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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, 28 May 2009 10:52:03 -0600
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/May/28/t1243529556adsp6oores5yhyo.htm/, Retrieved Mon, 06 May 2024 07:35:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40660, Retrieved Mon, 06 May 2024 07:35:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

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] [Dorien Storms opg...] [2009-05-28 16:52:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
65
65.05
65.84
66.6
67.55
68.07
69.06
69.06
69.11
69.29
69.38
69.28
69.75
69.9
70.21
70.48
71.55
72.18
72.64
72.77
72.74
73.13
73.44
73.34
73.34
73.81
74.26
74.72
75.11
75.26
75.89
75.91
76.43
76.56
76.76
76.76
76.56
76.82
77.09
77.51
77.76
77.86
77.89
77.94
77.99
78.17
78.91
78.87
78.88
79.08
79.41
79.51
79.73
80.38
80.56
80.46
80.45
80.58
80.68
80.52
81.49
81.66
81.95
82.3
82.4
83.14
83.17
83.11
83.21
83.33
83.88
83.8
83.73

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=40660&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=40660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40660&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
167.77416666666671.721777402640204.3800
271.84416666666671.402163641943363.69
375.40083333333331.177180439813203.42
477.78083333333330.7176154748170992.34999999999999
580.020.6535497477065341.80000000000001
682.78666666666670.803971204067472.39

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 67.7741666666667 & 1.72177740264020 & 4.3800 \tabularnewline
2 & 71.8441666666667 & 1.40216364194336 & 3.69 \tabularnewline
3 & 75.4008333333333 & 1.17718043981320 & 3.42 \tabularnewline
4 & 77.7808333333333 & 0.717615474817099 & 2.34999999999999 \tabularnewline
5 & 80.02 & 0.653549747706534 & 1.80000000000001 \tabularnewline
6 & 82.7866666666667 & 0.80397120406747 & 2.39 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40660&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]67.7741666666667[/C][C]1.72177740264020[/C][C]4.3800[/C][/ROW]
[ROW][C]2[/C][C]71.8441666666667[/C][C]1.40216364194336[/C][C]3.69[/C][/ROW]
[ROW][C]3[/C][C]75.4008333333333[/C][C]1.17718043981320[/C][C]3.42[/C][/ROW]
[ROW][C]4[/C][C]77.7808333333333[/C][C]0.717615474817099[/C][C]2.34999999999999[/C][/ROW]
[ROW][C]5[/C][C]80.02[/C][C]0.653549747706534[/C][C]1.80000000000001[/C][/ROW]
[ROW][C]6[/C][C]82.7866666666667[/C][C]0.80397120406747[/C][C]2.39[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40660&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
167.77416666666671.721777402640204.3800
271.84416666666671.402163641943363.69
375.40083333333331.177180439813203.42
477.78083333333330.7176154748170992.34999999999999
580.020.6535497477065341.80000000000001
682.78666666666670.803971204067472.39






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha6.57791571160998
beta-0.0724116628934433
S.D.0.0143739078099417
T-STAT-5.0377158286322
p-value0.00729377593160956

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.57791571160998 \tabularnewline
beta & -0.0724116628934433 \tabularnewline
S.D. & 0.0143739078099417 \tabularnewline
T-STAT & -5.0377158286322 \tabularnewline
p-value & 0.00729377593160956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40660&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.57791571160998[/C][/ROW]
[ROW][C]beta[/C][C]-0.0724116628934433[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0143739078099417[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.0377158286322[/C][/ROW]
[ROW][C]p-value[/C][C]0.00729377593160956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40660&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)
alpha6.57791571160998
beta-0.0724116628934433
S.D.0.0143739078099417
T-STAT-5.0377158286322
p-value0.00729377593160956






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha21.1012821346725
beta-4.87325161463629
S.D.1.13246383476345
T-STAT-4.30322935270974
p-value0.0126133575515627
Lambda5.8732516146363

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 21.1012821346725 \tabularnewline
beta & -4.87325161463629 \tabularnewline
S.D. & 1.13246383476345 \tabularnewline
T-STAT & -4.30322935270974 \tabularnewline
p-value & 0.0126133575515627 \tabularnewline
Lambda & 5.8732516146363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40660&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.1012821346725[/C][/ROW]
[ROW][C]beta[/C][C]-4.87325161463629[/C][/ROW]
[ROW][C]S.D.[/C][C]1.13246383476345[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.30322935270974[/C][/ROW]
[ROW][C]p-value[/C][C]0.0126133575515627[/C][/ROW]
[ROW][C]Lambda[/C][C]5.8732516146363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40660&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)
alpha21.1012821346725
beta-4.87325161463629
S.D.1.13246383476345
T-STAT-4.30322935270974
p-value0.0126133575515627
Lambda5.8732516146363


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')