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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 22 Dec 2008 15:23:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t1229984621o57dm8o06zimbq1.htm/, Retrieved Sun, 12 May 2024 16:00:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36242, Retrieved Sun, 12 May 2024 16:00:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

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] [Paper: Standard D...] [2008-12-14 15:51:58] [9e54d1454d464f1bf9ee4a54d5d56945]
-         [Standard Deviation-Mean Plot] [] [2008-12-22 22:23:07] [27189814204044fdc56e2241a9375b9f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17,3
15,4
16,9
20,8
16,4
11,3
17,5
16,6
17,5
19,5
18,8
20,2
19,2
14,4
24,5
25,7
27,1
21
18,6
20
21,8
20,4
18
21,5
19,1
19,7
26
26,3
24,6
22,4
32
24
30
24,1
26,3
29,8
21,9
22,8
29,2
27,5
27,4
31
26,1
22,2
34
26,9
31,9
34,2
31,2
28,5
37,1
36
34,8
32,1
37,2
36,3
39,5
37,1
35,6
36,2
35,9
32,5
39,2
39,4
42,8
34,5
43,7
46,3
40,8
48,4
43,2
48,1
42,8

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36242&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36242&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
117.352.502180866945699.5
221.01666666666673.5078699398853912.7
325.35833333333333.948638046750112.9
427.9254.2994978565155512.3
535.13333333333333.0648545370593611
641.23333333333335.172713958549215.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 17.35 & 2.50218086694569 & 9.5 \tabularnewline
2 & 21.0166666666667 & 3.50786993988539 & 12.7 \tabularnewline
3 & 25.3583333333333 & 3.9486380467501 & 12.9 \tabularnewline
4 & 27.925 & 4.29949785651555 & 12.3 \tabularnewline
5 & 35.1333333333333 & 3.06485453705936 & 11 \tabularnewline
6 & 41.2333333333333 & 5.1727139585492 & 15.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36242&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]17.35[/C][C]2.50218086694569[/C][C]9.5[/C][/ROW]
[ROW][C]2[/C][C]21.0166666666667[/C][C]3.50786993988539[/C][C]12.7[/C][/ROW]
[ROW][C]3[/C][C]25.3583333333333[/C][C]3.9486380467501[/C][C]12.9[/C][/ROW]
[ROW][C]4[/C][C]27.925[/C][C]4.29949785651555[/C][C]12.3[/C][/ROW]
[ROW][C]5[/C][C]35.1333333333333[/C][C]3.06485453705936[/C][C]11[/C][/ROW]
[ROW][C]6[/C][C]41.2333333333333[/C][C]5.1727139585492[/C][C]15.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36242&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
117.352.502180866945699.5
221.01666666666673.5078699398853912.7
325.35833333333333.948638046750112.9
427.9254.2994978565155512.3
535.13333333333333.0648545370593611
641.23333333333335.172713958549215.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.74009338511544
beta0.071749994415312
S.D.0.0390967699175006
T-STAT1.83518982685051
p-value0.140379542636673

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.74009338511544 \tabularnewline
beta & 0.071749994415312 \tabularnewline
S.D. & 0.0390967699175006 \tabularnewline
T-STAT & 1.83518982685051 \tabularnewline
p-value & 0.140379542636673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36242&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.74009338511544[/C][/ROW]
[ROW][C]beta[/C][C]0.071749994415312[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0390967699175006[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.83518982685051[/C][/ROW]
[ROW][C]p-value[/C][C]0.140379542636673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36242&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)
alpha1.74009338511544
beta0.071749994415312
S.D.0.0390967699175006
T-STAT1.83518982685051
p-value0.140379542636673






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.499673868989378
beta0.5453655886741
S.D.0.294046056070376
T-STAT1.85469445148271
p-value0.137241052499562
Lambda0.4546344113259

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.499673868989378 \tabularnewline
beta & 0.5453655886741 \tabularnewline
S.D. & 0.294046056070376 \tabularnewline
T-STAT & 1.85469445148271 \tabularnewline
p-value & 0.137241052499562 \tabularnewline
Lambda & 0.4546344113259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36242&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.499673868989378[/C][/ROW]
[ROW][C]beta[/C][C]0.5453655886741[/C][/ROW]
[ROW][C]S.D.[/C][C]0.294046056070376[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.85469445148271[/C][/ROW]
[ROW][C]p-value[/C][C]0.137241052499562[/C][/ROW]
[ROW][C]Lambda[/C][C]0.4546344113259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36242&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36242&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-0.499673868989378
beta0.5453655886741
S.D.0.294046056070376
T-STAT1.85469445148271
p-value0.137241052499562
Lambda0.4546344113259


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')