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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 computationSun, 18 Dec 2016 16:13:41 +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/18/t1482074045mi6dhgucq2609q6.htm/, Retrieved Thu, 03 Apr 2025 23:08:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301129, Retrieved Thu, 03 Apr 2025 23:08:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

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] [Standaard deviati...] [2016-12-18 15:13:41] [33f2a624cfeb2efbc43d2c77b7c0dad6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4870
4240
3800
3990
3290
4710
4210
4440
5040
5070
4900
4790
3890
3450
4080
3280
3130
3310
3860
4570
5110
4820
4250
4210
3610
3710
2760
2710
2710
3290
2670
3620
4440
3910
4610
3760
3460
3020
3360
2610
2670
2480
2610
3320
2800
3030
3740
3060
3040
2620
3190
2750
2630
3290
2430
2730
3690
2980
2590
3360
2370
2200
2330
2370
2200
2430
2400
2840
2870
3320
3090
2680
2420
2550
2420
2430
2330
2520
2630
2570
2800
2680
2430
2790
2420
2750
2350
2330
2290
2330
2490
2480
2760
2590
2950
2570
2960
2540
2400
2470
2390
2310
2470
2490
2510
2690
3060
2690
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

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=301129&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=301129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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
14445.83333333333553.9848756277041780
23996.66666666667634.4551468254741980
33483.33333333333670.6487135376441940
43013.33333333333395.1371070063321260
52941.66666666667380.9994830188171260
62591.66666666667364.5877705357691120
72547.5152.442239433945470
82525.83333333333206.461897578016660
92581.66666666667229.459179706359750
10NaNNA-Inf
11NaNNA-Inf
12NaNNA-Inf

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4445.83333333333 & 553.984875627704 & 1780 \tabularnewline
2 & 3996.66666666667 & 634.455146825474 & 1980 \tabularnewline
3 & 3483.33333333333 & 670.648713537644 & 1940 \tabularnewline
4 & 3013.33333333333 & 395.137107006332 & 1260 \tabularnewline
5 & 2941.66666666667 & 380.999483018817 & 1260 \tabularnewline
6 & 2591.66666666667 & 364.587770535769 & 1120 \tabularnewline
7 & 2547.5 & 152.442239433945 & 470 \tabularnewline
8 & 2525.83333333333 & 206.461897578016 & 660 \tabularnewline
9 & 2581.66666666667 & 229.459179706359 & 750 \tabularnewline
10 & NaN & NA & -Inf \tabularnewline
11 & NaN & NA & -Inf \tabularnewline
12 & NaN & NA & -Inf \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301129&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]4445.83333333333[/C][C]553.984875627704[/C][C]1780[/C][/ROW]
[ROW][C]2[/C][C]3996.66666666667[/C][C]634.455146825474[/C][C]1980[/C][/ROW]
[ROW][C]3[/C][C]3483.33333333333[/C][C]670.648713537644[/C][C]1940[/C][/ROW]
[ROW][C]4[/C][C]3013.33333333333[/C][C]395.137107006332[/C][C]1260[/C][/ROW]
[ROW][C]5[/C][C]2941.66666666667[/C][C]380.999483018817[/C][C]1260[/C][/ROW]
[ROW][C]6[/C][C]2591.66666666667[/C][C]364.587770535769[/C][C]1120[/C][/ROW]
[ROW][C]7[/C][C]2547.5[/C][C]152.442239433945[/C][C]470[/C][/ROW]
[ROW][C]8[/C][C]2525.83333333333[/C][C]206.461897578016[/C][C]660[/C][/ROW]
[ROW][C]9[/C][C]2581.66666666667[/C][C]229.459179706359[/C][C]750[/C][/ROW]
[ROW][C]10[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]11[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]12[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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
14445.83333333333553.9848756277041780
23996.66666666667634.4551468254741980
33483.33333333333670.6487135376441940
43013.33333333333395.1371070063321260
52941.66666666667380.9994830188171260
62591.66666666667364.5877705357691120
72547.5152.442239433945470
82525.83333333333206.461897578016660
92581.66666666667229.459179706359750
10NaNNA-Inf
11NaNNA-Inf
12NaNNA-Inf






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-296.792599054343
beta0.222533456750836
S.D.0.0556718876709218
T-STAT3.99723210511988
p-value0.00520823430244478

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -296.792599054343 \tabularnewline
beta & 0.222533456750836 \tabularnewline
S.D. & 0.0556718876709218 \tabularnewline
T-STAT & 3.99723210511988 \tabularnewline
p-value & 0.00520823430244478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301129&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-296.792599054343[/C][/ROW]
[ROW][C]beta[/C][C]0.222533456750836[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0556718876709218[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.99723210511988[/C][/ROW]
[ROW][C]p-value[/C][C]0.00520823430244478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301129&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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-296.792599054343
beta0.222533456750836
S.D.0.0556718876709218
T-STAT3.99723210511988
p-value0.00520823430244478






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.5211403384711
beta2.04294761262818
S.D.0.517682481423202
T-STAT3.9463332949026
p-value0.00555805097815544
Lambda-1.04294761262818

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.5211403384711 \tabularnewline
beta & 2.04294761262818 \tabularnewline
S.D. & 0.517682481423202 \tabularnewline
T-STAT & 3.9463332949026 \tabularnewline
p-value & 0.00555805097815544 \tabularnewline
Lambda & -1.04294761262818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301129&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.5211403384711[/C][/ROW]
[ROW][C]beta[/C][C]2.04294761262818[/C][/ROW]
[ROW][C]S.D.[/C][C]0.517682481423202[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.9463332949026[/C][/ROW]
[ROW][C]p-value[/C][C]0.00555805097815544[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.04294761262818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301129&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301129&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-10.5211403384711
beta2.04294761262818
S.D.0.517682481423202
T-STAT3.9463332949026
p-value0.00555805097815544
Lambda-1.04294761262818


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par4 = 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')