FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 25 Apr 2013 03:39:54 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Apr/25/t1366875609ssq9tz70r8cb2od.htm/, Retrieved Tue, 30 Apr 2024 08:07:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208313, Retrieved Tue, 30 Apr 2024 08:07:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164

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] [oef 8 3 2] [2013-04-25 07:39:54] [480fcaba71e70207c3e0ad7177944aa6] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
79.57
77.45
75.79
74.88
74.5
74.59
74.59
73.57
73.3
73.23
73
72.31
72.31
71.24
70.82
70.66
69.94
69.87
69.87
68.88
68.09
68.38
66.78
67.2
67.2
66.67
65.86
66.05
66.31
66.39
66.39
65.72
65.52
64.93
65.27
65.04
65.02
64.72
64.68
64.41
64.79
64.71
64.71
64.83
64.77
64.19
64.27
64.23
64.23
63.03
62.85
62.15
61.69
62.1
62.1
61.81
61.28
61.05
61.08
60.98
60.98
61.11
60.58
60.37
59.44
59.29
59.29
59.33
59.06
58.75
58.92
58.73

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208313&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208313&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
174.73166666666672.057181802781897.25999999999999
269.50333333333331.673164303910045.53
365.94583333333330.6865123760168072.27
464.61083333333330.2676313045058720.829999999999998
562.02916666666670.9642939794418933.25000000000001
659.65416666666670.8648011682497082.38

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 74.7316666666667 & 2.05718180278189 & 7.25999999999999 \tabularnewline
2 & 69.5033333333333 & 1.67316430391004 & 5.53 \tabularnewline
3 & 65.9458333333333 & 0.686512376016807 & 2.27 \tabularnewline
4 & 64.6108333333333 & 0.267631304505872 & 0.829999999999998 \tabularnewline
5 & 62.0291666666667 & 0.964293979441893 & 3.25000000000001 \tabularnewline
6 & 59.6541666666667 & 0.864801168249708 & 2.38 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208313&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]74.7316666666667[/C][C]2.05718180278189[/C][C]7.25999999999999[/C][/ROW]
[ROW][C]2[/C][C]69.5033333333333[/C][C]1.67316430391004[/C][C]5.53[/C][/ROW]
[ROW][C]3[/C][C]65.9458333333333[/C][C]0.686512376016807[/C][C]2.27[/C][/ROW]
[ROW][C]4[/C][C]64.6108333333333[/C][C]0.267631304505872[/C][C]0.829999999999998[/C][/ROW]
[ROW][C]5[/C][C]62.0291666666667[/C][C]0.964293979441893[/C][C]3.25000000000001[/C][/ROW]
[ROW][C]6[/C][C]59.6541666666667[/C][C]0.864801168249708[/C][C]2.38[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208313&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
174.73166666666672.057181802781897.25999999999999
269.50333333333331.673164303910045.53
365.94583333333330.6865123760168072.27
464.61083333333330.2676313045058720.829999999999998
562.02916666666670.9642939794418933.25000000000001
659.65416666666670.8648011682497082.38






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.04311028212252
beta0.0927479579485248
S.D.0.0396566919337512
T-STAT2.33877193043397
p-value0.0794850776992192

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.04311028212252 \tabularnewline
beta & 0.0927479579485248 \tabularnewline
S.D. & 0.0396566919337512 \tabularnewline
T-STAT & 2.33877193043397 \tabularnewline
p-value & 0.0794850776992192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208313&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.04311028212252[/C][/ROW]
[ROW][C]beta[/C][C]0.0927479579485248[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0396566919337512[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.33877193043397[/C][/ROW]
[ROW][C]p-value[/C][C]0.0794850776992192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208313&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-5.04311028212252
beta0.0927479579485248
S.D.0.0396566919337512
T-STAT2.33877193043397
p-value0.0794850776992192






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-20.7187408422955
beta4.92157530615555
S.D.3.74318440498388
T-STAT1.31480973782716
p-value0.258888035723474
Lambda-3.92157530615555

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -20.7187408422955 \tabularnewline
beta & 4.92157530615555 \tabularnewline
S.D. & 3.74318440498388 \tabularnewline
T-STAT & 1.31480973782716 \tabularnewline
p-value & 0.258888035723474 \tabularnewline
Lambda & -3.92157530615555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208313&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20.7187408422955[/C][/ROW]
[ROW][C]beta[/C][C]4.92157530615555[/C][/ROW]
[ROW][C]S.D.[/C][C]3.74318440498388[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.31480973782716[/C][/ROW]
[ROW][C]p-value[/C][C]0.258888035723474[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.92157530615555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208313&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-20.7187408422955
beta4.92157530615555
S.D.3.74318440498388
T-STAT1.31480973782716
p-value0.258888035723474
Lambda-3.92157530615555


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')