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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, 29 Nov 2012 10:53:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/29/t1354204408mxx60tqxmew6s3r.htm/, Retrieved Sun, 28 Apr 2024 03:34:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194734, Retrieved Sun, 28 Apr 2024 03:34:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

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] [] [2012-11-29 15:53:04] [b91e71fa3b5e2ab5567c9d258a8f1839] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
49.98
50.12
50.37
50.39
50.34
50.32
50.32
50.32
50.67
50.86
50.95
51.02
51.02
51.06
50.9
51.23
51.29
51.3
51.3
51.3
51.46
51.47
51.77
51.82
51.82
51.84
51.9
51.94
52.22
52.27
52.27
52.28
52.53
52.73
52.72
52.67
52.67
52.65
52.69
52.73
52.84
52.83
52.83
52.84
52.82
53.09
53.4
53.43
53.43
53.42
53.6
53.69
54.05
54.04
54.04
54.08
54.05
54.39
54.38
54.46
54.46
54.69
54.91
55.52
56.01
56.07
56.07
56.09
56.29
56.45
56.87
56.87

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194734&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]3 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=194734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194734&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
150.47166666666670.3286842456421271.04000000000001
251.32666666666670.2760544522482130.920000000000002
352.26583333333330.3407600684388120.909999999999997
452.90166666666670.2660769995639790.780000000000001
553.96916666666670.3603901505397461.04
655.85833333333330.8024828894616932.41

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 50.4716666666667 & 0.328684245642127 & 1.04000000000001 \tabularnewline
2 & 51.3266666666667 & 0.276054452248213 & 0.920000000000002 \tabularnewline
3 & 52.2658333333333 & 0.340760068438812 & 0.909999999999997 \tabularnewline
4 & 52.9016666666667 & 0.266076999563979 & 0.780000000000001 \tabularnewline
5 & 53.9691666666667 & 0.360390150539746 & 1.04 \tabularnewline
6 & 55.8583333333333 & 0.802482889461693 & 2.41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194734&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]50.4716666666667[/C][C]0.328684245642127[/C][C]1.04000000000001[/C][/ROW]
[ROW][C]2[/C][C]51.3266666666667[/C][C]0.276054452248213[/C][C]0.920000000000002[/C][/ROW]
[ROW][C]3[/C][C]52.2658333333333[/C][C]0.340760068438812[/C][C]0.909999999999997[/C][/ROW]
[ROW][C]4[/C][C]52.9016666666667[/C][C]0.266076999563979[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]5[/C][C]53.9691666666667[/C][C]0.360390150539746[/C][C]1.04[/C][/ROW]
[ROW][C]6[/C][C]55.8583333333333[/C][C]0.802482889461693[/C][C]2.41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194734&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
150.47166666666670.3286842456421271.04000000000001
251.32666666666670.2760544522482130.920000000000002
352.26583333333330.3407600684388120.909999999999997
452.90166666666670.2660769995639790.780000000000001
553.96916666666670.3603901505397461.04
655.85833333333330.8024828894616932.41






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.00592825856604
beta0.0833667112858777
S.D.0.0319586522457762
T-STAT2.60858031949379
p-value0.059508701336647

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.00592825856604 \tabularnewline
beta & 0.0833667112858777 \tabularnewline
S.D. & 0.0319586522457762 \tabularnewline
T-STAT & 2.60858031949379 \tabularnewline
p-value & 0.059508701336647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194734&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.00592825856604[/C][/ROW]
[ROW][C]beta[/C][C]0.0833667112858777[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0319586522457762[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.60858031949379[/C][/ROW]
[ROW][C]p-value[/C][C]0.059508701336647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194734&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-4.00592825856604
beta0.0833667112858777
S.D.0.0319586522457762
T-STAT2.60858031949379
p-value0.059508701336647






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-35.1924886709575
beta8.61981556169532
S.D.3.51008566298618
T-STAT2.45572797626884
p-value0.0700123520051322
Lambda-7.61981556169532

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -35.1924886709575 \tabularnewline
beta & 8.61981556169532 \tabularnewline
S.D. & 3.51008566298618 \tabularnewline
T-STAT & 2.45572797626884 \tabularnewline
p-value & 0.0700123520051322 \tabularnewline
Lambda & -7.61981556169532 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194734&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-35.1924886709575[/C][/ROW]
[ROW][C]beta[/C][C]8.61981556169532[/C][/ROW]
[ROW][C]S.D.[/C][C]3.51008566298618[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.45572797626884[/C][/ROW]
[ROW][C]p-value[/C][C]0.0700123520051322[/C][/ROW]
[ROW][C]Lambda[/C][C]-7.61981556169532[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194734&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194734&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-35.1924886709575
beta8.61981556169532
S.D.3.51008566298618
T-STAT2.45572797626884
p-value0.0700123520051322
Lambda-7.61981556169532


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')