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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 computationThu, 08 Dec 2011 03:49:37 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/08/t1323334232crudvdgu3zjbwcc.htm/, Retrieved Fri, 03 May 2024 06:44:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152789, Retrieved Fri, 03 May 2024 06:44:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact101

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] [Standard deviatio...] [2011-12-08 08:49:37] [459538fe31c621d37110fb87514358a8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.71
105.82
105.82
105.72
105.76
105.8
105.09
105.06
105.16
105.2
105.21
105.23
105.19
105.16
104.88
104.52
104.09
104.35
104.48
104.47
104.55
104.59
104.59
104.72
104.65
104.72
104.92
105.05
103.74
103.81
103.79
104.28
103.8
103.8
104.02
104.02
104.91
104.97
103.86
104.17
103.21
103.21
101.91
101.84
101.91
101.79
101.79
101.79
102.09
102.18
102.2
101.97
102.05
102.04
101.78
101.79
101.8
101.83
101.83
101.88
101.9

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'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152789&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152789&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152789&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1105.76750.0607590871118590.109999999999999
2105.42750.4075434537158780.739999999999995
3105.20.02943920288776170.0700000000000074
4104.93750.3113813310610220.670000000000002
5104.34750.1815443012967720.390000000000001
6104.61250.07410578025138530.170000000000002
7104.8350.1833939293797160.399999999999991
8103.9050.2517273657484760.540000000000006
9103.910.1270170592217170.219999999999999
10104.47750.5493860209360981.11
11102.54250.7712922057603471.36999999999999
12101.820.05999999999999520.11999999999999
13102.110.1048808848170180.230000000000004
14101.9150.1502220578565820.269999999999996
15101.8350.03316624790355310.0799999999999983

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 105.7675 & 0.060759087111859 & 0.109999999999999 \tabularnewline
2 & 105.4275 & 0.407543453715878 & 0.739999999999995 \tabularnewline
3 & 105.2 & 0.0294392028877617 & 0.0700000000000074 \tabularnewline
4 & 104.9375 & 0.311381331061022 & 0.670000000000002 \tabularnewline
5 & 104.3475 & 0.181544301296772 & 0.390000000000001 \tabularnewline
6 & 104.6125 & 0.0741057802513853 & 0.170000000000002 \tabularnewline
7 & 104.835 & 0.183393929379716 & 0.399999999999991 \tabularnewline
8 & 103.905 & 0.251727365748476 & 0.540000000000006 \tabularnewline
9 & 103.91 & 0.127017059221717 & 0.219999999999999 \tabularnewline
10 & 104.4775 & 0.549386020936098 & 1.11 \tabularnewline
11 & 102.5425 & 0.771292205760347 & 1.36999999999999 \tabularnewline
12 & 101.82 & 0.0599999999999952 & 0.11999999999999 \tabularnewline
13 & 102.11 & 0.104880884817018 & 0.230000000000004 \tabularnewline
14 & 101.915 & 0.150222057856582 & 0.269999999999996 \tabularnewline
15 & 101.835 & 0.0331662479035531 & 0.0799999999999983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152789&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]105.7675[/C][C]0.060759087111859[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]2[/C][C]105.4275[/C][C]0.407543453715878[/C][C]0.739999999999995[/C][/ROW]
[ROW][C]3[/C][C]105.2[/C][C]0.0294392028877617[/C][C]0.0700000000000074[/C][/ROW]
[ROW][C]4[/C][C]104.9375[/C][C]0.311381331061022[/C][C]0.670000000000002[/C][/ROW]
[ROW][C]5[/C][C]104.3475[/C][C]0.181544301296772[/C][C]0.390000000000001[/C][/ROW]
[ROW][C]6[/C][C]104.6125[/C][C]0.0741057802513853[/C][C]0.170000000000002[/C][/ROW]
[ROW][C]7[/C][C]104.835[/C][C]0.183393929379716[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]8[/C][C]103.905[/C][C]0.251727365748476[/C][C]0.540000000000006[/C][/ROW]
[ROW][C]9[/C][C]103.91[/C][C]0.127017059221717[/C][C]0.219999999999999[/C][/ROW]
[ROW][C]10[/C][C]104.4775[/C][C]0.549386020936098[/C][C]1.11[/C][/ROW]
[ROW][C]11[/C][C]102.5425[/C][C]0.771292205760347[/C][C]1.36999999999999[/C][/ROW]
[ROW][C]12[/C][C]101.82[/C][C]0.0599999999999952[/C][C]0.11999999999999[/C][/ROW]
[ROW][C]13[/C][C]102.11[/C][C]0.104880884817018[/C][C]0.230000000000004[/C][/ROW]
[ROW][C]14[/C][C]101.915[/C][C]0.150222057856582[/C][C]0.269999999999996[/C][/ROW]
[ROW][C]15[/C][C]101.835[/C][C]0.0331662479035531[/C][C]0.0799999999999983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152789&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152789&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
1105.76750.0607590871118590.109999999999999
2105.42750.4075434537158780.739999999999995
3105.20.02943920288776170.0700000000000074
4104.93750.3113813310610220.670000000000002
5104.34750.1815443012967720.390000000000001
6104.61250.07410578025138530.170000000000002
7104.8350.1833939293797160.399999999999991
8103.9050.2517273657484760.540000000000006
9103.910.1270170592217170.219999999999999
10104.47750.5493860209360981.11
11102.54250.7712922057603471.36999999999999
12101.820.05999999999999520.11999999999999
13102.110.1048808848170180.230000000000004
14101.9150.1502220578565820.269999999999996
15101.8350.03316624790355310.0799999999999983






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.464868877763111
beta0.00659258597168146
S.D.0.0415386098873297
T-STAT0.15870983621174
p-value0.876336517112044

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.464868877763111 \tabularnewline
beta & 0.00659258597168146 \tabularnewline
S.D. & 0.0415386098873297 \tabularnewline
T-STAT & 0.15870983621174 \tabularnewline
p-value & 0.876336517112044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152789&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.464868877763111[/C][/ROW]
[ROW][C]beta[/C][C]0.00659258597168146[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0415386098873297[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.15870983621174[/C][/ROW]
[ROW][C]p-value[/C][C]0.876336517112044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152789&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152789&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-0.464868877763111
beta0.00659258597168146
S.D.0.0415386098873297
T-STAT0.15870983621174
p-value0.876336517112044






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-43.8660016210234
beta9.03081800130467
S.D.19.7461972560748
T-STAT0.457344666630755
p-value0.65497264744945
Lambda-8.03081800130467

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -43.8660016210234 \tabularnewline
beta & 9.03081800130467 \tabularnewline
S.D. & 19.7461972560748 \tabularnewline
T-STAT & 0.457344666630755 \tabularnewline
p-value & 0.65497264744945 \tabularnewline
Lambda & -8.03081800130467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152789&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-43.8660016210234[/C][/ROW]
[ROW][C]beta[/C][C]9.03081800130467[/C][/ROW]
[ROW][C]S.D.[/C][C]19.7461972560748[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.457344666630755[/C][/ROW]
[ROW][C]p-value[/C][C]0.65497264744945[/C][/ROW]
[ROW][C]Lambda[/C][C]-8.03081800130467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152789&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152789&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-43.8660016210234
beta9.03081800130467
S.D.19.7461972560748
T-STAT0.457344666630755
p-value0.65497264744945
Lambda-8.03081800130467


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')