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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 19 Nov 2015 15:03:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/19/t1447945441jaawbpozq3zhlre.htm/, Retrieved Tue, 14 May 2024 12:58:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283633, Retrieved Tue, 14 May 2024 12:58:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

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] [] [2015-11-19 15:03:32] [bdd544630eb102d4e9b9d691f462dd0a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86.48
86.48
86.7
87.86
88.24
88.23
88.73
88.82
87.16
86.29
86.37
86.59
85.46
85.85
86.93
87.66
87.84
88.09
88.58
88.06
88.26
89
90.78
90
89.84
89.82
91.12
91.5
93.03
94.23
94.76
92.83
92.49
90.85
88.19
86.31
85.74
86.62
86.66
87.39
87.59
88.8
88.64
89.55
89.04
88.49
89.5
89.46
90.33
90.27
91.5
92.53
93.14
93.01
92.84
92.88
93.05
93.17
93.67
94.9
95.72
96.08
97.52
98.26
98.48
98.09
98.03
98.14
98.71
98.69
98.72
98.47
99.49
99.84
100.9
101.31
100.09
99.28
99.57
101.04
101.87
101.39
100.3
99.95
99.87
100.51
100.27
100.04
99.23
99.32
99.95
100.23
101.02
99.83
99.61
100.12
99.83
100.03
100.07
100.46
100.43
100.68
101.8
101.21
100.63
100.55
99.76
98.8

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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283633&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283633&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
187.32916666666670.9779706105765712.52999999999999
288.04251.522038853882285.32000000000001
391.24752.457685995920858.45
488.12333333333331.290548391775823.81
592.60751.326445180993864.63000000000001
697.90916666666671.00282744217933
7100.4191666666670.8537559618674682.59
81000.4952501663530541.78999999999999
9100.3541666666670.7561560485091483

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 87.3291666666667 & 0.977970610576571 & 2.52999999999999 \tabularnewline
2 & 88.0425 & 1.52203885388228 & 5.32000000000001 \tabularnewline
3 & 91.2475 & 2.45768599592085 & 8.45 \tabularnewline
4 & 88.1233333333333 & 1.29054839177582 & 3.81 \tabularnewline
5 & 92.6075 & 1.32644518099386 & 4.63000000000001 \tabularnewline
6 & 97.9091666666667 & 1.0028274421793 & 3 \tabularnewline
7 & 100.419166666667 & 0.853755961867468 & 2.59 \tabularnewline
8 & 100 & 0.495250166353054 & 1.78999999999999 \tabularnewline
9 & 100.354166666667 & 0.756156048509148 & 3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283633&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]87.3291666666667[/C][C]0.977970610576571[/C][C]2.52999999999999[/C][/ROW]
[ROW][C]2[/C][C]88.0425[/C][C]1.52203885388228[/C][C]5.32000000000001[/C][/ROW]
[ROW][C]3[/C][C]91.2475[/C][C]2.45768599592085[/C][C]8.45[/C][/ROW]
[ROW][C]4[/C][C]88.1233333333333[/C][C]1.29054839177582[/C][C]3.81[/C][/ROW]
[ROW][C]5[/C][C]92.6075[/C][C]1.32644518099386[/C][C]4.63000000000001[/C][/ROW]
[ROW][C]6[/C][C]97.9091666666667[/C][C]1.0028274421793[/C][C]3[/C][/ROW]
[ROW][C]7[/C][C]100.419166666667[/C][C]0.853755961867468[/C][C]2.59[/C][/ROW]
[ROW][C]8[/C][C]100[/C][C]0.495250166353054[/C][C]1.78999999999999[/C][/ROW]
[ROW][C]9[/C][C]100.354166666667[/C][C]0.756156048509148[/C][C]3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283633&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
187.32916666666670.9779706105765712.52999999999999
288.04251.522038853882285.32000000000001
391.24752.457685995920858.45
488.12333333333331.290548391775823.81
592.60751.326445180993864.63000000000001
697.90916666666671.00282744217933
7100.4191666666670.8537559618674682.59
81000.4952501663530541.78999999999999
9100.3541666666670.7561560485091483






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.54719508015692
beta-0.0570215412166246
S.D.0.0314130020729011
T-STAT-1.8152210057572
p-value0.1123524026883

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.54719508015692 \tabularnewline
beta & -0.0570215412166246 \tabularnewline
S.D. & 0.0314130020729011 \tabularnewline
T-STAT & -1.8152210057572 \tabularnewline
p-value & 0.1123524026883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283633&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.54719508015692[/C][/ROW]
[ROW][C]beta[/C][C]-0.0570215412166246[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0314130020729011[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.8152210057572[/C][/ROW]
[ROW][C]p-value[/C][C]0.1123524026883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283633&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283633&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)
alpha6.54719508015692
beta-0.0570215412166246
S.D.0.0314130020729011
T-STAT-1.8152210057572
p-value0.1123524026883






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha22.6023176934197
beta-4.95954782369029
S.D.2.16892060019873
T-STAT-2.28664332997523
p-value0.0560843269643078
Lambda5.95954782369029

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 22.6023176934197 \tabularnewline
beta & -4.95954782369029 \tabularnewline
S.D. & 2.16892060019873 \tabularnewline
T-STAT & -2.28664332997523 \tabularnewline
p-value & 0.0560843269643078 \tabularnewline
Lambda & 5.95954782369029 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283633&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]22.6023176934197[/C][/ROW]
[ROW][C]beta[/C][C]-4.95954782369029[/C][/ROW]
[ROW][C]S.D.[/C][C]2.16892060019873[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.28664332997523[/C][/ROW]
[ROW][C]p-value[/C][C]0.0560843269643078[/C][/ROW]
[ROW][C]Lambda[/C][C]5.95954782369029[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283633&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283633&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)
alpha22.6023176934197
beta-4.95954782369029
S.D.2.16892060019873
T-STAT-2.28664332997523
p-value0.0560843269643078
Lambda5.95954782369029


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 <- '12'
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')