FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 23 Nov 2014 11:35:22 +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/2014/Nov/23/t1416742615mf8nzgo15rua333.htm/, Retrieved Tue, 28 May 2024 17:36:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257948, Retrieved Tue, 28 May 2024 17:36:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

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] [] [2014-11-23 11:35:22] [e5757b82694375e1f239be852782e5f7] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
220.05
220.05
220.62
221.53
221.61
221.5
221.5
221.87
222.27
220.86
221.49
221.67
221.67
221.72
221.67
220.29
220.75
219.59
219.59
219.59
219.82
221.59
220.9
221.01
221.01
219.69
221
219.82
218.04
217.97
217.97
217.53
217
217.18
217.68
217.71
217.71
218.5
218.8
218.94
220
219.89
219.89
220.08
220.16
221
222.16
221.5
221.5
221.6
221.85
223.11
222.79
222.45
222.45
222.4
223.15
224.4
224.24
223.92
212.42
212.34
212.95
213.37
214.26
214.1
213.54
213.69
211.82
212.82
212.36
212.7

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257948&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257948&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257948&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1221.2516666666670.7019949926437982.22
2220.68250.8784296422387122.13
3218.551.435960242549154.00999999999999
4219.8858333333331.274686830225964.44999999999999
5222.8216666666670.9788010600482212.90000000000001
6213.0308333333330.7621555357051862.44

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 221.251666666667 & 0.701994992643798 & 2.22 \tabularnewline
2 & 220.6825 & 0.878429642238712 & 2.13 \tabularnewline
3 & 218.55 & 1.43596024254915 & 4.00999999999999 \tabularnewline
4 & 219.885833333333 & 1.27468683022596 & 4.44999999999999 \tabularnewline
5 & 222.821666666667 & 0.978801060048221 & 2.90000000000001 \tabularnewline
6 & 213.030833333333 & 0.762155535705186 & 2.44 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257948&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]221.251666666667[/C][C]0.701994992643798[/C][C]2.22[/C][/ROW]
[ROW][C]2[/C][C]220.6825[/C][C]0.878429642238712[/C][C]2.13[/C][/ROW]
[ROW][C]3[/C][C]218.55[/C][C]1.43596024254915[/C][C]4.00999999999999[/C][/ROW]
[ROW][C]4[/C][C]219.885833333333[/C][C]1.27468683022596[/C][C]4.44999999999999[/C][/ROW]
[ROW][C]5[/C][C]222.821666666667[/C][C]0.978801060048221[/C][C]2.90000000000001[/C][/ROW]
[ROW][C]6[/C][C]213.030833333333[/C][C]0.762155535705186[/C][C]2.44[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257948&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257948&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
1221.2516666666670.7019949926437982.22
2220.68250.8784296422387122.13
3218.551.435960242549154.00999999999999
4219.8858333333331.274686830225964.44999999999999
5222.8216666666670.9788010600482212.90000000000001
6213.0308333333330.7621555357051862.44






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.870190559300415
beta0.00854959678869911
S.D.0.0425233912360165
T-STAT0.201056325476172
p-value0.850464335847748

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.870190559300415 \tabularnewline
beta & 0.00854959678869911 \tabularnewline
S.D. & 0.0425233912360165 \tabularnewline
T-STAT & 0.201056325476172 \tabularnewline
p-value & 0.850464335847748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257948&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.870190559300415[/C][/ROW]
[ROW][C]beta[/C][C]0.00854959678869911[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0425233912360165[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.201056325476172[/C][/ROW]
[ROW][C]p-value[/C][C]0.850464335847748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257948&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257948&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-0.870190559300415
beta0.00854959678869911
S.D.0.0425233912360165
T-STAT0.201056325476172
p-value0.850464335847748






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-13.3006527428262
beta2.4620354539591
S.D.8.93920472459687
T-STAT0.275419965177062
p-value0.79663574055691
Lambda-1.4620354539591

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -13.3006527428262 \tabularnewline
beta & 2.4620354539591 \tabularnewline
S.D. & 8.93920472459687 \tabularnewline
T-STAT & 0.275419965177062 \tabularnewline
p-value & 0.79663574055691 \tabularnewline
Lambda & -1.4620354539591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257948&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.3006527428262[/C][/ROW]
[ROW][C]beta[/C][C]2.4620354539591[/C][/ROW]
[ROW][C]S.D.[/C][C]8.93920472459687[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.275419965177062[/C][/ROW]
[ROW][C]p-value[/C][C]0.79663574055691[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.4620354539591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257948&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257948&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-13.3006527428262
beta2.4620354539591
S.D.8.93920472459687
T-STAT0.275419965177062
p-value0.79663574055691
Lambda-1.4620354539591


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')