FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 22 Dec 2010 22:35:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293057199oku680p1tgoxt9r.htm/, Retrieved Mon, 06 May 2024 02:24:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114614, Retrieved Mon, 06 May 2024 02:24:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

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] [] [2010-12-22 22:35:15] [f149abcac50db27facd6576b094a0cd9] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
120.9
119.6
125.9
116.1
107.5
116.7
112.5
113
126.4
114.1
112.5
112.4
113.1
116.3
111.7
118.8
116.5
125.1
113.1
119.6
114.4
114
117.8
117
120.9
115
117.3
119.4
114.9
125.8
117.6
117.6
114.9
121.9
117
106.4
110.5
113.6
114.2
125.4
124.6
120.2
120.8
111.4
124.1
120.2
125.5
116
117
105.7
102
106.4
96.9
107.6
98.8
101.1
105.7
104.6
103.2
101.6

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114614&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114614&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1116.4666666666675.747305033797618.9
2116.453.6634558944948513.4
3117.3916666666674.73448822871919.4
4118.8755.5409426503570215
5104.2166666666675.130626992223620.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 116.466666666667 & 5.7473050337976 & 18.9 \tabularnewline
2 & 116.45 & 3.66345589449485 & 13.4 \tabularnewline
3 & 117.391666666667 & 4.734488228719 & 19.4 \tabularnewline
4 & 118.875 & 5.54094265035702 & 15 \tabularnewline
5 & 104.216666666667 & 5.1306269922236 & 20.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114614&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]116.466666666667[/C][C]5.7473050337976[/C][C]18.9[/C][/ROW]
[ROW][C]2[/C][C]116.45[/C][C]3.66345589449485[/C][C]13.4[/C][/ROW]
[ROW][C]3[/C][C]117.391666666667[/C][C]4.734488228719[/C][C]19.4[/C][/ROW]
[ROW][C]4[/C][C]118.875[/C][C]5.54094265035702[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]104.216666666667[/C][C]5.1306269922236[/C][C]20.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114614&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
1116.4666666666675.747305033797618.9
2116.453.6634558944948513.4
3117.3916666666674.73448822871919.4
4118.8755.5409426503570215
5104.2166666666675.130626992223620.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.65427197609233
beta-0.00602466180828319
S.D.0.0801571512209108
T-STAT-0.0751606277982534
p-value0.944818274647489

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.65427197609233 \tabularnewline
beta & -0.00602466180828319 \tabularnewline
S.D. & 0.0801571512209108 \tabularnewline
T-STAT & -0.0751606277982534 \tabularnewline
p-value & 0.944818274647489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114614&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.65427197609233[/C][/ROW]
[ROW][C]beta[/C][C]-0.00602466180828319[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0801571512209108[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0751606277982534[/C][/ROW]
[ROW][C]p-value[/C][C]0.944818274647489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114614&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)
alpha5.65427197609233
beta-0.00602466180828319
S.D.0.0801571512209108
T-STAT-0.0751606277982534
p-value0.944818274647489






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.73687416872214
beta-0.241929374778462
S.D.1.92788190123263
T-STAT-0.125489727676669
p-value0.908073152686169
Lambda1.24192937477846

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.73687416872214 \tabularnewline
beta & -0.241929374778462 \tabularnewline
S.D. & 1.92788190123263 \tabularnewline
T-STAT & -0.125489727676669 \tabularnewline
p-value & 0.908073152686169 \tabularnewline
Lambda & 1.24192937477846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114614&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.73687416872214[/C][/ROW]
[ROW][C]beta[/C][C]-0.241929374778462[/C][/ROW]
[ROW][C]S.D.[/C][C]1.92788190123263[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.125489727676669[/C][/ROW]
[ROW][C]p-value[/C][C]0.908073152686169[/C][/ROW]
[ROW][C]Lambda[/C][C]1.24192937477846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114614&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)
alpha2.73687416872214
beta-0.241929374778462
S.D.1.92788190123263
T-STAT-0.125489727676669
p-value0.908073152686169
Lambda1.24192937477846


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')