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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 computationSun, 19 Dec 2010 20:06:19 +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/19/t1292789070h4hsfpvcrkjx44z.htm/, Retrieved Sun, 05 May 2024 04:23:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112726, Retrieved Sun, 05 May 2024 04:23:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
-   PD    [Standard Deviation-Mean Plot] [] [2010-12-05 17:46:34] [8ef75e99f9f5061c72c54640f2f1c3e7]
-    D        [Standard Deviation-Mean Plot] [] [2010-12-19 20:06:19] [e26438ba7029caa0090c95690001dbf5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,031636
3,702076
3,056176
3,280707
2,984728
3,693712
3,226317
2,190349
2,599515
3,080288
2,929672
2,922548
3,234943
2,983081
3,284389
3,806511
3,784579
2,645654
3,092081
3,204859
3,107225
3,466909
2,984404
3,218072
2,82731
3,182049
2,236319
2,033218
1,644804
1,627971
1,677559
2,330828
2,493615
2,257172
2,655517
2,298655
2,600402
3,04523
2,790583
3,227052
2,967479
2,938817
3,277961
3,423985
3,072646
2,754253
2,910431
3,174369
3,068387
3,089543
2,906654
2,931161
3,02566
2,939551
2,691019
3,19812
3,07639
2,863873
3,013802
3,053364
2,864753
3,057062
2,959365
3,252258
3,602988
3,497704
3,296867
3,602417
3,3001
3,40193
3,502591
3,402348
3,498551
3,199823
2,700064
2,801034
2,898628
2,800854
2,399942
2,402724
2,202331
2,102594
1,798293
1,202484
1,400201
1,200832
1,298083
1,099742
1,001377
0,8361743

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112726&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112726&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112726&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' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13.1414770.501357225939931.841287
23.234392250.3297955430864081.160857
32.272084750.4821303234830191.554078
43.015267333333330.2374596737849620.823583
52.9881270.1317342057457160.507101
63.311698583333330.2429722133460230.738235
72.500610166666670.6258717134222892.296067

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3.141477 & 0.50135722593993 & 1.841287 \tabularnewline
2 & 3.23439225 & 0.329795543086408 & 1.160857 \tabularnewline
3 & 2.27208475 & 0.482130323483019 & 1.554078 \tabularnewline
4 & 3.01526733333333 & 0.237459673784962 & 0.823583 \tabularnewline
5 & 2.988127 & 0.131734205745716 & 0.507101 \tabularnewline
6 & 3.31169858333333 & 0.242972213346023 & 0.738235 \tabularnewline
7 & 2.50061016666667 & 0.625871713422289 & 2.296067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112726&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]3.141477[/C][C]0.50135722593993[/C][C]1.841287[/C][/ROW]
[ROW][C]2[/C][C]3.23439225[/C][C]0.329795543086408[/C][C]1.160857[/C][/ROW]
[ROW][C]3[/C][C]2.27208475[/C][C]0.482130323483019[/C][C]1.554078[/C][/ROW]
[ROW][C]4[/C][C]3.01526733333333[/C][C]0.237459673784962[/C][C]0.823583[/C][/ROW]
[ROW][C]5[/C][C]2.988127[/C][C]0.131734205745716[/C][C]0.507101[/C][/ROW]
[ROW][C]6[/C][C]3.31169858333333[/C][C]0.242972213346023[/C][C]0.738235[/C][/ROW]
[ROW][C]7[/C][C]2.50061016666667[/C][C]0.625871713422289[/C][C]2.296067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112726&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112726&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
13.1414770.501357225939931.841287
23.234392250.3297955430864081.160857
32.272084750.4821303234830191.554078
43.015267333333330.2374596737849620.823583
52.9881270.1317342057457160.507101
63.311698583333330.2429722133460230.738235
72.500610166666670.6258717134222892.296067






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.14133140403735
beta-0.265739349878088
S.D.0.164270498814737
T-STAT-1.61769369299710
p-value0.166652399091552

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.14133140403735 \tabularnewline
beta & -0.265739349878088 \tabularnewline
S.D. & 0.164270498814737 \tabularnewline
T-STAT & -1.61769369299710 \tabularnewline
p-value & 0.166652399091552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112726&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.14133140403735[/C][/ROW]
[ROW][C]beta[/C][C]-0.265739349878088[/C][/ROW]
[ROW][C]S.D.[/C][C]0.164270498814737[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.61769369299710[/C][/ROW]
[ROW][C]p-value[/C][C]0.166652399091552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112726&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112726&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)
alpha1.14133140403735
beta-0.265739349878088
S.D.0.164270498814737
T-STAT-1.61769369299710
p-value0.166652399091552






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.961612305111002
beta-1.96048666539951
S.D.1.47917982997196
T-STAT-1.32538764095821
p-value0.242372229214905
Lambda2.96048666539951

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.961612305111002 \tabularnewline
beta & -1.96048666539951 \tabularnewline
S.D. & 1.47917982997196 \tabularnewline
T-STAT & -1.32538764095821 \tabularnewline
p-value & 0.242372229214905 \tabularnewline
Lambda & 2.96048666539951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112726&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.961612305111002[/C][/ROW]
[ROW][C]beta[/C][C]-1.96048666539951[/C][/ROW]
[ROW][C]S.D.[/C][C]1.47917982997196[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.32538764095821[/C][/ROW]
[ROW][C]p-value[/C][C]0.242372229214905[/C][/ROW]
[ROW][C]Lambda[/C][C]2.96048666539951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112726&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112726&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)
alpha0.961612305111002
beta-1.96048666539951
S.D.1.47917982997196
T-STAT-1.32538764095821
p-value0.242372229214905
Lambda2.96048666539951


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')