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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 computationWed, 16 Dec 2009 06:27:38 -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/16/t1260970276ku2uii5g8jrjrci.htm/, Retrieved Tue, 30 Apr 2024 09:43:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68315, Retrieved Tue, 30 Apr 2024 09:43:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

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...] [2009-12-16 13:27:38] [91da2e1ebdd83187f2515f461585cbee] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8715.1  
8919.9  
10085.8  
9511.7  
8991.3  
10311.2  
8895.4  
7449.8  
10084.0  
9859.4  
9100.1  
8920.8  
8502.7  
8599.6  
10394.4  
9290.4  
8742.2  
10217.3  
8639.0  
8139.6  
10779.1  
10427.7  
10349.1  
10036.4  
9492.1  
10638.8  
12054.5  
10324.7  
11817.3  
11008.9  
9996.6  
9419.5  
11958.8  
12594.6  
11890.6  
10871.7  
11835.7  
11542.2  
13093.7  
11180.2  
12035.7  
12112.0  
10875.2  
9897.3  
11672.1  
12385.7  
11405.6  
9830.9  
11025.1  
10853.8  
12252.6  
11839.4  
11669.1  
11601.4  
11178.4  
9516.4  
12102.8  
12989.0  
11610.2  
10205.5  
11356.2  
11307.1  
12648.6  
11947.2  
11714.1  
12192.5  
11268.8  
9097.4  
12639.8  
13040.1  
11687.3  
11191.7  
11391.9  
11793.1  
13933.2  
12778.1  
11810.3  
13698.4  
11956.6  
10723.8  
13938.9  
13979.8  
13807.4  
12973.9  
12509.8  
12934.1  
14908.3  
13772.1  
13012.6  
14049.9  
11816.5  
11593.2  
14466.2  
13615.9  
14733.9  
13880.7  
13527.5  
13584.0  
16170.2  
13260.6  
14741.9  
15486.5  
13154.5  
12621.2  
15031.6  
15452.4  
15428.0  
13105.9  
14716.8  
14180.0  
16202.2  
14392.4  
15140.6  
15960.1  
14351.3  
13230.2  
15202.1  
17056.0  
16077.7  
13348.2  
16402.4
16559.1
16579.0
17561.2
16129.6
18484.3
16402.6
14032.3
17109.1
17157.2
13879.8
12362.4

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=68315&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=68315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68315&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
19237.04166666667793.0044634270052861.4
29509.79166666667945.5286933373532639.5
311005.6751062.431511482463175.1
411488.8583333333952.7265805030163262.8
511403.6416666667932.1831584154123472.6
611674.23333333331016.472916361753942.7
712732.11666666671158.705907336703256
813441.11084.639858117983315.1
914297.0251205.382893618153549
1014988.13333333331176.195719128823825.8
1116054.91666666671751.103134823276121.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9237.04166666667 & 793.004463427005 & 2861.4 \tabularnewline
2 & 9509.79166666667 & 945.528693337353 & 2639.5 \tabularnewline
3 & 11005.675 & 1062.43151148246 & 3175.1 \tabularnewline
4 & 11488.8583333333 & 952.726580503016 & 3262.8 \tabularnewline
5 & 11403.6416666667 & 932.183158415412 & 3472.6 \tabularnewline
6 & 11674.2333333333 & 1016.47291636175 & 3942.7 \tabularnewline
7 & 12732.1166666667 & 1158.70590733670 & 3256 \tabularnewline
8 & 13441.1 & 1084.63985811798 & 3315.1 \tabularnewline
9 & 14297.025 & 1205.38289361815 & 3549 \tabularnewline
10 & 14988.1333333333 & 1176.19571912882 & 3825.8 \tabularnewline
11 & 16054.9166666667 & 1751.10313482327 & 6121.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68315&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]9237.04166666667[/C][C]793.004463427005[/C][C]2861.4[/C][/ROW]
[ROW][C]2[/C][C]9509.79166666667[/C][C]945.528693337353[/C][C]2639.5[/C][/ROW]
[ROW][C]3[/C][C]11005.675[/C][C]1062.43151148246[/C][C]3175.1[/C][/ROW]
[ROW][C]4[/C][C]11488.8583333333[/C][C]952.726580503016[/C][C]3262.8[/C][/ROW]
[ROW][C]5[/C][C]11403.6416666667[/C][C]932.183158415412[/C][C]3472.6[/C][/ROW]
[ROW][C]6[/C][C]11674.2333333333[/C][C]1016.47291636175[/C][C]3942.7[/C][/ROW]
[ROW][C]7[/C][C]12732.1166666667[/C][C]1158.70590733670[/C][C]3256[/C][/ROW]
[ROW][C]8[/C][C]13441.1[/C][C]1084.63985811798[/C][C]3315.1[/C][/ROW]
[ROW][C]9[/C][C]14297.025[/C][C]1205.38289361815[/C][C]3549[/C][/ROW]
[ROW][C]10[/C][C]14988.1333333333[/C][C]1176.19571912882[/C][C]3825.8[/C][/ROW]
[ROW][C]11[/C][C]16054.9166666667[/C][C]1751.10313482327[/C][C]6121.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68315&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
19237.04166666667793.0044634270052861.4
29509.79166666667945.5286933373532639.5
311005.6751062.431511482463175.1
411488.8583333333952.7265805030163262.8
511403.6416666667932.1831584154123472.6
611674.23333333331016.472916361753942.7
712732.11666666671158.705907336703256
813441.11084.639858117983315.1
914297.0251205.382893618153549
1014988.13333333331176.195719128823825.8
1116054.91666666671751.103134823276121.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-101.408507992590
beta0.0971333457507756
S.D.0.0201192339855739
T-STAT4.8278848896744
p-value0.000936652964988294

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -101.408507992590 \tabularnewline
beta & 0.0971333457507756 \tabularnewline
S.D. & 0.0201192339855739 \tabularnewline
T-STAT & 4.8278848896744 \tabularnewline
p-value & 0.000936652964988294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68315&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-101.408507992590[/C][/ROW]
[ROW][C]beta[/C][C]0.0971333457507756[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0201192339855739[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.8278848896744[/C][/ROW]
[ROW][C]p-value[/C][C]0.000936652964988294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68315&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-101.408507992590
beta0.0971333457507756
S.D.0.0201192339855739
T-STAT4.8278848896744
p-value0.000936652964988294






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.35563855193620
beta0.99253745623437
S.D.0.190448189101639
T-STAT5.21158778624391
p-value0.000555395433098457
Lambda0.00746254376563049

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.35563855193620 \tabularnewline
beta & 0.99253745623437 \tabularnewline
S.D. & 0.190448189101639 \tabularnewline
T-STAT & 5.21158778624391 \tabularnewline
p-value & 0.000555395433098457 \tabularnewline
Lambda & 0.00746254376563049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68315&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.35563855193620[/C][/ROW]
[ROW][C]beta[/C][C]0.99253745623437[/C][/ROW]
[ROW][C]S.D.[/C][C]0.190448189101639[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.21158778624391[/C][/ROW]
[ROW][C]p-value[/C][C]0.000555395433098457[/C][/ROW]
[ROW][C]Lambda[/C][C]0.00746254376563049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68315&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68315&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-2.35563855193620
beta0.99253745623437
S.D.0.190448189101639
T-STAT5.21158778624391
p-value0.000555395433098457
Lambda0.00746254376563049


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')