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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 computationFri, 16 Dec 2016 18:58:53 +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/16/t1481911224a7t3r7q0tjkhx3s.htm/, Retrieved Wed, 14 May 2025 05:45:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300466, Retrieved Wed, 14 May 2025 05:45:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

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] [Standar deviation...] [2016-12-16 17:58:53] [9fb47d69755d1f4b66b6f2591280f9e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4307.5
4234
5156.5
4844
4606
4850
4294
3190
3811.5
4160.5
4538.5
3792.5
4660
3504.5
3521
4560
4549
3543
2996
3762
4156.5
4525
4058
4871.5
4870
4953
5028.5
5252.5
4907
4641
5447.5
4544.5
4493
5522
3896.5
3108.5
4415
2912.5
3536
3183
3643.5
3412
3202.5
3374.5
3226.5
3927.5
3498.5
3614.5
3740
2857.5
4100
3684
3601.5
3663.5
2586.5
2825
2866.5
2722
2164
2113.5
2379
2811
3539
3474
3909.5
4049.5
3156.5
3435
3058.5
4103
3726.5
4703.5
4020.5
3636
4289
5570.5
5283
4618
4765
3937.5
4717.5
4206.5
4506.5
4306
5281.5
5495.5
5304
5935
5974
9239
6054.5
6072
6279
5260
5966
6764.5
8028.5
6063.5
7531.5
7347
6571
7337.5
7519.5
7358
4746
5173.5
6433.5
4508
4912.5
6246
7557.5
7111
6304.5
6166
5735
4583
4657.5
4712.5
5647
5277
4812.5
4702
6047
5470
4540.5
5112.5

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=300466&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=300466&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300466&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
14315.41666666667542.0408754015331966.5
24058.875589.3347221848781875.5
34722675.9877285061542413.5
43495.5391.6384000115881502.5
53077657.6915897840931986.5
63528.75630.5656731711762324.5
74488551.8522941380731934.5
86135.416666666671076.626039434253979
96551.458333333331189.616677344073520.5
105742.45833333333972.9550923564892974.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4315.41666666667 & 542.040875401533 & 1966.5 \tabularnewline
2 & 4058.875 & 589.334722184878 & 1875.5 \tabularnewline
3 & 4722 & 675.987728506154 & 2413.5 \tabularnewline
4 & 3495.5 & 391.638400011588 & 1502.5 \tabularnewline
5 & 3077 & 657.691589784093 & 1986.5 \tabularnewline
6 & 3528.75 & 630.565673171176 & 2324.5 \tabularnewline
7 & 4488 & 551.852294138073 & 1934.5 \tabularnewline
8 & 6135.41666666667 & 1076.62603943425 & 3979 \tabularnewline
9 & 6551.45833333333 & 1189.61667734407 & 3520.5 \tabularnewline
10 & 5742.45833333333 & 972.955092356489 & 2974.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300466&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]4315.41666666667[/C][C]542.040875401533[/C][C]1966.5[/C][/ROW]
[ROW][C]2[/C][C]4058.875[/C][C]589.334722184878[/C][C]1875.5[/C][/ROW]
[ROW][C]3[/C][C]4722[/C][C]675.987728506154[/C][C]2413.5[/C][/ROW]
[ROW][C]4[/C][C]3495.5[/C][C]391.638400011588[/C][C]1502.5[/C][/ROW]
[ROW][C]5[/C][C]3077[/C][C]657.691589784093[/C][C]1986.5[/C][/ROW]
[ROW][C]6[/C][C]3528.75[/C][C]630.565673171176[/C][C]2324.5[/C][/ROW]
[ROW][C]7[/C][C]4488[/C][C]551.852294138073[/C][C]1934.5[/C][/ROW]
[ROW][C]8[/C][C]6135.41666666667[/C][C]1076.62603943425[/C][C]3979[/C][/ROW]
[ROW][C]9[/C][C]6551.45833333333[/C][C]1189.61667734407[/C][C]3520.5[/C][/ROW]
[ROW][C]10[/C][C]5742.45833333333[/C][C]972.955092356489[/C][C]2974.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300466&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300466&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
14315.41666666667542.0408754015331966.5
24058.875589.3347221848781875.5
34722675.9877285061542413.5
43495.5391.6384000115881502.5
53077657.6915897840931986.5
63528.75630.5656731711762324.5
74488551.8522941380731934.5
86135.416666666671076.626039434253979
96551.458333333331189.616677344073520.5
105742.45833333333972.9550923564892974.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-168.29135625636
beta0.19432390643791
S.D.0.036731447459998
T-STAT5.29039610131173
p-value0.00073688623889139

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -168.29135625636 \tabularnewline
beta & 0.19432390643791 \tabularnewline
S.D. & 0.036731447459998 \tabularnewline
T-STAT & 5.29039610131173 \tabularnewline
p-value & 0.00073688623889139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300466&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-168.29135625636[/C][/ROW]
[ROW][C]beta[/C][C]0.19432390643791[/C][/ROW]
[ROW][C]S.D.[/C][C]0.036731447459998[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.29039610131173[/C][/ROW]
[ROW][C]p-value[/C][C]0.00073688623889139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300466&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300466&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-168.29135625636
beta0.19432390643791
S.D.0.036731447459998
T-STAT5.29039610131173
p-value0.00073688623889139






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.69812024306128
beta1.09826869511307
S.D.0.28633304706012
T-STAT3.83563373627101
p-value0.00497793798664907
Lambda-0.0982686951130711

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.69812024306128 \tabularnewline
beta & 1.09826869511307 \tabularnewline
S.D. & 0.28633304706012 \tabularnewline
T-STAT & 3.83563373627101 \tabularnewline
p-value & 0.00497793798664907 \tabularnewline
Lambda & -0.0982686951130711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300466&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.69812024306128[/C][/ROW]
[ROW][C]beta[/C][C]1.09826869511307[/C][/ROW]
[ROW][C]S.D.[/C][C]0.28633304706012[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.83563373627101[/C][/ROW]
[ROW][C]p-value[/C][C]0.00497793798664907[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0982686951130711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300466&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300466&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-2.69812024306128
beta1.09826869511307
S.D.0.28633304706012
T-STAT3.83563373627101
p-value0.00497793798664907
Lambda-0.0982686951130711


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;
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')