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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 computationWed, 29 Dec 2010 14:28:24 +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/2010/Dec/29/t1293632834zhtufeq3t0va93m.htm/, Retrieved Fri, 03 May 2024 14:35:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116867, Retrieved Fri, 03 May 2024 14:35:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

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] [] [2010-12-29 14:28:24] [95fdfecfb4f2f50e2168e1a971ea5f83] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
60178
53200
59909
55970
47682
50173
43090
36031
42143
48478
36046
31060
54874
60051
71622
66526
50140
55973
40393
38483
42879
47875
40578
31027
62027
56493
65566
62653
53470
59600
42542
42018
44038
44988
43309
26843
69770
64886
79354
63025
54003
55926
45629
40361
43039
44570
43269
25563
68707
60223
74283
61232
61531
65305
51699
44599
35221
55066
45335
28702
69517
69240
71525
77740
62107
65450
51493
43067
49172
54483
38158
27898
58648
56000
62381
59849
48345
55376
45400
38389
44098
48290
41267
31238

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116867&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116867&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
146996.66666666679559.3433336028429118
250035.083333333312172.952181398240595
350295.583333333311494.56320067238723
452449.583333333314940.243191755253791
554325.2513699.716832674145581
656654.166666666715188.753715306749842
749106.759559.1768295753831143

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 46996.6666666667 & 9559.34333360284 & 29118 \tabularnewline
2 & 50035.0833333333 & 12172.9521813982 & 40595 \tabularnewline
3 & 50295.5833333333 & 11494.563200672 & 38723 \tabularnewline
4 & 52449.5833333333 & 14940.2431917552 & 53791 \tabularnewline
5 & 54325.25 & 13699.7168326741 & 45581 \tabularnewline
6 & 56654.1666666667 & 15188.7537153067 & 49842 \tabularnewline
7 & 49106.75 & 9559.17682957538 & 31143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116867&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]46996.6666666667[/C][C]9559.34333360284[/C][C]29118[/C][/ROW]
[ROW][C]2[/C][C]50035.0833333333[/C][C]12172.9521813982[/C][C]40595[/C][/ROW]
[ROW][C]3[/C][C]50295.5833333333[/C][C]11494.563200672[/C][C]38723[/C][/ROW]
[ROW][C]4[/C][C]52449.5833333333[/C][C]14940.2431917552[/C][C]53791[/C][/ROW]
[ROW][C]5[/C][C]54325.25[/C][C]13699.7168326741[/C][C]45581[/C][/ROW]
[ROW][C]6[/C][C]56654.1666666667[/C][C]15188.7537153067[/C][C]49842[/C][/ROW]
[ROW][C]7[/C][C]49106.75[/C][C]9559.17682957538[/C][C]31143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116867&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
146996.66666666679559.3433336028429118
250035.083333333312172.952181398240595
350295.583333333311494.56320067238723
452449.583333333314940.243191755253791
554325.2513699.716832674145581
656654.166666666715188.753715306749842
749106.759559.1768295753831143






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-20416.1415351763
beta0.637819633803926
S.D.0.141254834240213
T-STAT4.51538269280945
p-value0.00630959536681439

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -20416.1415351763 \tabularnewline
beta & 0.637819633803926 \tabularnewline
S.D. & 0.141254834240213 \tabularnewline
T-STAT & 4.51538269280945 \tabularnewline
p-value & 0.00630959536681439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116867&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20416.1415351763[/C][/ROW]
[ROW][C]beta[/C][C]0.637819633803926[/C][/ROW]
[ROW][C]S.D.[/C][C]0.141254834240213[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.51538269280945[/C][/ROW]
[ROW][C]p-value[/C][C]0.00630959536681439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116867&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-20416.1415351763
beta0.637819633803926
S.D.0.141254834240213
T-STAT4.51538269280945
p-value0.00630959536681439






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-20.2060412030018
beta2.73040657225417
S.D.0.60551708790384
T-STAT4.50921473034923
p-value0.00634548141088133
Lambda-1.73040657225417

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -20.2060412030018 \tabularnewline
beta & 2.73040657225417 \tabularnewline
S.D. & 0.60551708790384 \tabularnewline
T-STAT & 4.50921473034923 \tabularnewline
p-value & 0.00634548141088133 \tabularnewline
Lambda & -1.73040657225417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116867&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20.2060412030018[/C][/ROW]
[ROW][C]beta[/C][C]2.73040657225417[/C][/ROW]
[ROW][C]S.D.[/C][C]0.60551708790384[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.50921473034923[/C][/ROW]
[ROW][C]p-value[/C][C]0.00634548141088133[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.73040657225417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116867&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116867&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-20.2060412030018
beta2.73040657225417
S.D.0.60551708790384
T-STAT4.50921473034923
p-value0.00634548141088133
Lambda-1.73040657225417


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')