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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 computationWed, 12 Dec 2012 09:43:33 -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/2012/Dec/12/t13553234274a0dv11d78hnl0v.htm/, Retrieved Mon, 29 Apr 2024 10:58:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198917, Retrieved Mon, 29 Apr 2024 10:58:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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] [] [2012-12-12 14:43:33] [19a5fa3cc9952272699ac0aa748608b8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.6
2
2.6
3
2.6
2.9
2.5
2.4
1.5
1.1
0.6
0.9
1.1
1.5
1.7
1.2
0.4
-0.7
-1.4
-1.6
-1.2
-0.4
-0.2
-0.3
-0.5
0
-0.5
0.2
0.7
1.6
2.6
3.3
3.3
3.2
3.5
3.9
4.5
4.6
6.6
7.1
8.9
8.8
8.5
7.6
7.5
7.5
6.1
6.3
8.4
7.1
5.6
4.2
2.1
1.2
0.9
1.4
1.7
1.7
1.9
1.3
-0.7
0.3
0.8
0.9
1.1
2.5
2.7
3.3
4.2
3.8
3.8
3.2
2.9
1.9
1.7
1.6
1.7
1.2
0.7
-0.2
-1.5
-1.2
-1
0
-0.6
0.7
1.3
0.8
1
0.5
0.3
1
1
1.1
1.5
1.5
2
1.7
0.6
1.2
1.5
2.1
3.2
3.9
4.6
4.2
4.4
3.7
3.7
2.8
2.9
3.9
3.1
3
2.8
2.4
2.1
3.1
3
3.1
3.3
3.3
3.8
3.1
3.9
4
4.4
3.7
3.6
3.4
2.8
2.8
2.6
3.3
2.4
1.6
0.7
0
-1.1
-1.2
-1.3
-1.6
-1.3
-1.6
-1.1
-1
0.3
1.2
0.7
1.1
2.1
2.5
2.3
2.3
2.6
3.2
2.2
2.7
2.2
1.4
2.4
2
1.3
1.1
1.4
1.8
1.9
1.6

