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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 computationWed, 19 Dec 2007 05:14:46 -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/2007/Dec/19/t11980654412lt2eodna6tktsi.htm/, Retrieved Mon, 06 May 2024 16:07:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4647, Retrieved Mon, 06 May 2024 16:07:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211

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] [] [2007-12-19 12:14:46] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25.62
27.5
24.5
25.66
28.31
27.85
24.61
25.68
25.62
20.54
18.8
18.71
19.46
20.12
23.54
25.6
25.39
24.09
25.69
26.56
28.33
27.5
24.23
28.23
31.29
32.72
30.46
24.89
25.68
27.52
28.4
29.71
26.85
29.62
28.69
29.76
31.3
30.86
33.46
33.15
37.99
35.24
38.24
43.16
43.33
49.67
43.17
39.56
44.36
45.22
53.1
52.1
48.52
54.84
57.57
64.14
62.85
58.75
55.33
57.03
63.18
60.19
62.12
70.12
69.75
68.56
73.77
73.23
61.96
57.81
58.76
62.47
53.68
57.56
62.05
67.49
67.21
71.05
76.93
70.76

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4647&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4647&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
124.453.325701566450448.85
224.8952.846367701283358.21
328.79916666666672.283929860144709.18
438.26083333333335.778081560098624.78
554.48416666666676.2505293715206638.75
665.165.6149815833908349.68

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 24.45 & 3.32570156645044 & 8.85 \tabularnewline
2 & 24.895 & 2.84636770128335 & 8.21 \tabularnewline
3 & 28.7991666666667 & 2.28392986014470 & 9.18 \tabularnewline
4 & 38.2608333333333 & 5.7780815600986 & 24.78 \tabularnewline
5 & 54.4841666666667 & 6.25052937152066 & 38.75 \tabularnewline
6 & 65.16 & 5.61498158339083 & 49.68 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4647&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]24.45[/C][C]3.32570156645044[/C][C]8.85[/C][/ROW]
[ROW][C]2[/C][C]24.895[/C][C]2.84636770128335[/C][C]8.21[/C][/ROW]
[ROW][C]3[/C][C]28.7991666666667[/C][C]2.28392986014470[/C][C]9.18[/C][/ROW]
[ROW][C]4[/C][C]38.2608333333333[/C][C]5.7780815600986[/C][C]24.78[/C][/ROW]
[ROW][C]5[/C][C]54.4841666666667[/C][C]6.25052937152066[/C][C]38.75[/C][/ROW]
[ROW][C]6[/C][C]65.16[/C][C]5.61498158339083[/C][C]49.68[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4647&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
124.453.325701566450448.85
224.8952.846367701283358.21
328.79916666666672.283929860144709.18
438.26083333333335.778081560098624.78
554.48416666666676.2505293715206638.75
665.165.6149815833908349.68






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.10527115212695
beta0.082474193851395
S.D.0.0296075986762278
T-STAT2.78557524212911
p-value0.0495354055487679

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.10527115212695 \tabularnewline
beta & 0.082474193851395 \tabularnewline
S.D. & 0.0296075986762278 \tabularnewline
T-STAT & 2.78557524212911 \tabularnewline
p-value & 0.0495354055487679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4647&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.10527115212695[/C][/ROW]
[ROW][C]beta[/C][C]0.082474193851395[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0296075986762278[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.78557524212911[/C][/ROW]
[ROW][C]p-value[/C][C]0.0495354055487679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4647&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)
alpha1.10527115212695
beta0.082474193851395
S.D.0.0296075986762278
T-STAT2.78557524212911
p-value0.0495354055487679






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.64918763215807
beta0.846698668840336
S.D.0.29252077013893
T-STAT2.89449076876901
p-value0.0443624455687725
Lambda0.153301331159664

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.64918763215807 \tabularnewline
beta & 0.846698668840336 \tabularnewline
S.D. & 0.29252077013893 \tabularnewline
T-STAT & 2.89449076876901 \tabularnewline
p-value & 0.0443624455687725 \tabularnewline
Lambda & 0.153301331159664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4647&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.64918763215807[/C][/ROW]
[ROW][C]beta[/C][C]0.846698668840336[/C][/ROW]
[ROW][C]S.D.[/C][C]0.29252077013893[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.89449076876901[/C][/ROW]
[ROW][C]p-value[/C][C]0.0443624455687725[/C][/ROW]
[ROW][C]Lambda[/C][C]0.153301331159664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4647&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4647&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-1.64918763215807
beta0.846698668840336
S.D.0.29252077013893
T-STAT2.89449076876901
p-value0.0443624455687725
Lambda0.153301331159664


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')