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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 computationSat, 12 Dec 2009 08:21:58 -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/2009/Dec/12/t12606313462jkv72590gvj198.htm/, Retrieved Mon, 29 Apr 2024 13:51:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67014, Retrieved Mon, 29 Apr 2024 13:51:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [smp] [2009-12-12 15:21:58] [5d37783481a916b2505b66314b556267] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17192.4
15386.1
14287.1
17526.6
14497
14398.3
16629.6
16670.7
16614.8
16869.2
15663.9
16359.9
18447.7
16889
16505
18320.9
15052.1
15699.8
18135.3
16768.7
18883
19021
18101.9
17776.1
21489.9
17065.3
18690
18953.1
16398.9
16895.6
18553
19270
19422.1
17579.4
18637.3
18076.7
20438.6
18075.2
19563
19899.2
19227.5
17789.6
19220.8
21968.9
21131.5
19484.6
22168.7
20866.8
22176.2
23533.8
21479.6
24347.7
22751.6
20328.3
23650.4
23335.7
19614.9
18042.3
17282.5
16847.2
18159.5

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=67014&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=67014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67014&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
116098.051530.225444174813239.5
215548.91272.362854430032272.4
316376.95518.8492684136061205.3
417540.65988.0533740643781942.7
516413.9751348.275321475553083.2
618445.5602.4294758171561244.90000000000
719049.5751828.581871970744424.6
817779.3751354.895814875322871.1
918428.875790.6899703212791842.70000000000
10194941012.292882519682363.4
1119551.71747.612914806944179.3
1220912.91105.589691823632684.1
1322884.3251295.888049112782868.1
1422516.51505.579522974463322.1
1517946.7251216.839141313812767.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16098.05 & 1530.22544417481 & 3239.5 \tabularnewline
2 & 15548.9 & 1272.36285443003 & 2272.4 \tabularnewline
3 & 16376.95 & 518.849268413606 & 1205.3 \tabularnewline
4 & 17540.65 & 988.053374064378 & 1942.7 \tabularnewline
5 & 16413.975 & 1348.27532147555 & 3083.2 \tabularnewline
6 & 18445.5 & 602.429475817156 & 1244.90000000000 \tabularnewline
7 & 19049.575 & 1828.58187197074 & 4424.6 \tabularnewline
8 & 17779.375 & 1354.89581487532 & 2871.1 \tabularnewline
9 & 18428.875 & 790.689970321279 & 1842.70000000000 \tabularnewline
10 & 19494 & 1012.29288251968 & 2363.4 \tabularnewline
11 & 19551.7 & 1747.61291480694 & 4179.3 \tabularnewline
12 & 20912.9 & 1105.58969182363 & 2684.1 \tabularnewline
13 & 22884.325 & 1295.88804911278 & 2868.1 \tabularnewline
14 & 22516.5 & 1505.57952297446 & 3322.1 \tabularnewline
15 & 17946.725 & 1216.83914131381 & 2767.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67014&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]16098.05[/C][C]1530.22544417481[/C][C]3239.5[/C][/ROW]
[ROW][C]2[/C][C]15548.9[/C][C]1272.36285443003[/C][C]2272.4[/C][/ROW]
[ROW][C]3[/C][C]16376.95[/C][C]518.849268413606[/C][C]1205.3[/C][/ROW]
[ROW][C]4[/C][C]17540.65[/C][C]988.053374064378[/C][C]1942.7[/C][/ROW]
[ROW][C]5[/C][C]16413.975[/C][C]1348.27532147555[/C][C]3083.2[/C][/ROW]
[ROW][C]6[/C][C]18445.5[/C][C]602.429475817156[/C][C]1244.90000000000[/C][/ROW]
[ROW][C]7[/C][C]19049.575[/C][C]1828.58187197074[/C][C]4424.6[/C][/ROW]
[ROW][C]8[/C][C]17779.375[/C][C]1354.89581487532[/C][C]2871.1[/C][/ROW]
[ROW][C]9[/C][C]18428.875[/C][C]790.689970321279[/C][C]1842.70000000000[/C][/ROW]
[ROW][C]10[/C][C]19494[/C][C]1012.29288251968[/C][C]2363.4[/C][/ROW]
[ROW][C]11[/C][C]19551.7[/C][C]1747.61291480694[/C][C]4179.3[/C][/ROW]
[ROW][C]12[/C][C]20912.9[/C][C]1105.58969182363[/C][C]2684.1[/C][/ROW]
[ROW][C]13[/C][C]22884.325[/C][C]1295.88804911278[/C][C]2868.1[/C][/ROW]
[ROW][C]14[/C][C]22516.5[/C][C]1505.57952297446[/C][C]3322.1[/C][/ROW]
[ROW][C]15[/C][C]17946.725[/C][C]1216.83914131381[/C][C]2767.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67014&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
116098.051530.225444174813239.5
215548.91272.362854430032272.4
316376.95518.8492684136061205.3
417540.65988.0533740643781942.7
516413.9751348.275321475553083.2
618445.5602.4294758171561244.90000000000
719049.5751828.581871970744424.6
817779.3751354.895814875322871.1
918428.875790.6899703212791842.70000000000
10194941012.292882519682363.4
1119551.71747.612914806944179.3
1220912.91105.589691823632684.1
1322884.3251295.888049112782868.1
1422516.51505.579522974463322.1
1517946.7251216.839141313812767.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha551.715965448056
beta0.0352790303395606
S.D.0.0467843953299983
T-STAT0.754076868808852
p-value0.464243654864214

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 551.715965448056 \tabularnewline
beta & 0.0352790303395606 \tabularnewline
S.D. & 0.0467843953299983 \tabularnewline
T-STAT & 0.754076868808852 \tabularnewline
p-value & 0.464243654864214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67014&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]551.715965448056[/C][/ROW]
[ROW][C]beta[/C][C]0.0352790303395606[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0467843953299983[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.754076868808852[/C][/ROW]
[ROW][C]p-value[/C][C]0.464243654864214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67014&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67014&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)
alpha551.715965448056
beta0.0352790303395606
S.D.0.0467843953299983
T-STAT0.754076868808852
p-value0.464243654864214






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.441958267223806
beta0.671690492982405
S.D.0.847654347348232
T-STAT0.792410839493355
p-value0.442342282796214
Lambda0.328309507017595

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.441958267223806 \tabularnewline
beta & 0.671690492982405 \tabularnewline
S.D. & 0.847654347348232 \tabularnewline
T-STAT & 0.792410839493355 \tabularnewline
p-value & 0.442342282796214 \tabularnewline
Lambda & 0.328309507017595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67014&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.441958267223806[/C][/ROW]
[ROW][C]beta[/C][C]0.671690492982405[/C][/ROW]
[ROW][C]S.D.[/C][C]0.847654347348232[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.792410839493355[/C][/ROW]
[ROW][C]p-value[/C][C]0.442342282796214[/C][/ROW]
[ROW][C]Lambda[/C][C]0.328309507017595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67014&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67014&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)
alpha0.441958267223806
beta0.671690492982405
S.D.0.847654347348232
T-STAT0.792410839493355
p-value0.442342282796214
Lambda0.328309507017595


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')