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=198917&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=198917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198917&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
11.9750.8158932639639932.4
20.008333333333333341.155585906749813.3
31.7751.706205252493494.4
471.459763368121394.4
53.1252.566966727836227.5
62.158333333333331.610453540484984.9
70.651.41260558736494.4
80.8416666666666670.5822500764406582.1
92.758333333333331.393137944832934
102.991666666666670.4851585182997281.8
113.508333333333330.4851585182997291.6
120.2083333333333331.836230493223124.9
131.351.40809348863184.3
141.833333333333330.4886592665527571.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.975 & 0.815893263963993 & 2.4 \tabularnewline
2 & 0.00833333333333334 & 1.15558590674981 & 3.3 \tabularnewline
3 & 1.775 & 1.70620525249349 & 4.4 \tabularnewline
4 & 7 & 1.45976336812139 & 4.4 \tabularnewline
5 & 3.125 & 2.56696672783622 & 7.5 \tabularnewline
6 & 2.15833333333333 & 1.61045354048498 & 4.9 \tabularnewline
7 & 0.65 & 1.4126055873649 & 4.4 \tabularnewline
8 & 0.841666666666667 & 0.582250076440658 & 2.1 \tabularnewline
9 & 2.75833333333333 & 1.39313794483293 & 4 \tabularnewline
10 & 2.99166666666667 & 0.485158518299728 & 1.8 \tabularnewline
11 & 3.50833333333333 & 0.485158518299729 & 1.6 \tabularnewline
12 & 0.208333333333333 & 1.83623049322312 & 4.9 \tabularnewline
13 & 1.35 & 1.4080934886318 & 4.3 \tabularnewline
14 & 1.83333333333333 & 0.488659266552757 & 1.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198917&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]1.975[/C][C]0.815893263963993[/C][C]2.4[/C][/ROW]
[ROW][C]2[/C][C]0.00833333333333334[/C][C]1.15558590674981[/C][C]3.3[/C][/ROW]
[ROW][C]3[/C][C]1.775[/C][C]1.70620525249349[/C][C]4.4[/C][/ROW]
[ROW][C]4[/C][C]7[/C][C]1.45976336812139[/C][C]4.4[/C][/ROW]
[ROW][C]5[/C][C]3.125[/C][C]2.56696672783622[/C][C]7.5[/C][/ROW]
[ROW][C]6[/C][C]2.15833333333333[/C][C]1.61045354048498[/C][C]4.9[/C][/ROW]
[ROW][C]7[/C][C]0.65[/C][C]1.4126055873649[/C][C]4.4[/C][/ROW]
[ROW][C]8[/C][C]0.841666666666667[/C][C]0.582250076440658[/C][C]2.1[/C][/ROW]
[ROW][C]9[/C][C]2.75833333333333[/C][C]1.39313794483293[/C][C]4[/C][/ROW]
[ROW][C]10[/C][C]2.99166666666667[/C][C]0.485158518299728[/C][C]1.8[/C][/ROW]
[ROW][C]11[/C][C]3.50833333333333[/C][C]0.485158518299729[/C][C]1.6[/C][/ROW]
[ROW][C]12[/C][C]0.208333333333333[/C][C]1.83623049322312[/C][C]4.9[/C][/ROW]
[ROW][C]13[/C][C]1.35[/C][C]1.4080934886318[/C][C]4.3[/C][/ROW]
[ROW][C]14[/C][C]1.83333333333333[/C][C]0.488659266552757[/C][C]1.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198917&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
11.9750.8158932639639932.4
20.008333333333333341.155585906749813.3
31.7751.706205252493494.4
471.459763368121394.4
53.1252.566966727836227.5
62.158333333333331.610453540484984.9
70.651.41260558736494.4
80.8416666666666670.5822500764406582.1
92.758333333333331.393137944832934
102.991666666666670.4851585182997281.8
113.508333333333330.4851585182997291.6
120.2083333333333331.836230493223124.9
131.351.40809348863184.3
141.833333333333330.4886592665527571.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.22087290995399
beta0.0104011445811033
S.D.0.100457573481327
T-STAT0.103537684822107
p-value0.919246497868159

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.22087290995399 \tabularnewline
beta & 0.0104011445811033 \tabularnewline
S.D. & 0.100457573481327 \tabularnewline
T-STAT & 0.103537684822107 \tabularnewline
p-value & 0.919246497868159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198917&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.22087290995399[/C][/ROW]
[ROW][C]beta[/C][C]0.0104011445811033[/C][/ROW]
[ROW][C]S.D.[/C][C]0.100457573481327[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.103537684822107[/C][/ROW]
[ROW][C]p-value[/C][C]0.919246497868159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198917&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)
alpha1.22087290995399
beta0.0104011445811033
S.D.0.100457573481327
T-STAT0.103537684822107
p-value0.919246497868159






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.0915166749357293
beta-0.0350462576604491
S.D.0.096678020500403
T-STAT-0.362504915585265
p-value0.72327890544988
Lambda1.03504625766045

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0915166749357293 \tabularnewline
beta & -0.0350462576604491 \tabularnewline
S.D. & 0.096678020500403 \tabularnewline
T-STAT & -0.362504915585265 \tabularnewline
p-value & 0.72327890544988 \tabularnewline
Lambda & 1.03504625766045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198917&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0915166749357293[/C][/ROW]
[ROW][C]beta[/C][C]-0.0350462576604491[/C][/ROW]
[ROW][C]S.D.[/C][C]0.096678020500403[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.362504915585265[/C][/ROW]
[ROW][C]p-value[/C][C]0.72327890544988[/C][/ROW]
[ROW][C]Lambda[/C][C]1.03504625766045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198917&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198917&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)
alpha0.0915166749357293
beta-0.0350462576604491
S.D.0.096678020500403
T-STAT-0.362504915585265
p-value0.72327890544988
Lambda1.03504625766045


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')