
beta0.566186223124256
S.D.0.542155127722943
T-STAT1.04432512794307
p-value0.331052139577559






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-34.0311870706069
beta5.73407491579722
S.D.4.92597356361625
T-STAT1.16404906395554
p-value0.282539860908879
Lambda-4.73407491579722

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -34.0311870706069 \tabularnewline
beta & 5.73407491579722 \tabularnewline
S.D. & 4.92597356361625 \tabularnewline
T-STAT & 1.16404906395554 \tabularnewline
p-value & 0.282539860908879 \tabularnewline
Lambda & -4.73407491579722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235605&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-34.0311870706069[/C][/ROW]
[ROW][C]beta[/C][C]5.73407491579722[/C][/ROW]
[ROW][C]S.D.[/C][C]4.92597356361625[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16404906395554[/C][/ROW]
[ROW][C]p-value[/C][C]0.282539860908879[/C][/ROW]
[ROW][C]Lambda[/C][C]-4.73407491579722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235605&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235605&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-34.0311870706069
beta5.73407491579722
S.D.4.92597356361625
T-STAT1.16404906395554
p-value0.282539860908879
Lambda-4.73407491579722


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')