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 computationSat, 23 Jan 2010 12:11:52 -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/2010/Jan/23/t1264273983alig5jqk3cso3we.htm/, Retrieved Sun, 05 May 2024 06:21:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72381, Retrieved Sun, 05 May 2024 06:21:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

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] [VAC Standard Devi...] [2008-12-14 12:27:57] [379d6c32f73e3218fd773d79e4063d07]
-  M D    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-01-23 19:11:52] [f32a893c5a60da9308cd5d37e6977c4f] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
188.5
188.6
191.9
193.5
194.9
194.9
196.2
196.2
198
198.6
201.3
203.5
204.1
204.8
206.5
207.8
208.6
209.7
210
211.7
212.4
213.7
214.8
216.4
217.5
218.6
220.4
221.8
222.5
223.4
225.5
226.5
227.8
228.5
229.1
229.9
230.8
231.9
236
237.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72381&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]1 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=72381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72381&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1190.6252.483780720326715
2195.550.7505553499465041.29999999999998
3200.352.543619468395385.5
4205.81.671326818229563.70000000000002
52101.283225103661343.09999999999999
6214.3251.695828214570494
7219.5751.905037182489284.30000000000001
8224.4751.844586674569674
9228.8250.8920949127381732.09999999999999
10234.053.208841951026366.69999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 190.625 & 2.48378072032671 & 5 \tabularnewline
2 & 195.55 & 0.750555349946504 & 1.29999999999998 \tabularnewline
3 & 200.35 & 2.54361946839538 & 5.5 \tabularnewline
4 & 205.8 & 1.67132681822956 & 3.70000000000002 \tabularnewline
5 & 210 & 1.28322510366134 & 3.09999999999999 \tabularnewline
6 & 214.325 & 1.69582821457049 & 4 \tabularnewline
7 & 219.575 & 1.90503718248928 & 4.30000000000001 \tabularnewline
8 & 224.475 & 1.84458667456967 & 4 \tabularnewline
9 & 228.825 & 0.892094912738173 & 2.09999999999999 \tabularnewline
10 & 234.05 & 3.20884195102636 & 6.69999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72381&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]190.625[/C][C]2.48378072032671[/C][C]5[/C][/ROW]
[ROW][C]2[/C][C]195.55[/C][C]0.750555349946504[/C][C]1.29999999999998[/C][/ROW]
[ROW][C]3[/C][C]200.35[/C][C]2.54361946839538[/C][C]5.5[/C][/ROW]
[ROW][C]4[/C][C]205.8[/C][C]1.67132681822956[/C][C]3.70000000000002[/C][/ROW]
[ROW][C]5[/C][C]210[/C][C]1.28322510366134[/C][C]3.09999999999999[/C][/ROW]
[ROW][C]6[/C][C]214.325[/C][C]1.69582821457049[/C][C]4[/C][/ROW]
[ROW][C]7[/C][C]219.575[/C][C]1.90503718248928[/C][C]4.30000000000001[/C][/ROW]
[ROW][C]8[/C][C]224.475[/C][C]1.84458667456967[/C][C]4[/C][/ROW]
[ROW][C]9[/C][C]228.825[/C][C]0.892094912738173[/C][C]2.09999999999999[/C][/ROW]
[ROW][C]10[/C][C]234.05[/C][C]3.20884195102636[/C][C]6.69999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72381&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
1190.6252.483780720326715
2195.550.7505553499465041.29999999999998
3200.352.543619468395385.5
4205.81.671326818229563.70000000000002
52101.283225103661343.09999999999999
6214.3251.695828214570494
7219.5751.905037182489284.30000000000001
8224.4751.844586674569674
9228.8250.8920949127381732.09999999999999
10234.053.208841951026366.69999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.412024405507921
beta0.00666736627662044
S.D.0.0184393531867307
T-STAT0.361583522431708
p-value0.727027078483301

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.412024405507921 \tabularnewline
beta & 0.00666736627662044 \tabularnewline
S.D. & 0.0184393531867307 \tabularnewline
T-STAT & 0.361583522431708 \tabularnewline
p-value & 0.727027078483301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72381&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.412024405507921[/C][/ROW]
[ROW][C]beta[/C][C]0.00666736627662044[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0184393531867307[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.361583522431708[/C][/ROW]
[ROW][C]p-value[/C][C]0.727027078483301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72381&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)
alpha0.412024405507921
beta0.00666736627662044
S.D.0.0184393531867307
T-STAT0.361583522431708
p-value0.727027078483301






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.0772242794932
beta0.670784468090184
S.D.2.35384882461326
T-STAT0.284973470290895
p-value0.78290270201204
Lambda0.329215531909816

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.0772242794932 \tabularnewline
beta & 0.670784468090184 \tabularnewline
S.D. & 2.35384882461326 \tabularnewline
T-STAT & 0.284973470290895 \tabularnewline
p-value & 0.78290270201204 \tabularnewline
Lambda & 0.329215531909816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72381&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.0772242794932[/C][/ROW]
[ROW][C]beta[/C][C]0.670784468090184[/C][/ROW]
[ROW][C]S.D.[/C][C]2.35384882461326[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.284973470290895[/C][/ROW]
[ROW][C]p-value[/C][C]0.78290270201204[/C][/ROW]
[ROW][C]Lambda[/C][C]0.329215531909816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72381&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-3.0772242794932
beta0.670784468090184
S.D.2.35384882461326
T-STAT0.284973470290895
p-value0.78290270201204
Lambda0.329215531909816


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')