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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 computationFri, 21 Nov 2014 18:46:08 +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/2014/Nov/21/t1416595584uskss0l3fu170g1.htm/, Retrieved Sun, 19 May 2024 15:55:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257708, Retrieved Sun, 19 May 2024 15:55:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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] [Gemiddelde consum...] [2014-11-21 18:46:08] [1ab96e54865215824aa8065210e49a0c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
48,74
48,79
48,82
48,82
49,20
49,30
49,30
49,34
49,47
49,65
49,70
49,75
49,75
49,70
50,09
50,19
50,53
50,55
50,55
50,55
50,58
50,61
50,94
51,01
51,01
51,04
51,15
51,31
51,31
51,34
51,34
51,34
51,47
51,95
51,97
51,92
51,92
51,91
51,97
52,14
52,33
52,40
52,40
52,41
52,71
53,17
53,33
53,32
53,32
53,30
53,31
53,72
53,87
53,91
53,91
53,96
54,02
54,33
54,48
54,54
52,40
52,45
52,38
52,45
52,83
52,76
52,86
52,88
53,32
53,20
53,22
53,22

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=257708&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=257708&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257708&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
149.240.3713366519627561.01
250.42083333333330.4125410906990361.31
351.42916666666670.3389410872202730.960000000000001
452.50083333333330.5227803003406331.42
553.88916666666670.4291102493073381.24
652.83083333333330.3523546336842860.939999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 49.24 & 0.371336651962756 & 1.01 \tabularnewline
2 & 50.4208333333333 & 0.412541090699036 & 1.31 \tabularnewline
3 & 51.4291666666667 & 0.338941087220273 & 0.960000000000001 \tabularnewline
4 & 52.5008333333333 & 0.522780300340633 & 1.42 \tabularnewline
5 & 53.8891666666667 & 0.429110249307338 & 1.24 \tabularnewline
6 & 52.8308333333333 & 0.352354633684286 & 0.939999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257708&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]49.24[/C][C]0.371336651962756[/C][C]1.01[/C][/ROW]
[ROW][C]2[/C][C]50.4208333333333[/C][C]0.412541090699036[/C][C]1.31[/C][/ROW]
[ROW][C]3[/C][C]51.4291666666667[/C][C]0.338941087220273[/C][C]0.960000000000001[/C][/ROW]
[ROW][C]4[/C][C]52.5008333333333[/C][C]0.522780300340633[/C][C]1.42[/C][/ROW]
[ROW][C]5[/C][C]53.8891666666667[/C][C]0.429110249307338[/C][C]1.24[/C][/ROW]
[ROW][C]6[/C][C]52.8308333333333[/C][C]0.352354633684286[/C][C]0.939999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257708&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257708&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
149.240.3713366519627561.01
250.42083333333330.4125410906990361.31
351.42916666666670.3389410872202730.960000000000001
452.50083333333330.5227803003406331.42
553.88916666666670.4291102493073381.24
652.83083333333330.3523546336842860.939999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.234052863384088
beta0.0123469140679443
S.D.0.0188512686268961
T-STAT0.654964623989724
p-value0.548243462424941

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.234052863384088 \tabularnewline
beta & 0.0123469140679443 \tabularnewline
S.D. & 0.0188512686268961 \tabularnewline
T-STAT & 0.654964623989724 \tabularnewline
p-value & 0.548243462424941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257708&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.234052863384088[/C][/ROW]
[ROW][C]beta[/C][C]0.0123469140679443[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0188512686268961[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.654964623989724[/C][/ROW]
[ROW][C]p-value[/C][C]0.548243462424941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257708&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257708&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-0.234052863384088
beta0.0123469140679443
S.D.0.0188512686268961
T-STAT0.654964623989724
p-value0.548243462424941






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.7048106256266
beta1.46725530593234
S.D.2.29399436919126
T-STAT0.639607195918973
p-value0.557222364832755
Lambda-0.467255305932337

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.7048106256266 \tabularnewline
beta & 1.46725530593234 \tabularnewline
S.D. & 2.29399436919126 \tabularnewline
T-STAT & 0.639607195918973 \tabularnewline
p-value & 0.557222364832755 \tabularnewline
Lambda & -0.467255305932337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257708&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.7048106256266[/C][/ROW]
[ROW][C]beta[/C][C]1.46725530593234[/C][/ROW]
[ROW][C]S.D.[/C][C]2.29399436919126[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.639607195918973[/C][/ROW]
[ROW][C]p-value[/C][C]0.557222364832755[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.467255305932337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257708&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257708&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-6.7048106256266
beta1.46725530593234
S.D.2.29399436919126
T-STAT0.639607195918973
p-value0.557222364832755
Lambda-0.467255305932337


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')