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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, 23 Dec 2009 04:27:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/23/t12615677463wrihuz70mwjh9e.htm/, Retrieved Mon, 29 Apr 2024 08:01:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70501, Retrieved Mon, 29 Apr 2024 08:01:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [VRM] [2009-12-23 10:57:13] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Standard Deviation-Mean Plot] [SMP s=12] [2009-12-23 11:27:41] [b08f24ccf7d7e0757793cda532be96b3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.87
84.23
84.61
84.82
85.04
85.06
84.93
84.98
85.23
85.30
85.33
85.55
85.70
85.88
86.04
86.07
86.31
86.38
86.35
86.55
86.70
86.74
86.85
86.95
86.80
87.01
87.17
87.43
87.66
87.68
87.59
87.65
87.72
87.70
87.71
87.80
87.62
87.84
88.17
88.47
88.58
88.57
88.55
88.68
88.79
88.85
88.95
89.27
89.09
89.42
89.72
89.85
89.96
90.25
90.20
90.27
90.78
90.79
90.98
91.25
90.75
91.01
91.50
92.09
92.56
92.66
92.38
92.38
92.66
92.69
92.59
92.98
92.98
93.15
93.65
94.06
94.24
94.24
94.11
94.16
94.43
94.67
94.60
95.00
94.84
95.26
95.81
95.92
95.85
95.90
95.80
96.00
96.34
96.43
96.48
96.75
96.51
96.69
97.28
97.69
98.08
98.09
97.92
98.06
98.23
98.57
98.53
98.92
98.42
98.73
99.32
99.73
100.00
100.08
100.02
100.26
100.71
100.95
100.75
101.03
100.64
100.93
101.41
102.07
102.42
102.53
102.43
102.60
102.65
102.74
102.82
103.21
102.75
103.09
103.71
104.30
104.58
104.71
104.44
104.57
104.95
105.49
106.03
106.48
106.25
106.70
107.60
108.05
108.72
109.17
109.08
109.04
109.34
109.37
108.96
108.77
108.11
108.67
109.05
109.43
109.62
109.85
109.34
109.65
109.69
109.91
110.09

