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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, 14 Dec 2016 09:55:07 +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/14/t148170594883igcimlefz1r23.htm/, Retrieved Thu, 08 May 2025 17:57:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299266, Retrieved Thu, 08 May 2025 17:57:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

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] [lambda] [2016-12-14 08:55:07] [037fdaa34a77b5f63489b3bcd360a80c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3455
3585
3675
3680
3735
3860
3765
3905
4110
4170
4110
4025
4145
4285
4370
4355
4385
4525
4375
4525
4610
4595
4500
4370
4390
4530
4590
4580
4595
4685
4490
4635
4710
4655
4665
4550
4590
4675
4645
4665
4635
4720
4565
4720
4830
4830
4765
4705
4675
4900
4945
4905
4955
5120
4860
5040
5140
5240
5145
5070
5085
5215
5255
5275
5315
5450
5205
5370
5500
5490
5440
5360
5380
5460
5450
5520
5475
5600
5250
5465
5515
5425
5325
5275
5160
5360
5435
5285
5415
5575
5265
5480
5565
5500
5280
5135
5050
5100
5070
5115
5140
5330
5080
5285
5405
5385
5255
5100
5040
5235
5310
5265
5380
5465
5225
5445

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=299266&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=299266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299266&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
13839.58333333333228.885226630504715
24420135.344677834711465
34589.5833333333390.7658910037078320
44695.4166666666784.2199051545561265
54999.58333333333156.21166196329565
65330128.363829513118415
75428.33333333333103.88659317941350
85371.25148.034470801414440
95192.91666666667130.531402236002355

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3839.58333333333 & 228.885226630504 & 715 \tabularnewline
2 & 4420 & 135.344677834711 & 465 \tabularnewline
3 & 4589.58333333333 & 90.7658910037078 & 320 \tabularnewline
4 & 4695.41666666667 & 84.2199051545561 & 265 \tabularnewline
5 & 4999.58333333333 & 156.21166196329 & 565 \tabularnewline
6 & 5330 & 128.363829513118 & 415 \tabularnewline
7 & 5428.33333333333 & 103.88659317941 & 350 \tabularnewline
8 & 5371.25 & 148.034470801414 & 440 \tabularnewline
9 & 5192.91666666667 & 130.531402236002 & 355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299266&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]3839.58333333333[/C][C]228.885226630504[/C][C]715[/C][/ROW]
[ROW][C]2[/C][C]4420[/C][C]135.344677834711[/C][C]465[/C][/ROW]
[ROW][C]3[/C][C]4589.58333333333[/C][C]90.7658910037078[/C][C]320[/C][/ROW]
[ROW][C]4[/C][C]4695.41666666667[/C][C]84.2199051545561[/C][C]265[/C][/ROW]
[ROW][C]5[/C][C]4999.58333333333[/C][C]156.21166196329[/C][C]565[/C][/ROW]
[ROW][C]6[/C][C]5330[/C][C]128.363829513118[/C][C]415[/C][/ROW]
[ROW][C]7[/C][C]5428.33333333333[/C][C]103.88659317941[/C][C]350[/C][/ROW]
[ROW][C]8[/C][C]5371.25[/C][C]148.034470801414[/C][C]440[/C][/ROW]
[ROW][C]9[/C][C]5192.91666666667[/C][C]130.531402236002[/C][C]355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299266&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
13839.58333333333228.885226630504715
24420135.344677834711465
34589.5833333333390.7658910037078320
44695.4166666666784.2199051545561265
54999.58333333333156.21166196329565
65330128.363829513118415
75428.33333333333103.88659317941350
85371.25148.034470801414440
95192.91666666667130.531402236002355






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha323.449736990943
beta-0.0388633124909219
S.D.0.0269863561508819
T-STAT-1.44010967148123
p-value0.193021066572816

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 323.449736990943 \tabularnewline
beta & -0.0388633124909219 \tabularnewline
S.D. & 0.0269863561508819 \tabularnewline
T-STAT & -1.44010967148123 \tabularnewline
p-value & 0.193021066572816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299266&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]323.449736990943[/C][/ROW]
[ROW][C]beta[/C][C]-0.0388633124909219[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0269863561508819[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.44010967148123[/C][/ROW]
[ROW][C]p-value[/C][C]0.193021066572816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299266&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299266&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)
alpha323.449736990943
beta-0.0388633124909219
S.D.0.0269863561508819
T-STAT-1.44010967148123
p-value0.193021066572816






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha13.7075639976034
beta-1.04311007739372
S.D.0.922466068484617
T-STAT-1.13078422397399
p-value0.295395508947134
Lambda2.04311007739372

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 13.7075639976034 \tabularnewline
beta & -1.04311007739372 \tabularnewline
S.D. & 0.922466068484617 \tabularnewline
T-STAT & -1.13078422397399 \tabularnewline
p-value & 0.295395508947134 \tabularnewline
Lambda & 2.04311007739372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299266&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.7075639976034[/C][/ROW]
[ROW][C]beta[/C][C]-1.04311007739372[/C][/ROW]
[ROW][C]S.D.[/C][C]0.922466068484617[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.13078422397399[/C][/ROW]
[ROW][C]p-value[/C][C]0.295395508947134[/C][/ROW]
[ROW][C]Lambda[/C][C]2.04311007739372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299266&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299266&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)
alpha13.7075639976034
beta-1.04311007739372
S.D.0.922466068484617
T-STAT-1.13078422397399
p-value0.295395508947134
Lambda2.04311007739372


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')