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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 computationSun, 23 May 2010 08:47:50 +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/2010/May/23/t1274604483qd1bn4dycbqerlk.htm/, Retrieved Thu, 02 May 2024 07:48:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76284, Retrieved Thu, 02 May 2024 07:48:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact198

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] [] [2010-05-23 08:47:50] [676a4f18bfa59791b951d67c8b4b8fd1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
77
70
67
76
85
106
108
120
108
111
109
104
104
117
111
110
116
118
115
111
112
97
106
93
95
97
81
71
75
70
72
80
78
80
81
99
87
100
95
128
112
104
102
108
103
99
96
85
78
74
106
100
109
87
107
106
109
83
84
83
65
68
61
75
66
78
68
68
174
64
48
45

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=76284&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=76284&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76284&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
195.083333333333318.613085979948953
2109.1666666666677.8720833944831325
381.583333333333310.094628034331729
4101.58333333333311.389455516823343
593.833333333333313.449118479617535
673.333333333333333.098567212421129

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 95.0833333333333 & 18.6130859799489 & 53 \tabularnewline
2 & 109.166666666667 & 7.87208339448313 & 25 \tabularnewline
3 & 81.5833333333333 & 10.0946280343317 & 29 \tabularnewline
4 & 101.583333333333 & 11.3894555168233 & 43 \tabularnewline
5 & 93.8333333333333 & 13.4491184796175 & 35 \tabularnewline
6 & 73.3333333333333 & 33.098567212421 & 129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76284&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]95.0833333333333[/C][C]18.6130859799489[/C][C]53[/C][/ROW]
[ROW][C]2[/C][C]109.166666666667[/C][C]7.87208339448313[/C][C]25[/C][/ROW]
[ROW][C]3[/C][C]81.5833333333333[/C][C]10.0946280343317[/C][C]29[/C][/ROW]
[ROW][C]4[/C][C]101.583333333333[/C][C]11.3894555168233[/C][C]43[/C][/ROW]
[ROW][C]5[/C][C]93.8333333333333[/C][C]13.4491184796175[/C][C]35[/C][/ROW]
[ROW][C]6[/C][C]73.3333333333333[/C][C]33.098567212421[/C][C]129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76284&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76284&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
195.083333333333318.613085979948953
2109.1666666666677.8720833944831325
381.583333333333310.094628034331729
4101.58333333333311.389455516823343
593.833333333333313.449118479617535
673.333333333333333.098567212421129






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha63.0199651246019
beta-0.511380048919584
S.D.0.244118903441203
T-STAT-2.09479905779911
p-value0.104263826332532

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 63.0199651246019 \tabularnewline
beta & -0.511380048919584 \tabularnewline
S.D. & 0.244118903441203 \tabularnewline
T-STAT & -2.09479905779911 \tabularnewline
p-value & 0.104263826332532 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76284&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]63.0199651246019[/C][/ROW]
[ROW][C]beta[/C][C]-0.511380048919584[/C][/ROW]
[ROW][C]S.D.[/C][C]0.244118903441203[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.09479905779911[/C][/ROW]
[ROW][C]p-value[/C][C]0.104263826332532[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76284&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76284&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)
alpha63.0199651246019
beta-0.511380048919584
S.D.0.244118903441203
T-STAT-2.09479905779911
p-value0.104263826332532






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha13.9479519014292
beta-2.50334808563223
S.D.1.22446537618073
T-STAT-2.0444417084626
p-value0.110384996402001
Lambda3.50334808563223

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 13.9479519014292 \tabularnewline
beta & -2.50334808563223 \tabularnewline
S.D. & 1.22446537618073 \tabularnewline
T-STAT & -2.0444417084626 \tabularnewline
p-value & 0.110384996402001 \tabularnewline
Lambda & 3.50334808563223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76284&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.9479519014292[/C][/ROW]
[ROW][C]beta[/C][C]-2.50334808563223[/C][/ROW]
[ROW][C]S.D.[/C][C]1.22446537618073[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.0444417084626[/C][/ROW]
[ROW][C]p-value[/C][C]0.110384996402001[/C][/ROW]
[ROW][C]Lambda[/C][C]3.50334808563223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76284&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76284&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)
alpha13.9479519014292
beta-2.50334808563223
S.D.1.22446537618073
T-STAT-2.0444417084626
p-value0.110384996402001
Lambda3.50334808563223


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')