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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 computationTue, 28 Dec 2010 10:00:39 +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/28/t1293530342lfj6tmhnuv0chkm.htm/, Retrieved Sun, 05 May 2024 01:22:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116257, Retrieved Sun, 05 May 2024 01:22:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

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] [] [2010-12-28 10:00:39] [1bb61589b71a2dccde96f07234cd79aa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46.194
36.943
45.062
35.062
47.177
38.064
47.663
35.483
46.228
36.255
45.134
33.472
44.720
35.487
41.753
33.142
41.744
33.462
42.743
31.518
39.946
31.647
39.603
31.372
42.638
29.654
38.626
29.534
36.721
30.310
37.285
28.979
35.801
28.451
36.125
28.141
34.333
27.082
34.356
27.975
33.537
26.218
33.191
25.219
32.272
24.838
31.723
24.753
30.393
24.346
30.192
23.387
28.385
23.000
28.581
22.512

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116257&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116257&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116257&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
140.815255.6290923705928611.132
242.096756.2395737234205412.18
340.272256.3636799822639312.756
438.77555.3775192855690111.578
537.366755.701442237130311.225
635.6424.775174063145068.574
735.1136.5800890571480913.104
833.323754.289224900841648.306
932.12954.430328317404937.984
1030.93653.952081519064777.274
1129.541254.435182399481078.318
1228.39654.164257316737287.519
1327.07953.731555395095547.006
1425.61953.313447801510286.069

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 40.81525 & 5.62909237059286 & 11.132 \tabularnewline
2 & 42.09675 & 6.23957372342054 & 12.18 \tabularnewline
3 & 40.27225 & 6.36367998226393 & 12.756 \tabularnewline
4 & 38.7755 & 5.37751928556901 & 11.578 \tabularnewline
5 & 37.36675 & 5.7014422371303 & 11.225 \tabularnewline
6 & 35.642 & 4.77517406314506 & 8.574 \tabularnewline
7 & 35.113 & 6.58008905714809 & 13.104 \tabularnewline
8 & 33.32375 & 4.28922490084164 & 8.306 \tabularnewline
9 & 32.1295 & 4.43032831740493 & 7.984 \tabularnewline
10 & 30.9365 & 3.95208151906477 & 7.274 \tabularnewline
11 & 29.54125 & 4.43518239948107 & 8.318 \tabularnewline
12 & 28.3965 & 4.16425731673728 & 7.519 \tabularnewline
13 & 27.0795 & 3.73155539509554 & 7.006 \tabularnewline
14 & 25.6195 & 3.31344780151028 & 6.069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116257&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]40.81525[/C][C]5.62909237059286[/C][C]11.132[/C][/ROW]
[ROW][C]2[/C][C]42.09675[/C][C]6.23957372342054[/C][C]12.18[/C][/ROW]
[ROW][C]3[/C][C]40.27225[/C][C]6.36367998226393[/C][C]12.756[/C][/ROW]
[ROW][C]4[/C][C]38.7755[/C][C]5.37751928556901[/C][C]11.578[/C][/ROW]
[ROW][C]5[/C][C]37.36675[/C][C]5.7014422371303[/C][C]11.225[/C][/ROW]
[ROW][C]6[/C][C]35.642[/C][C]4.77517406314506[/C][C]8.574[/C][/ROW]
[ROW][C]7[/C][C]35.113[/C][C]6.58008905714809[/C][C]13.104[/C][/ROW]
[ROW][C]8[/C][C]33.32375[/C][C]4.28922490084164[/C][C]8.306[/C][/ROW]
[ROW][C]9[/C][C]32.1295[/C][C]4.43032831740493[/C][C]7.984[/C][/ROW]
[ROW][C]10[/C][C]30.9365[/C][C]3.95208151906477[/C][C]7.274[/C][/ROW]
[ROW][C]11[/C][C]29.54125[/C][C]4.43518239948107[/C][C]8.318[/C][/ROW]
[ROW][C]12[/C][C]28.3965[/C][C]4.16425731673728[/C][C]7.519[/C][/ROW]
[ROW][C]13[/C][C]27.0795[/C][C]3.73155539509554[/C][C]7.006[/C][/ROW]
[ROW][C]14[/C][C]25.6195[/C][C]3.31344780151028[/C][C]6.069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116257&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116257&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
140.815255.6290923705928611.132
242.096756.2395737234205412.18
340.272256.3636799822639312.756
438.77555.3775192855690111.578
537.366755.701442237130311.225
635.6424.775174063145068.574
735.1136.5800890571480913.104
833.323754.289224900841648.306
932.12954.430328317404937.984
1030.93653.952081519064777.274
1129.541254.435182399481078.318
1228.39654.164257316737287.519
1327.07953.731555395095547.006
1425.61953.313447801510286.069






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.877882959516999
beta0.17034509964755
S.D.0.0280046083440679
T-STAT6.08275243683719
p-value5.47800983482351e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.877882959516999 \tabularnewline
beta & 0.17034509964755 \tabularnewline
S.D. & 0.0280046083440679 \tabularnewline
T-STAT & 6.08275243683719 \tabularnewline
p-value & 5.47800983482351e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116257&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.877882959516999[/C][/ROW]
[ROW][C]beta[/C][C]0.17034509964755[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0280046083440679[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.08275243683719[/C][/ROW]
[ROW][C]p-value[/C][C]5.47800983482351e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116257&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116257&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-0.877882959516999
beta0.17034509964755
S.D.0.0280046083440679
T-STAT6.08275243683719
p-value5.47800983482351e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.64344295549882
beta1.19904161403527
S.D.0.174474724108562
T-STAT6.87229408248955
p-value1.71705748552071e-05
Lambda-0.199041614035265

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.64344295549882 \tabularnewline
beta & 1.19904161403527 \tabularnewline
S.D. & 0.174474724108562 \tabularnewline
T-STAT & 6.87229408248955 \tabularnewline
p-value & 1.71705748552071e-05 \tabularnewline
Lambda & -0.199041614035265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116257&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.64344295549882[/C][/ROW]
[ROW][C]beta[/C][C]1.19904161403527[/C][/ROW]
[ROW][C]S.D.[/C][C]0.174474724108562[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.87229408248955[/C][/ROW]
[ROW][C]p-value[/C][C]1.71705748552071e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.199041614035265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116257&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116257&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-2.64344295549882
beta1.19904161403527
S.D.0.174474724108562
T-STAT6.87229408248955
p-value1.71705748552071e-05
Lambda-0.199041614035265


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')