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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, 29 Dec 2007 08:49:10 -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/2007/Dec/29/t119894496257k5rmy2cbq7qr9.htm/, Retrieved Sat, 27 Apr 2024 11:55:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4916, Retrieved Sat, 27 Apr 2024 11:55:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact290

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] [PAPER-St.dev-Mean...] [2007-12-29 15:49:10] [6bdd947de0ee04552c8f0fc807f31807] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7272,2
6680,1
8427,6
8752,8
7952,7
8694,3
7787
8474,2
9154,7
8557,2
7951,1
9156,7
7865,7
7337,4
9131,7
8814,6
8598,8
8439,6
7451,8
8016,2
9544,1
8270,7
8102,2
9369
7657,7
7816,6
9391,3
9445,4
9533,1
10068,7
8955,5
10423,9
11617,2
9391,1
10872
10230,4
9221
9428,6
10934,5
10986
11724,6
11180,9
11163,2
11240,9
12107,1
10762,3
11340,4
11266,8
9542,7
9227,7
10571,9
10774,4
10392,8
9920,2
9884,9
10174,5
11395,4
10760,2
10570,1
10536
9902,6
8889
10837,3
11624,1
10509
10984,9
10649,1
10855,7
11677,4
10760,2
10046,2
10772,8
9987,7
8638,7
11063,7
11855,7
10684,5
11337,4
10478
11123,9
12909,3
11339,9
10462,2
12733,5
10519,2
10414,9
12476,8
12384,6
12266,7
12919,9
11497,3
12142
13919,4
12656,8
12034,1
13199,7
10881,3
11301,2
13643,9
12517
13981,1
14275,7
13435
13565,7
16216,3
12970
14079,9
14235
12213,4
12581
14130,4
14210,8
14378,5
13142,8
13714,7
13621,9
15379,8
13306,3
14391,2
14909,9

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4916&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 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=4916&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4916&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18238.38333333333743.34217843632476.6
28411.81666666667711.0173323975282206.7
39616.908333333331146.676659234563959.5
410946.3583333333837.515763171422886.1
510312.5666666667595.5649607089412167.7
610625.6916666667754.2781322783612788.4
711051.20833333331162.353625160714270.6
812202.61666666671015.071227982943504.5
913425.1751413.876870764155335
1013831.725924.198749900793166.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8238.38333333333 & 743.3421784363 & 2476.6 \tabularnewline
2 & 8411.81666666667 & 711.017332397528 & 2206.7 \tabularnewline
3 & 9616.90833333333 & 1146.67665923456 & 3959.5 \tabularnewline
4 & 10946.3583333333 & 837.51576317142 & 2886.1 \tabularnewline
5 & 10312.5666666667 & 595.564960708941 & 2167.7 \tabularnewline
6 & 10625.6916666667 & 754.278132278361 & 2788.4 \tabularnewline
7 & 11051.2083333333 & 1162.35362516071 & 4270.6 \tabularnewline
8 & 12202.6166666667 & 1015.07122798294 & 3504.5 \tabularnewline
9 & 13425.175 & 1413.87687076415 & 5335 \tabularnewline
10 & 13831.725 & 924.19874990079 & 3166.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4916&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]8238.38333333333[/C][C]743.3421784363[/C][C]2476.6[/C][/ROW]
[ROW][C]2[/C][C]8411.81666666667[/C][C]711.017332397528[/C][C]2206.7[/C][/ROW]
[ROW][C]3[/C][C]9616.90833333333[/C][C]1146.67665923456[/C][C]3959.5[/C][/ROW]
[ROW][C]4[/C][C]10946.3583333333[/C][C]837.51576317142[/C][C]2886.1[/C][/ROW]
[ROW][C]5[/C][C]10312.5666666667[/C][C]595.564960708941[/C][C]2167.7[/C][/ROW]
[ROW][C]6[/C][C]10625.6916666667[/C][C]754.278132278361[/C][C]2788.4[/C][/ROW]
[ROW][C]7[/C][C]11051.2083333333[/C][C]1162.35362516071[/C][C]4270.6[/C][/ROW]
[ROW][C]8[/C][C]12202.6166666667[/C][C]1015.07122798294[/C][C]3504.5[/C][/ROW]
[ROW][C]9[/C][C]13425.175[/C][C]1413.87687076415[/C][C]5335[/C][/ROW]
[ROW][C]10[/C][C]13831.725[/C][C]924.19874990079[/C][C]3166.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4916&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4916&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
18238.38333333333743.34217843632476.6
28411.81666666667711.0173323975282206.7
39616.908333333331146.676659234563959.5
410946.3583333333837.515763171422886.1
510312.5666666667595.5649607089412167.7
610625.6916666667754.2781322783612788.4
711051.20833333331162.353625160714270.6
812202.61666666671015.071227982943504.5
913425.1751413.876870764155335
1013831.725924.198749900793166.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha131.302981693106
beta0.0735384273325756
S.D.0.0396731618637654
T-STAT1.85360641496387
p-value0.100916478576764

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 131.302981693106 \tabularnewline
beta & 0.0735384273325756 \tabularnewline
S.D. & 0.0396731618637654 \tabularnewline
T-STAT & 1.85360641496387 \tabularnewline
p-value & 0.100916478576764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4916&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]131.302981693106[/C][/ROW]
[ROW][C]beta[/C][C]0.0735384273325756[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0396731618637654[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.85360641496387[/C][/ROW]
[ROW][C]p-value[/C][C]0.100916478576764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4916&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4916&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)
alpha131.302981693106
beta0.0735384273325756
S.D.0.0396731618637654
T-STAT1.85360641496387
p-value0.100916478576764






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.919087878847302
beta0.832167286584739
S.D.0.452936898502705
T-STAT1.83726980366509
p-value0.103477657455791
Lambda0.167832713415261

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.919087878847302 \tabularnewline
beta & 0.832167286584739 \tabularnewline
S.D. & 0.452936898502705 \tabularnewline
T-STAT & 1.83726980366509 \tabularnewline
p-value & 0.103477657455791 \tabularnewline
Lambda & 0.167832713415261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4916&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.919087878847302[/C][/ROW]
[ROW][C]beta[/C][C]0.832167286584739[/C][/ROW]
[ROW][C]S.D.[/C][C]0.452936898502705[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.83726980366509[/C][/ROW]
[ROW][C]p-value[/C][C]0.103477657455791[/C][/ROW]
[ROW][C]Lambda[/C][C]0.167832713415261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4916&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4916&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-0.919087878847302
beta0.832167286584739
S.D.0.452936898502705
T-STAT1.83726980366509
p-value0.103477657455791
Lambda0.167832713415261


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')