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70501&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70501&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
184.91250.479320067671621.67999999999999
286.37666666666670.3973167578401471.25
387.49333333333330.3239622125364541
488.52833333333330.463030203871161.64999999999999
590.21333333333330.6502913100132812.16000000000000
692.18750.7158608930384572.23000000000000
794.10750.5952100469582122.02000000000000
895.94833333333330.5282532679988981.91000000000000
997.88083333333330.7329821817669772.41000000000000
101000.8393179048814252.61
11102.2041666666670.795218189993772.56999999999999
12104.5916666666671.091985958395683.73000000000000
13108.4208333333331.049332760578953.12000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 84.9125 & 0.47932006767162 & 1.67999999999999 \tabularnewline
2 & 86.3766666666667 & 0.397316757840147 & 1.25 \tabularnewline
3 & 87.4933333333333 & 0.323962212536454 & 1 \tabularnewline
4 & 88.5283333333333 & 0.46303020387116 & 1.64999999999999 \tabularnewline
5 & 90.2133333333333 & 0.650291310013281 & 2.16000000000000 \tabularnewline
6 & 92.1875 & 0.715860893038457 & 2.23000000000000 \tabularnewline
7 & 94.1075 & 0.595210046958212 & 2.02000000000000 \tabularnewline
8 & 95.9483333333333 & 0.528253267998898 & 1.91000000000000 \tabularnewline
9 & 97.8808333333333 & 0.732982181766977 & 2.41000000000000 \tabularnewline
10 & 100 & 0.839317904881425 & 2.61 \tabularnewline
11 & 102.204166666667 & 0.79521818999377 & 2.56999999999999 \tabularnewline
12 & 104.591666666667 & 1.09198595839568 & 3.73000000000000 \tabularnewline
13 & 108.420833333333 & 1.04933276057895 & 3.12000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70501&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]84.9125[/C][C]0.47932006767162[/C][C]1.67999999999999[/C][/ROW]
[ROW][C]2[/C][C]86.3766666666667[/C][C]0.397316757840147[/C][C]1.25[/C][/ROW]
[ROW][C]3[/C][C]87.4933333333333[/C][C]0.323962212536454[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]88.5283333333333[/C][C]0.46303020387116[/C][C]1.64999999999999[/C][/ROW]
[ROW][C]5[/C][C]90.2133333333333[/C][C]0.650291310013281[/C][C]2.16000000000000[/C][/ROW]
[ROW][C]6[/C][C]92.1875[/C][C]0.715860893038457[/C][C]2.23000000000000[/C][/ROW]
[ROW][C]7[/C][C]94.1075[/C][C]0.595210046958212[/C][C]2.02000000000000[/C][/ROW]
[ROW][C]8[/C][C]95.9483333333333[/C][C]0.528253267998898[/C][C]1.91000000000000[/C][/ROW]
[ROW][C]9[/C][C]97.8808333333333[/C][C]0.732982181766977[/C][C]2.41000000000000[/C][/ROW]
[ROW][C]10[/C][C]100[/C][C]0.839317904881425[/C][C]2.61[/C][/ROW]
[ROW][C]11[/C][C]102.204166666667[/C][C]0.79521818999377[/C][C]2.56999999999999[/C][/ROW]
[ROW][C]12[/C][C]104.591666666667[/C][C]1.09198595839568[/C][C]3.73000000000000[/C][/ROW]
[ROW][C]13[/C][C]108.420833333333[/C][C]1.04933276057895[/C][C]3.12000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70501&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
184.91250.479320067671621.67999999999999
286.37666666666670.3973167578401471.25
387.49333333333330.3239622125364541
488.52833333333330.463030203871161.64999999999999
590.21333333333330.6502913100132812.16000000000000
692.18750.7158608930384572.23000000000000
794.10750.5952100469582122.02000000000000
895.94833333333330.5282532679988981.91000000000000
997.88083333333330.7329821817669772.41000000000000
101000.8393179048814252.61
11102.2041666666670.795218189993772.56999999999999
12104.5916666666671.091985958395683.73000000000000
13108.4208333333331.049332760578953.12000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.07236670249749
beta0.028878140662613
S.D.0.00401936220995791
T-STAT7.1847569724042
p-value1.78713101715724e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.07236670249749 \tabularnewline
beta & 0.028878140662613 \tabularnewline
S.D. & 0.00401936220995791 \tabularnewline
T-STAT & 7.1847569724042 \tabularnewline
p-value & 1.78713101715724e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70501&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.07236670249749[/C][/ROW]
[ROW][C]beta[/C][C]0.028878140662613[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00401936220995791[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.1847569724042[/C][/ROW]
[ROW][C]p-value[/C][C]1.78713101715724e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70501&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70501&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-2.07236670249749
beta0.028878140662613
S.D.0.00401936220995791
T-STAT7.1847569724042
p-value1.78713101715724e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-19.3376663336536
beta4.14825385555548
S.D.0.663220411979307
T-STAT6.25471378840027
p-value6.21904940187061e-05
Lambda-3.14825385555548

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -19.3376663336536 \tabularnewline
beta & 4.14825385555548 \tabularnewline
S.D. & 0.663220411979307 \tabularnewline
T-STAT & 6.25471378840027 \tabularnewline
p-value & 6.21904940187061e-05 \tabularnewline
Lambda & -3.14825385555548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70501&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.3376663336536[/C][/ROW]
[ROW][C]beta[/C][C]4.14825385555548[/C][/ROW]
[ROW][C]S.D.[/C][C]0.663220411979307[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.25471378840027[/C][/ROW]
[ROW][C]p-value[/C][C]6.21904940187061e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.14825385555548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70501&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70501&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-19.3376663336536
beta4.14825385555548
S.D.0.663220411979307
T-STAT6.25471378840027
p-value6.21904940187061e-05
Lambda-3.14825385555548


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')