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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 computationThu, 15 Dec 2016 09:48:56 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/15/t1481792205111rkrp53kbxa8p.htm/, Retrieved Fri, 03 May 2024 08:41:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299771, Retrieved Fri, 03 May 2024 08:41:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

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] [zlamzd] [2016-12-15 08:48:56] [4c05fa0998bf98e29c2e453b139976f4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3281
3397
3498.5
3538
3449.5
3673
3350.5
3604
3673.5
3747
3616
3580.5
3710
3994.5
4091
3954.5
4004
4287
3831
4046.5
4079.5
4029.5
3880
3855
3841.5
4123.5
4133
3958.5
4003
4151.5
3723
3957
3965.5
3861.5
3917.5
3704
3950
4140.5
4090
4162
4066
4358.5
4022.5
4285.5
4373.5
4284.5
4077.5
4122
4181.5
4535.5
4497
4420.5
4370
4712
4475
4578.5
4751.5
4746
4581.5
4645.5
4751
4952.5
4996.5
4998
4986.5
5348
4933
5263
5330.5
5301
5159
5258.5
5411.5
5536.5
5613
5505.5
5476
5782.5
5283
5451.5
5578
5548.5
5379.5
5117.5
5316.5
5505.5
5620.5
5383.5
5461.5
5658.5
5357.5
5622
5608
5604.5
5399
5185
5221
5379.5
5333
5214
5206.5
5630
5285.5
5512.5
5592.5
5554.5
5284.5
5198.5
5241.5
5455
5548.5
5375
5346
5730.5
5457
5603

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299771&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299771&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299771&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13534.04166666667142.319496258073466
23980.20833333333149.394148956458577
33944.95833333333147.637371829107447.5
44161.04166666667135.37783126114423.5
54541.20833333333167.567145067464570
65106.45833333333194.270600678226597
75473.58333333333168.59740013812665
85476.83333333333150.502088981777473.5
95367.66666666667162.362855880577431.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3534.04166666667 & 142.319496258073 & 466 \tabularnewline
2 & 3980.20833333333 & 149.394148956458 & 577 \tabularnewline
3 & 3944.95833333333 & 147.637371829107 & 447.5 \tabularnewline
4 & 4161.04166666667 & 135.37783126114 & 423.5 \tabularnewline
5 & 4541.20833333333 & 167.567145067464 & 570 \tabularnewline
6 & 5106.45833333333 & 194.270600678226 & 597 \tabularnewline
7 & 5473.58333333333 & 168.59740013812 & 665 \tabularnewline
8 & 5476.83333333333 & 150.502088981777 & 473.5 \tabularnewline
9 & 5367.66666666667 & 162.362855880577 & 431.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299771&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]3534.04166666667[/C][C]142.319496258073[/C][C]466[/C][/ROW]
[ROW][C]2[/C][C]3980.20833333333[/C][C]149.394148956458[/C][C]577[/C][/ROW]
[ROW][C]3[/C][C]3944.95833333333[/C][C]147.637371829107[/C][C]447.5[/C][/ROW]
[ROW][C]4[/C][C]4161.04166666667[/C][C]135.37783126114[/C][C]423.5[/C][/ROW]
[ROW][C]5[/C][C]4541.20833333333[/C][C]167.567145067464[/C][C]570[/C][/ROW]
[ROW][C]6[/C][C]5106.45833333333[/C][C]194.270600678226[/C][C]597[/C][/ROW]
[ROW][C]7[/C][C]5473.58333333333[/C][C]168.59740013812[/C][C]665[/C][/ROW]
[ROW][C]8[/C][C]5476.83333333333[/C][C]150.502088981777[/C][C]473.5[/C][/ROW]
[ROW][C]9[/C][C]5367.66666666667[/C][C]162.362855880577[/C][C]431.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299771&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299771&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
13534.04166666667142.319496258073466
23980.20833333333149.394148956458577
33944.95833333333147.637371829107447.5
44161.04166666667135.37783126114423.5
54541.20833333333167.567145067464570
65106.45833333333194.270600678226597
75473.58333333333168.59740013812665
85476.83333333333150.502088981777473.5
95367.66666666667162.362855880577431.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha93.4682847433792
beta0.0138703981234196
S.D.0.0072490000213576
T-STAT1.91342227652829
p-value0.0972666258174896

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 93.4682847433792 \tabularnewline
beta & 0.0138703981234196 \tabularnewline
S.D. & 0.0072490000213576 \tabularnewline
T-STAT & 1.91342227652829 \tabularnewline
p-value & 0.0972666258174896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299771&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]93.4682847433792[/C][/ROW]
[ROW][C]beta[/C][C]0.0138703981234196[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0072490000213576[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.91342227652829[/C][/ROW]
[ROW][C]p-value[/C][C]0.0972666258174896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299771&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299771&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)
alpha93.4682847433792
beta0.0138703981234196
S.D.0.0072490000213576
T-STAT1.91342227652829
p-value0.0972666258174896






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.6378317608453
beta0.405464842528773
S.D.0.196759312269378
T-STAT2.06071487977993
p-value0.0782824425371239
Lambda0.594535157471227

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.6378317608453 \tabularnewline
beta & 0.405464842528773 \tabularnewline
S.D. & 0.196759312269378 \tabularnewline
T-STAT & 2.06071487977993 \tabularnewline
p-value & 0.0782824425371239 \tabularnewline
Lambda & 0.594535157471227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299771&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.6378317608453[/C][/ROW]
[ROW][C]beta[/C][C]0.405464842528773[/C][/ROW]
[ROW][C]S.D.[/C][C]0.196759312269378[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.06071487977993[/C][/ROW]
[ROW][C]p-value[/C][C]0.0782824425371239[/C][/ROW]
[ROW][C]Lambda[/C][C]0.594535157471227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299771&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299771&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)
alpha1.6378317608453
beta0.405464842528773
S.D.0.196759312269378
T-STAT2.06071487977993
p-value0.0782824425371239
Lambda0.594535157471227


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')