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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, 17 Mar 2016 19:12:30 +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/2016/Mar/17/t14582420776iggsqgcupu1ztt.htm/, Retrieved Sun, 05 May 2024 08:28:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294217, Retrieved Sun, 05 May 2024 08:28:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

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] [] [2016-03-17 19:12:30] [70e23d918d09c907c02097a361cd6415] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
81.83
82.58
82.6
82.71
82.98
83.11
83.22
83.32
83.39
83.45
83.52
83.59
83.97
84.48
84.8
84.93
85.14
85.22
85.54
85.5
85.61
85.75
85.89
85.94
86.08
86.3
86.97
87.3
87.62
87.59
87.78
87.87
88.17
88.67
88.84
88.9
88.98
89.27
89.69
89.72
89.79
89.82
89.98
90.09
90.31
90.3
90.48
90.52
90.53
91.38
91.87
91.9
92.08
92.14
92.09
92.32
92.67
92.78
92.96
93.12
93.32
94.12
94.34
94.52
94.81
94.95
94.99
95.03
95.16
95.41
95.46
95.62
95.66
95.96
96.18
96.24
97.03
97.11
97.28
97.74
97.83
98.14
98.18
98.21
98.43
98.67
99.51
99.64
99.83
99.84
99.94
100.17
100.56
101.05
101.17
101.21
101.01
101.92
102.33
102.41
102.5
102.69
102.98
103.11
103.36
103.8
104.07
104.15
104.19
104.64
104.98
105.25
105.43
105.59
105.84
105.87
106
106.14
106.24
106.31

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294217&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294217&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294217&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'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
183.0250.5150728103870371.76000000000001
285.23083333333330.5997493163182781.97
387.67416666666670.9157456805877692.82000000000001
489.91250.4697992801573491.53999999999999
592.15333333333330.7173097889568592.59
694.81083333333330.6510614875770652.30000000000001
797.130.9248292225644112.55
8100.0016666666670.9014920292425632.77999999999999
9102.8608333333330.9188278930080953.14
10105.540.6673012131645722.12

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 83.025 & 0.515072810387037 & 1.76000000000001 \tabularnewline
2 & 85.2308333333333 & 0.599749316318278 & 1.97 \tabularnewline
3 & 87.6741666666667 & 0.915745680587769 & 2.82000000000001 \tabularnewline
4 & 89.9125 & 0.469799280157349 & 1.53999999999999 \tabularnewline
5 & 92.1533333333333 & 0.717309788956859 & 2.59 \tabularnewline
6 & 94.8108333333333 & 0.651061487577065 & 2.30000000000001 \tabularnewline
7 & 97.13 & 0.924829222564411 & 2.55 \tabularnewline
8 & 100.001666666667 & 0.901492029242563 & 2.77999999999999 \tabularnewline
9 & 102.860833333333 & 0.918827893008095 & 3.14 \tabularnewline
10 & 105.54 & 0.667301213164572 & 2.12 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294217&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]83.025[/C][C]0.515072810387037[/C][C]1.76000000000001[/C][/ROW]
[ROW][C]2[/C][C]85.2308333333333[/C][C]0.599749316318278[/C][C]1.97[/C][/ROW]
[ROW][C]3[/C][C]87.6741666666667[/C][C]0.915745680587769[/C][C]2.82000000000001[/C][/ROW]
[ROW][C]4[/C][C]89.9125[/C][C]0.469799280157349[/C][C]1.53999999999999[/C][/ROW]
[ROW][C]5[/C][C]92.1533333333333[/C][C]0.717309788956859[/C][C]2.59[/C][/ROW]
[ROW][C]6[/C][C]94.8108333333333[/C][C]0.651061487577065[/C][C]2.30000000000001[/C][/ROW]
[ROW][C]7[/C][C]97.13[/C][C]0.924829222564411[/C][C]2.55[/C][/ROW]
[ROW][C]8[/C][C]100.001666666667[/C][C]0.901492029242563[/C][C]2.77999999999999[/C][/ROW]
[ROW][C]9[/C][C]102.860833333333[/C][C]0.918827893008095[/C][C]3.14[/C][/ROW]
[ROW][C]10[/C][C]105.54[/C][C]0.667301213164572[/C][C]2.12[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294217&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294217&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
183.0250.5150728103870371.76000000000001
285.23083333333330.5997493163182781.97
387.67416666666670.9157456805877692.82000000000001
489.91250.4697992801573491.53999999999999
592.15333333333330.7173097889568592.59
694.81083333333330.6510614875770652.30000000000001
797.130.9248292225644112.55
8100.0016666666670.9014920292425632.77999999999999
9102.8608333333330.9188278930080953.14
10105.540.6673012131645722.12






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.352400683408737
beta0.011515234512096
S.D.0.00714259786684257
T-STAT1.61219135205022
p-value0.145585315462636

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.352400683408737 \tabularnewline
beta & 0.011515234512096 \tabularnewline
S.D. & 0.00714259786684257 \tabularnewline
T-STAT & 1.61219135205022 \tabularnewline
p-value & 0.145585315462636 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294217&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.352400683408737[/C][/ROW]
[ROW][C]beta[/C][C]0.011515234512096[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00714259786684257[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.61219135205022[/C][/ROW]
[ROW][C]p-value[/C][C]0.145585315462636[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294217&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294217&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-0.352400683408737
beta0.011515234512096
S.D.0.00714259786684257
T-STAT1.61219135205022
p-value0.145585315462636






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.74682008519738
beta1.63084667164437
S.D.0.942672872924381
T-STAT1.73002397595798
p-value0.121877445137364
Lambda-0.630846671644372

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.74682008519738 \tabularnewline
beta & 1.63084667164437 \tabularnewline
S.D. & 0.942672872924381 \tabularnewline
T-STAT & 1.73002397595798 \tabularnewline
p-value & 0.121877445137364 \tabularnewline
Lambda & -0.630846671644372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294217&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.74682008519738[/C][/ROW]
[ROW][C]beta[/C][C]1.63084667164437[/C][/ROW]
[ROW][C]S.D.[/C][C]0.942672872924381[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.73002397595798[/C][/ROW]
[ROW][C]p-value[/C][C]0.121877445137364[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.630846671644372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294217&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294217&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-7.74682008519738
beta1.63084667164437
S.D.0.942672872924381
T-STAT1.73002397595798
p-value0.121877445137364
Lambda-0.630846671644372


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')