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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, 04 Dec 2011 09:10:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/04/t1323007964u5662gnee86c5dc.htm/, Retrieved Sun, 05 May 2024 18:20:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150649, Retrieved Sun, 05 May 2024 18:20:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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] [WS9 smp] [2011-12-04 14:10:20] [c98b04636162cea751932dfe577607eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150649&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150649&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150649&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
122708.58333333334962.7772367410515936
223017.66666666677054.578092317523808
322694.756102.6543721862221757
424344.41666666676133.0682141728219196
521035.58333333334753.6816633069416277
624607.66666666675913.095456593620132
724637.41666666674970.3069131197617307

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 22708.5833333333 & 4962.77723674105 & 15936 \tabularnewline
2 & 23017.6666666667 & 7054.5780923175 & 23808 \tabularnewline
3 & 22694.75 & 6102.65437218622 & 21757 \tabularnewline
4 & 24344.4166666667 & 6133.06821417282 & 19196 \tabularnewline
5 & 21035.5833333333 & 4753.68166330694 & 16277 \tabularnewline
6 & 24607.6666666667 & 5913.0954565936 & 20132 \tabularnewline
7 & 24637.4166666667 & 4970.30691311976 & 17307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150649&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]22708.5833333333[/C][C]4962.77723674105[/C][C]15936[/C][/ROW]
[ROW][C]2[/C][C]23017.6666666667[/C][C]7054.5780923175[/C][C]23808[/C][/ROW]
[ROW][C]3[/C][C]22694.75[/C][C]6102.65437218622[/C][C]21757[/C][/ROW]
[ROW][C]4[/C][C]24344.4166666667[/C][C]6133.06821417282[/C][C]19196[/C][/ROW]
[ROW][C]5[/C][C]21035.5833333333[/C][C]4753.68166330694[/C][C]16277[/C][/ROW]
[ROW][C]6[/C][C]24607.6666666667[/C][C]5913.0954565936[/C][C]20132[/C][/ROW]
[ROW][C]7[/C][C]24637.4166666667[/C][C]4970.30691311976[/C][C]17307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150649&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150649&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
122708.58333333334962.7772367410515936
223017.66666666677054.578092317523808
322694.756102.6543721862221757
424344.41666666676133.0682141728219196
521035.58333333334753.6816633069416277
624607.66666666675913.095456593620132
724637.41666666674970.3069131197617307






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1914.8755608235
beta0.162445073694442
S.D.0.273229889782549
T-STAT0.594536248664904
p-value0.578033668657839

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1914.8755608235 \tabularnewline
beta & 0.162445073694442 \tabularnewline
S.D. & 0.273229889782549 \tabularnewline
T-STAT & 0.594536248664904 \tabularnewline
p-value & 0.578033668657839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150649&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1914.8755608235[/C][/ROW]
[ROW][C]beta[/C][C]0.162445073694442[/C][/ROW]
[ROW][C]S.D.[/C][C]0.273229889782549[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.594536248664904[/C][/ROW]
[ROW][C]p-value[/C][C]0.578033668657839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150649&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150649&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)
alpha1914.8755608235
beta0.162445073694442
S.D.0.273229889782549
T-STAT0.594536248664904
p-value0.578033668657839






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.988916174260496
beta0.76084883164684
S.D.1.07628365776666
T-STAT0.706922219023223
p-value0.511189363704565
Lambda0.23915116835316

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.988916174260496 \tabularnewline
beta & 0.76084883164684 \tabularnewline
S.D. & 1.07628365776666 \tabularnewline
T-STAT & 0.706922219023223 \tabularnewline
p-value & 0.511189363704565 \tabularnewline
Lambda & 0.23915116835316 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150649&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.988916174260496[/C][/ROW]
[ROW][C]beta[/C][C]0.76084883164684[/C][/ROW]
[ROW][C]S.D.[/C][C]1.07628365776666[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.706922219023223[/C][/ROW]
[ROW][C]p-value[/C][C]0.511189363704565[/C][/ROW]
[ROW][C]Lambda[/C][C]0.23915116835316[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150649&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150649&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)
alpha0.988916174260496
beta0.76084883164684
S.D.1.07628365776666
T-STAT0.706922219023223
p-value0.511189363704565
Lambda0.23915116835316


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')