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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, 06 Dec 2010 11:16:00 +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/06/t1291634085unkyzt2pjlucvsy.htm/, Retrieved Sun, 28 Apr 2024 23:53:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105547, Retrieved Sun, 28 Apr 2024 23:53:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

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] [WS9: SMP] [2010-12-03 10:37:40] [1fd136673b2a4fecb5c545b9b4a05d64]
-         [Standard Deviation-Mean Plot] [ws9 stationality ...] [2010-12-06 11:16:00] [2953e4eb3235e2fd3d6373a16d27c72f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65

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=105547&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=105547&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105547&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
158.258.6554414483991920
246.7515.840349322747534
3598.6023252670426321
449.2515.692354826475236
549.59.7467943448089621
652.755.9090326337452814
758.512.714820748507129
845.2515.30522786501434
949.512.124355652982125
1055.57.7244201508376418
1139.7517.211914478058537
125411.489125293076124
13564.3204937989385710
1440.7514.384598244882231
1561.256.515
1648.257.804912982645419
1745.7510.904891868637123
1865.258.0570879768478818

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 58.25 & 8.65544144839919 & 20 \tabularnewline
2 & 46.75 & 15.8403493227475 & 34 \tabularnewline
3 & 59 & 8.60232526704263 & 21 \tabularnewline
4 & 49.25 & 15.6923548264752 & 36 \tabularnewline
5 & 49.5 & 9.74679434480896 & 21 \tabularnewline
6 & 52.75 & 5.90903263374528 & 14 \tabularnewline
7 & 58.5 & 12.7148207485071 & 29 \tabularnewline
8 & 45.25 & 15.305227865014 & 34 \tabularnewline
9 & 49.5 & 12.1243556529821 & 25 \tabularnewline
10 & 55.5 & 7.72442015083764 & 18 \tabularnewline
11 & 39.75 & 17.2119144780585 & 37 \tabularnewline
12 & 54 & 11.4891252930761 & 24 \tabularnewline
13 & 56 & 4.32049379893857 & 10 \tabularnewline
14 & 40.75 & 14.3845982448822 & 31 \tabularnewline
15 & 61.25 & 6.5 & 15 \tabularnewline
16 & 48.25 & 7.8049129826454 & 19 \tabularnewline
17 & 45.75 & 10.9048918686371 & 23 \tabularnewline
18 & 65.25 & 8.05708797684788 & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105547&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]58.25[/C][C]8.65544144839919[/C][C]20[/C][/ROW]
[ROW][C]2[/C][C]46.75[/C][C]15.8403493227475[/C][C]34[/C][/ROW]
[ROW][C]3[/C][C]59[/C][C]8.60232526704263[/C][C]21[/C][/ROW]
[ROW][C]4[/C][C]49.25[/C][C]15.6923548264752[/C][C]36[/C][/ROW]
[ROW][C]5[/C][C]49.5[/C][C]9.74679434480896[/C][C]21[/C][/ROW]
[ROW][C]6[/C][C]52.75[/C][C]5.90903263374528[/C][C]14[/C][/ROW]
[ROW][C]7[/C][C]58.5[/C][C]12.7148207485071[/C][C]29[/C][/ROW]
[ROW][C]8[/C][C]45.25[/C][C]15.305227865014[/C][C]34[/C][/ROW]
[ROW][C]9[/C][C]49.5[/C][C]12.1243556529821[/C][C]25[/C][/ROW]
[ROW][C]10[/C][C]55.5[/C][C]7.72442015083764[/C][C]18[/C][/ROW]
[ROW][C]11[/C][C]39.75[/C][C]17.2119144780585[/C][C]37[/C][/ROW]
[ROW][C]12[/C][C]54[/C][C]11.4891252930761[/C][C]24[/C][/ROW]
[ROW][C]13[/C][C]56[/C][C]4.32049379893857[/C][C]10[/C][/ROW]
[ROW][C]14[/C][C]40.75[/C][C]14.3845982448822[/C][C]31[/C][/ROW]
[ROW][C]15[/C][C]61.25[/C][C]6.5[/C][C]15[/C][/ROW]
[ROW][C]16[/C][C]48.25[/C][C]7.8049129826454[/C][C]19[/C][/ROW]
[ROW][C]17[/C][C]45.75[/C][C]10.9048918686371[/C][C]23[/C][/ROW]
[ROW][C]18[/C][C]65.25[/C][C]8.05708797684788[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105547&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105547&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
158.258.6554414483991920
246.7515.840349322747534
3598.6023252670426321
449.2515.692354826475236
549.59.7467943448089621
652.755.9090326337452814
758.512.714820748507129
845.2515.30522786501434
949.512.124355652982125
1055.57.7244201508376418
1139.7517.211914478058537
125411.489125293076124
13564.3204937989385710
1440.7514.384598244882231
1561.256.515
1648.257.804912982645419
1745.7510.904891868637123
1865.258.0570879768478818






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha29.7832267369449
beta-0.366864404556388
S.D.0.100264736545311
T-STAT-3.65895744802158
p-value0.00211825529961951

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 29.7832267369449 \tabularnewline
beta & -0.366864404556388 \tabularnewline
S.D. & 0.100264736545311 \tabularnewline
T-STAT & -3.65895744802158 \tabularnewline
p-value & 0.00211825529961951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105547&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]29.7832267369449[/C][/ROW]
[ROW][C]beta[/C][C]-0.366864404556388[/C][/ROW]
[ROW][C]S.D.[/C][C]0.100264736545311[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.65895744802158[/C][/ROW]
[ROW][C]p-value[/C][C]0.00211825529961951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105547&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105547&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)
alpha29.7832267369449
beta-0.366864404556388
S.D.0.100264736545311
T-STAT-3.65895744802158
p-value0.00211825529961951






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.33101024475173
beta-1.78227502679297
S.D.0.539730090944166
T-STAT-3.30215983265855
p-value0.00449878662143262
Lambda2.78227502679297

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.33101024475173 \tabularnewline
beta & -1.78227502679297 \tabularnewline
S.D. & 0.539730090944166 \tabularnewline
T-STAT & -3.30215983265855 \tabularnewline
p-value & 0.00449878662143262 \tabularnewline
Lambda & 2.78227502679297 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105547&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.33101024475173[/C][/ROW]
[ROW][C]beta[/C][C]-1.78227502679297[/C][/ROW]
[ROW][C]S.D.[/C][C]0.539730090944166[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.30215983265855[/C][/ROW]
[ROW][C]p-value[/C][C]0.00449878662143262[/C][/ROW]
[ROW][C]Lambda[/C][C]2.78227502679297[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105547&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105547&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)
alpha9.33101024475173
beta-1.78227502679297
S.D.0.539730090944166
T-STAT-3.30215983265855
p-value0.00449878662143262
Lambda2.78227502679297


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')