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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, 05 Dec 2013 05:38:14 -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/Dec/05/t1386239973gpqdgll24vbgjuk.htm/, Retrieved Fri, 19 Apr 2024 22:00:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230905, Retrieved Fri, 19 Apr 2024 22:00:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

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] [] [2013-12-05 10:38:14] [2358c8bdbef440d7990b31f18da12314] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.1
20.1
20.1
20.3
20.7
20.6
20.3
19.9
19.7
19.4
19.1
18.8
18.9
18.7
18.8
19.5
19.3
19.1
19.1
19
18.8
19.2
18.9
18.7
18.5
18.4
18.3
18.3
18.3
18.5
19.2
19.4
19.1
19.5
18.8
19.3
20.4
20.9
21.1
20.6
20.4
20.8
21.1
21.6
22
22.2
22.4
22.8
22.7
22.8
22.9
22.9
22.6
21.9
20.8
20.3
20.4
21.2
21.4
20.9
20
19.5
19.2
19.3
19.4
19.5
20
20.1
19.5
18.6
18.4
18.4
19.3
19.8
19.8
19.8
20.1
20.3
19.7
20.2
20.6
21
21.4
21.9

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230905&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230905&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230905&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
119.9250.5801645534595421.9
2190.2486326242032250.800000000000001
318.80.4709757762541311.2
421.35833333333330.8207073815073232.4
521.73333333333331.016530045465132.6
619.3250.5925676025875561.7
720.3250.7688539286732972.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 19.925 & 0.580164553459542 & 1.9 \tabularnewline
2 & 19 & 0.248632624203225 & 0.800000000000001 \tabularnewline
3 & 18.8 & 0.470975776254131 & 1.2 \tabularnewline
4 & 21.3583333333333 & 0.820707381507323 & 2.4 \tabularnewline
5 & 21.7333333333333 & 1.01653004546513 & 2.6 \tabularnewline
6 & 19.325 & 0.592567602587556 & 1.7 \tabularnewline
7 & 20.325 & 0.768853928673297 & 2.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230905&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]19.925[/C][C]0.580164553459542[/C][C]1.9[/C][/ROW]
[ROW][C]2[/C][C]19[/C][C]0.248632624203225[/C][C]0.800000000000001[/C][/ROW]
[ROW][C]3[/C][C]18.8[/C][C]0.470975776254131[/C][C]1.2[/C][/ROW]
[ROW][C]4[/C][C]21.3583333333333[/C][C]0.820707381507323[/C][C]2.4[/C][/ROW]
[ROW][C]5[/C][C]21.7333333333333[/C][C]1.01653004546513[/C][C]2.6[/C][/ROW]
[ROW][C]6[/C][C]19.325[/C][C]0.592567602587556[/C][C]1.7[/C][/ROW]
[ROW][C]7[/C][C]20.325[/C][C]0.768853928673297[/C][C]2.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230905&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230905&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
119.9250.5801645534595421.9
2190.2486326242032250.800000000000001
318.80.4709757762541311.2
421.35833333333330.8207073815073232.4
521.73333333333331.016530045465132.6
619.3250.5925676025875561.7
720.3250.7688539286732972.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.3820014686367
beta0.200563185993881
S.D.0.0403732953414227
T-STAT4.96771899092677
p-value0.00422003367276601

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.3820014686367 \tabularnewline
beta & 0.200563185993881 \tabularnewline
S.D. & 0.0403732953414227 \tabularnewline
T-STAT & 4.96771899092677 \tabularnewline
p-value & 0.00422003367276601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230905&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.3820014686367[/C][/ROW]
[ROW][C]beta[/C][C]0.200563185993881[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0403732953414227[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.96771899092677[/C][/ROW]
[ROW][C]p-value[/C][C]0.00422003367276601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230905&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230905&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-3.3820014686367
beta0.200563185993881
S.D.0.0403732953414227
T-STAT4.96771899092677
p-value0.00422003367276601






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-20.8004602615154
beta6.76458195347014
S.D.2.04110106458039
T-STAT3.3141827569723
p-value0.021142968679663
Lambda-5.76458195347014

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -20.8004602615154 \tabularnewline
beta & 6.76458195347014 \tabularnewline
S.D. & 2.04110106458039 \tabularnewline
T-STAT & 3.3141827569723 \tabularnewline
p-value & 0.021142968679663 \tabularnewline
Lambda & -5.76458195347014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230905&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20.8004602615154[/C][/ROW]
[ROW][C]beta[/C][C]6.76458195347014[/C][/ROW]
[ROW][C]S.D.[/C][C]2.04110106458039[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.3141827569723[/C][/ROW]
[ROW][C]p-value[/C][C]0.021142968679663[/C][/ROW]
[ROW][C]Lambda[/C][C]-5.76458195347014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230905&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230905&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-20.8004602615154
beta6.76458195347014
S.D.2.04110106458039
T-STAT3.3141827569723
p-value0.021142968679663
Lambda-5.76458195347014


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')