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 computationMon, 22 Apr 2013 04:37:53 -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/22/t1366619890f39vtzejureyv88.htm/, Retrieved Mon, 29 Apr 2024 11:22:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208239, Retrieved Mon, 29 Apr 2024 11:22:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

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] [Standard Deviatio...] [2013-04-22 08:37:53] [38b7061a49f7215900abdc4599fce3db] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226
33.865
32.810
32.242
32.700
32.819
33.947
34.148
35.261
39.506
41.591
39.148
41.216
40.225

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=208239&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=208239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208239&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
115.46091666666670.6951090768993592.52
216.3220.7756835109056462.166
319.10791666666670.7032356980200142.069
422.481.260966944992474.147
529.74083333333332.835123945770068.661
636.30108333333333.704161626611439.349

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.4609166666667 & 0.695109076899359 & 2.52 \tabularnewline
2 & 16.322 & 0.775683510905646 & 2.166 \tabularnewline
3 & 19.1079166666667 & 0.703235698020014 & 2.069 \tabularnewline
4 & 22.48 & 1.26096694499247 & 4.147 \tabularnewline
5 & 29.7408333333333 & 2.83512394577006 & 8.661 \tabularnewline
6 & 36.3010833333333 & 3.70416162661143 & 9.349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208239&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]15.4609166666667[/C][C]0.695109076899359[/C][C]2.52[/C][/ROW]
[ROW][C]2[/C][C]16.322[/C][C]0.775683510905646[/C][C]2.166[/C][/ROW]
[ROW][C]3[/C][C]19.1079166666667[/C][C]0.703235698020014[/C][C]2.069[/C][/ROW]
[ROW][C]4[/C][C]22.48[/C][C]1.26096694499247[/C][C]4.147[/C][/ROW]
[ROW][C]5[/C][C]29.7408333333333[/C][C]2.83512394577006[/C][C]8.661[/C][/ROW]
[ROW][C]6[/C][C]36.3010833333333[/C][C]3.70416162661143[/C][C]9.349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208239&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
115.46091666666670.6951090768993592.52
216.3220.7756835109056462.166
319.10791666666670.7032356980200142.069
422.481.260966944992474.147
529.74083333333332.835123945770068.661
636.30108333333333.704161626611439.349






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.91804661266186
beta0.154093226617868
S.D.0.0148914161852683
T-STAT10.3477885985289
p-value0.000492259492444802

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.91804661266186 \tabularnewline
beta & 0.154093226617868 \tabularnewline
S.D. & 0.0148914161852683 \tabularnewline
T-STAT & 10.3477885985289 \tabularnewline
p-value & 0.000492259492444802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208239&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.91804661266186[/C][/ROW]
[ROW][C]beta[/C][C]0.154093226617868[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0148914161852683[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.3477885985289[/C][/ROW]
[ROW][C]p-value[/C][C]0.000492259492444802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208239&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208239&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-1.91804661266186
beta0.154093226617868
S.D.0.0148914161852683
T-STAT10.3477885985289
p-value0.000492259492444802






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.29704974055941
beta2.12057892850792
S.D.0.258402993365512
T-STAT8.20647973496325
p-value0.00120146317862548
Lambda-1.12057892850792

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.29704974055941 \tabularnewline
beta & 2.12057892850792 \tabularnewline
S.D. & 0.258402993365512 \tabularnewline
T-STAT & 8.20647973496325 \tabularnewline
p-value & 0.00120146317862548 \tabularnewline
Lambda & -1.12057892850792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208239&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.29704974055941[/C][/ROW]
[ROW][C]beta[/C][C]2.12057892850792[/C][/ROW]
[ROW][C]S.D.[/C][C]0.258402993365512[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.20647973496325[/C][/ROW]
[ROW][C]p-value[/C][C]0.00120146317862548[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.12057892850792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208239&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208239&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-6.29704974055941
beta2.12057892850792
S.D.0.258402993365512
T-STAT8.20647973496325
p-value0.00120146317862548
Lambda-1.12057892850792


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')