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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, 30 Nov 2013 10:27:08 -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/2013/Nov/30/t1385825240j56l8y1vizfx1og.htm/, Retrieved Fri, 03 May 2024 12:14:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229699, Retrieved Fri, 03 May 2024 12:14:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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] [] [2013-11-30 15:27:08] [154a417cb3d2e1b589b01477b4193420] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13953.3
14657.7
16686.2
15232.4
15014.1
16688.6
13969.6
14546.8
16292
15039
17433.8
17798.4
16870.9
16659.3
19620.4
15953.5
17420.9
17647.5
15200.8
15637.3
17124.5
17659.4
17815
16165.6
17416.6
16823.9
19171.2
16806.8
18112.8
18485.5
17668
16324.3
17877.5
20136.7
19307
17776.3
19861.3
18757
19879.3
21068.4
19358
20639.2
20008.1
18150.1
21180.4
20428.9
17241.2
15969.3
14972.4
14488.3
15885.1
14305.3
13891.5
15431.6
14199.3
13542.6
16226.3
16786.1
16034.3
16744.5
15896.5
15781.8
18590.3
17416.8
16983
18829.4
16748.6
16502.8
18616.6
19136.4
19523.9
18970.2
20118.2
20125.4
23117.8
20014.6
22228.5
20819.1
19208.9
19953.3
21041.3
20006.8
21045.1
20496.3
20873.5
21304.2
23137.8
20514.2
21343.5
20967.2
20024.4
19602.7
19804.1
22173.9
21802.6
19452.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229699&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229699&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229699&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
115609.3251321.108352947353845.1
216981.25833333331190.547187761954419.6
317992.21666666671129.106158817143812.4
419378.43333333331588.651453468025211.1
515208.94166666671127.827235688433243.5
617749.69166666671339.837561700083742.1
720681.2751081.624018127793908.9
820916.69166666671116.114501667883685.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15609.325 & 1321.10835294735 & 3845.1 \tabularnewline
2 & 16981.2583333333 & 1190.54718776195 & 4419.6 \tabularnewline
3 & 17992.2166666667 & 1129.10615881714 & 3812.4 \tabularnewline
4 & 19378.4333333333 & 1588.65145346802 & 5211.1 \tabularnewline
5 & 15208.9416666667 & 1127.82723568843 & 3243.5 \tabularnewline
6 & 17749.6916666667 & 1339.83756170008 & 3742.1 \tabularnewline
7 & 20681.275 & 1081.62401812779 & 3908.9 \tabularnewline
8 & 20916.6916666667 & 1116.11450166788 & 3685.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229699&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]15609.325[/C][C]1321.10835294735[/C][C]3845.1[/C][/ROW]
[ROW][C]2[/C][C]16981.2583333333[/C][C]1190.54718776195[/C][C]4419.6[/C][/ROW]
[ROW][C]3[/C][C]17992.2166666667[/C][C]1129.10615881714[/C][C]3812.4[/C][/ROW]
[ROW][C]4[/C][C]19378.4333333333[/C][C]1588.65145346802[/C][C]5211.1[/C][/ROW]
[ROW][C]5[/C][C]15208.9416666667[/C][C]1127.82723568843[/C][C]3243.5[/C][/ROW]
[ROW][C]6[/C][C]17749.6916666667[/C][C]1339.83756170008[/C][C]3742.1[/C][/ROW]
[ROW][C]7[/C][C]20681.275[/C][C]1081.62401812779[/C][C]3908.9[/C][/ROW]
[ROW][C]8[/C][C]20916.6916666667[/C][C]1116.11450166788[/C][C]3685.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229699&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229699&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
115609.3251321.108352947353845.1
216981.25833333331190.547187761954419.6
317992.21666666671129.106158817143812.4
419378.43333333331588.651453468025211.1
515208.94166666671127.827235688433243.5
617749.69166666671339.837561700083742.1
720681.2751081.624018127793908.9
820916.69166666671116.114501667883685.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1325.76563465905
beta-0.00492194347705929
S.D.0.0325901131001329
T-STAT-0.151025664192593
p-value0.88490515148231

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1325.76563465905 \tabularnewline
beta & -0.00492194347705929 \tabularnewline
S.D. & 0.0325901131001329 \tabularnewline
T-STAT & -0.151025664192593 \tabularnewline
p-value & 0.88490515148231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229699&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1325.76563465905[/C][/ROW]
[ROW][C]beta[/C][C]-0.00492194347705929[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0325901131001329[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.151025664192593[/C][/ROW]
[ROW][C]p-value[/C][C]0.88490515148231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229699&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229699&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)
alpha1325.76563465905
beta-0.00492194347705929
S.D.0.0325901131001329
T-STAT-0.151025664192593
p-value0.88490515148231






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.94334449483178
beta-0.0848137761044625
S.D.0.446461262684413
T-STAT-0.189968947349446
p-value0.855597492235452
Lambda1.08481377610446

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.94334449483178 \tabularnewline
beta & -0.0848137761044625 \tabularnewline
S.D. & 0.446461262684413 \tabularnewline
T-STAT & -0.189968947349446 \tabularnewline
p-value & 0.855597492235452 \tabularnewline
Lambda & 1.08481377610446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229699&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.94334449483178[/C][/ROW]
[ROW][C]beta[/C][C]-0.0848137761044625[/C][/ROW]
[ROW][C]S.D.[/C][C]0.446461262684413[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.189968947349446[/C][/ROW]
[ROW][C]p-value[/C][C]0.855597492235452[/C][/ROW]
[ROW][C]Lambda[/C][C]1.08481377610446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229699&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229699&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)
alpha7.94334449483178
beta-0.0848137761044625
S.D.0.446461262684413
T-STAT-0.189968947349446
p-value0.855597492235452
Lambda1.08481377610446


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')