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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, 21 Dec 2016 13:04:02 +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/21/t1482322641jt5j4xwealof8lu.htm/, Retrieved Mon, 06 May 2024 20:15:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302206, Retrieved Mon, 06 May 2024 20:15:54 +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] [standard deviatio...] [2016-12-21 12:04:02] [d4ebbcc95b180bc93fc42d05f31a3dde] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3606.1
3102.8
3602.5
3247.3
3467.7
3330.2
3367.1
3579.2
3303.8
3513.1
3892.7
4698.2
3876.6
3937.9
4011.5
3881.2
4054.6
3609.9
3788
3603.2
4110.8
4398.5
4402
4249.8
4054.5
3868.7
4165.4
4043.8
4220.2
4078
4129.3
4129.3
4161.5
4193.3
3959.8
3962.8
4079.3
3824.5
4160
3906.2
3907.8
4076.7
4099.4
4213.7
4012.2
4088.4
3911.9
3992.5
4333
4159
4540.8
4515.4
4661.1
4394.3
4916.4
4999.7
4783.4
4889.5
4840.6
4979.2
5442.4
5229.9
5670.3
5129.1
5358
5363.5
5388.7
5409.2
5431.2
5591.9
5622.5
5528.7
4968.7
4812.5
5175.1
4943.2
5007.1
5028.5
5023
5158.3
5248.8
5494
5193.3
4318.2
5726.3
5378.7
5776.1
5626.3
5755.2
5540.9
5560.8
5742.6
5592.9
5782.6
5611.5
5653.5
5438.7
5084.7
5736.2
5497.2
5650.9
5645.8
5634
5747.2
5585.2
5952.5
5833.5
5778.4
6096.9
5797.6
6187.9
5849.6
6096.6
5757.8
6248.1
6110.5
5919.8
6082.2
5886.9
6167.4
6458.9
6282.3
6762.1
6698.1
6017.3
5790.5

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=302206&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=302206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302206&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
13559.225413.8148842285531595.4
23993.66666666667267.222186522184798.8
34080.55107.060709200647351.5
44022.71666666667117.166414931408389.2
54667.7277.402543083316840.7
65430.45157.604744390978541.2
75030.89166666667284.9521122713061175.8
85645.61666666667119.657327651114403.900000000001
95632.025222.934813648213867.8
106016.775165.327400385362490.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3559.225 & 413.814884228553 & 1595.4 \tabularnewline
2 & 3993.66666666667 & 267.222186522184 & 798.8 \tabularnewline
3 & 4080.55 & 107.060709200647 & 351.5 \tabularnewline
4 & 4022.71666666667 & 117.166414931408 & 389.2 \tabularnewline
5 & 4667.7 & 277.402543083316 & 840.7 \tabularnewline
6 & 5430.45 & 157.604744390978 & 541.2 \tabularnewline
7 & 5030.89166666667 & 284.952112271306 & 1175.8 \tabularnewline
8 & 5645.61666666667 & 119.657327651114 & 403.900000000001 \tabularnewline
9 & 5632.025 & 222.934813648213 & 867.8 \tabularnewline
10 & 6016.775 & 165.327400385362 & 490.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302206&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]3559.225[/C][C]413.814884228553[/C][C]1595.4[/C][/ROW]
[ROW][C]2[/C][C]3993.66666666667[/C][C]267.222186522184[/C][C]798.8[/C][/ROW]
[ROW][C]3[/C][C]4080.55[/C][C]107.060709200647[/C][C]351.5[/C][/ROW]
[ROW][C]4[/C][C]4022.71666666667[/C][C]117.166414931408[/C][C]389.2[/C][/ROW]
[ROW][C]5[/C][C]4667.7[/C][C]277.402543083316[/C][C]840.7[/C][/ROW]
[ROW][C]6[/C][C]5430.45[/C][C]157.604744390978[/C][C]541.2[/C][/ROW]
[ROW][C]7[/C][C]5030.89166666667[/C][C]284.952112271306[/C][C]1175.8[/C][/ROW]
[ROW][C]8[/C][C]5645.61666666667[/C][C]119.657327651114[/C][C]403.900000000001[/C][/ROW]
[ROW][C]9[/C][C]5632.025[/C][C]222.934813648213[/C][C]867.8[/C][/ROW]
[ROW][C]10[/C][C]6016.775[/C][C]165.327400385362[/C][C]490.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302206&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
13559.225413.8148842285531595.4
23993.66666666667267.222186522184798.8
34080.55107.060709200647351.5
44022.71666666667117.166414931408389.2
54667.7277.402543083316840.7
65430.45157.604744390978541.2
75030.89166666667284.9521122713061175.8
85645.61666666667119.657327651114403.900000000001
95632.025222.934813648213867.8
106016.775165.327400385362490.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha428.009431164223
beta-0.0446540826274437
S.D.0.0372121437931904
T-STAT-1.19998683428755
p-value0.264471940036975

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 428.009431164223 \tabularnewline
beta & -0.0446540826274437 \tabularnewline
S.D. & 0.0372121437931904 \tabularnewline
T-STAT & -1.19998683428755 \tabularnewline
p-value & 0.264471940036975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302206&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]428.009431164223[/C][/ROW]
[ROW][C]beta[/C][C]-0.0446540826274437[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0372121437931904[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.19998683428755[/C][/ROW]
[ROW][C]p-value[/C][C]0.264471940036975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302206&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)
alpha428.009431164223
beta-0.0446540826274437
S.D.0.0372121437931904
T-STAT-1.19998683428755
p-value0.264471940036975






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha11.1770615804021
beta-0.698112760548742
S.D.0.849887141808689
T-STAT-0.821418193318059
p-value0.435202062705107
Lambda1.69811276054874

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 11.1770615804021 \tabularnewline
beta & -0.698112760548742 \tabularnewline
S.D. & 0.849887141808689 \tabularnewline
T-STAT & -0.821418193318059 \tabularnewline
p-value & 0.435202062705107 \tabularnewline
Lambda & 1.69811276054874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302206&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.1770615804021[/C][/ROW]
[ROW][C]beta[/C][C]-0.698112760548742[/C][/ROW]
[ROW][C]S.D.[/C][C]0.849887141808689[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.821418193318059[/C][/ROW]
[ROW][C]p-value[/C][C]0.435202062705107[/C][/ROW]
[ROW][C]Lambda[/C][C]1.69811276054874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302206&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302206&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)
alpha11.1770615804021
beta-0.698112760548742
S.D.0.849887141808689
T-STAT-0.821418193318059
p-value0.435202062705107
Lambda1.69811276054874


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 <- '6'
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')