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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 computationMon, 28 Apr 2014 11:05:02 -0400
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/Apr/28/t1398697538eyf1fud0wnurc6j.htm/, Retrieved Fri, 17 May 2024 06:28:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234689, Retrieved Fri, 17 May 2024 06:28:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

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] [Standard deviatio...] [2014-04-28 15:05:02] [1195732e18620915cb775ad7ef5494bd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
227,81
227,81
227,01
227,26
227,1
227,59
227,59
227,7
227,75
226,33
225,95
226,33
226,33
226,22
224,84
221,88
222,37
221,8
221,8
221,8
221,9
220,2
219,95
220,05
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

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=234689&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=234689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234689&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
1227.1858333333330.6553619171299481.86000000000001
2222.4283333333332.214570893519616.38000000000002
3221.2516666666670.7019949926437982.22
4220.68250.8784296422387122.13
5218.551.435960242549154.00999999999999
6219.8858333333331.274686830225964.44999999999999
7222.8216666666670.9788010600482212.90000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 227.185833333333 & 0.655361917129948 & 1.86000000000001 \tabularnewline
2 & 222.428333333333 & 2.21457089351961 & 6.38000000000002 \tabularnewline
3 & 221.251666666667 & 0.701994992643798 & 2.22 \tabularnewline
4 & 220.6825 & 0.878429642238712 & 2.13 \tabularnewline
5 & 218.55 & 1.43596024254915 & 4.00999999999999 \tabularnewline
6 & 219.885833333333 & 1.27468683022596 & 4.44999999999999 \tabularnewline
7 & 222.821666666667 & 0.978801060048221 & 2.90000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234689&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]227.185833333333[/C][C]0.655361917129948[/C][C]1.86000000000001[/C][/ROW]
[ROW][C]2[/C][C]222.428333333333[/C][C]2.21457089351961[/C][C]6.38000000000002[/C][/ROW]
[ROW][C]3[/C][C]221.251666666667[/C][C]0.701994992643798[/C][C]2.22[/C][/ROW]
[ROW][C]4[/C][C]220.6825[/C][C]0.878429642238712[/C][C]2.13[/C][/ROW]
[ROW][C]5[/C][C]218.55[/C][C]1.43596024254915[/C][C]4.00999999999999[/C][/ROW]
[ROW][C]6[/C][C]219.885833333333[/C][C]1.27468683022596[/C][C]4.44999999999999[/C][/ROW]
[ROW][C]7[/C][C]222.821666666667[/C][C]0.978801060048221[/C][C]2.90000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234689&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
1227.1858333333330.6553619171299481.86000000000001
2222.4283333333332.214570893519616.38000000000002
3221.2516666666670.7019949926437982.22
4220.68250.8784296422387122.13
5218.551.435960242549154.00999999999999
6219.8858333333331.274686830225964.44999999999999
7222.8216666666670.9788010600482212.90000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha14.5620739656436
beta-0.0604033744385189
S.D.0.0834521330478561
T-STAT-0.723808634152949
p-value0.501618703537277

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 14.5620739656436 \tabularnewline
beta & -0.0604033744385189 \tabularnewline
S.D. & 0.0834521330478561 \tabularnewline
T-STAT & -0.723808634152949 \tabularnewline
p-value & 0.501618703537277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234689&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.5620739656436[/C][/ROW]
[ROW][C]beta[/C][C]-0.0604033744385189[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0834521330478561[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.723808634152949[/C][/ROW]
[ROW][C]p-value[/C][C]0.501618703537277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234689&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234689&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)
alpha14.5620739656436
beta-0.0604033744385189
S.D.0.0834521330478561
T-STAT-0.723808634152949
p-value0.501618703537277






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha81.050404567123
beta-14.9917295291972
S.D.13.9340714740422
T-STAT-1.07590445169779
p-value0.331122090640494
Lambda15.9917295291972

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 81.050404567123 \tabularnewline
beta & -14.9917295291972 \tabularnewline
S.D. & 13.9340714740422 \tabularnewline
T-STAT & -1.07590445169779 \tabularnewline
p-value & 0.331122090640494 \tabularnewline
Lambda & 15.9917295291972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234689&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]81.050404567123[/C][/ROW]
[ROW][C]beta[/C][C]-14.9917295291972[/C][/ROW]
[ROW][C]S.D.[/C][C]13.9340714740422[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.07590445169779[/C][/ROW]
[ROW][C]p-value[/C][C]0.331122090640494[/C][/ROW]
[ROW][C]Lambda[/C][C]15.9917295291972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234689&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234689&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)
alpha81.050404567123
beta-14.9917295291972
S.D.13.9340714740422
T-STAT-1.07590445169779
p-value0.331122090640494
Lambda15.9917295291972


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')