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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 computationSat, 15 May 2010 14:38:11 +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/May/15/t1273934565cb8tecwmxcpnlpw.htm/, Retrieved Sun, 28 Apr 2024 12:22:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76013, Retrieved Sun, 28 Apr 2024 12:22:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact224

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...] [2010-05-15 14:38:11] [2aa5bad7942f7e33426bcac9d4e6ffec] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3592.21
5955.74
4652.25
4211.65
4787.85
3599.73
4174.27
5106.33
5325.75
6604.61
5711.90
6919.30
7048.76
8655.98
6658.53
7247.03
8779.57
6602.49
9832.48
9369.49
8582.76
8206.94
6515.83
8618.10
8505.39
9881.64
9375.29
15642.50
12232.73
6288.93
12473.94
11142.82
10236.32
10581.51
8763.71
10819.04
11636.25
14650.13
10671.38
17468.63
13873.19
13077.58
16866.81
14186.64
19919.87
17681.78
9984.28
17423.09
13514.45
12334.57
12274.56
11752.23
13054.00
12460.98
8626.68
13722.62
12066.22
6798.83
6593.82
6606.19
6315.28
7232.95
6747.44
7803.61
6700.31
5369.53
8081.19
10718.39
9447.21
6815.10
5497.80
6805.31

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=76013&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=76013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76013&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
15053.465833333331094.354707516213327.09
28009.831146.615744012873316.65
310495.31833333332341.495927078299353.57
414786.63583333333122.64205731589935.59
510817.09583333332809.040128142967128.8
67294.511544.874971134035348.86

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5053.46583333333 & 1094.35470751621 & 3327.09 \tabularnewline
2 & 8009.83 & 1146.61574401287 & 3316.65 \tabularnewline
3 & 10495.3183333333 & 2341.49592707829 & 9353.57 \tabularnewline
4 & 14786.6358333333 & 3122.6420573158 & 9935.59 \tabularnewline
5 & 10817.0958333333 & 2809.04012814296 & 7128.8 \tabularnewline
6 & 7294.51 & 1544.87497113403 & 5348.86 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76013&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]5053.46583333333[/C][C]1094.35470751621[/C][C]3327.09[/C][/ROW]
[ROW][C]2[/C][C]8009.83[/C][C]1146.61574401287[/C][C]3316.65[/C][/ROW]
[ROW][C]3[/C][C]10495.3183333333[/C][C]2341.49592707829[/C][C]9353.57[/C][/ROW]
[ROW][C]4[/C][C]14786.6358333333[/C][C]3122.6420573158[/C][C]9935.59[/C][/ROW]
[ROW][C]5[/C][C]10817.0958333333[/C][C]2809.04012814296[/C][C]7128.8[/C][/ROW]
[ROW][C]6[/C][C]7294.51[/C][C]1544.87497113403[/C][C]5348.86[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76013&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
15053.465833333331094.354707516213327.09
28009.831146.615744012873316.65
310495.31833333332341.495927078299353.57
414786.63583333333122.64205731589935.59
510817.09583333332809.040128142967128.8
67294.511544.874971134035348.86






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-224.337085357952
beta0.237438763627238
S.D.0.0487253861069912
T-STAT4.87299912012744
p-value0.00820191718059148

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -224.337085357952 \tabularnewline
beta & 0.237438763627238 \tabularnewline
S.D. & 0.0487253861069912 \tabularnewline
T-STAT & 4.87299912012744 \tabularnewline
p-value & 0.00820191718059148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76013&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-224.337085357952[/C][/ROW]
[ROW][C]beta[/C][C]0.237438763627238[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0487253861069912[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.87299912012744[/C][/ROW]
[ROW][C]p-value[/C][C]0.00820191718059148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76013&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-224.337085357952
beta0.237438763627238
S.D.0.0487253861069912
T-STAT4.87299912012744
p-value0.00820191718059148






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.56112991196893
beta1.10882236487679
S.D.0.260047985611106
T-STAT4.26391445513829
p-value0.0130129832672958
Lambda-0.108822364876789

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.56112991196893 \tabularnewline
beta & 1.10882236487679 \tabularnewline
S.D. & 0.260047985611106 \tabularnewline
T-STAT & 4.26391445513829 \tabularnewline
p-value & 0.0130129832672958 \tabularnewline
Lambda & -0.108822364876789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76013&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.56112991196893[/C][/ROW]
[ROW][C]beta[/C][C]1.10882236487679[/C][/ROW]
[ROW][C]S.D.[/C][C]0.260047985611106[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.26391445513829[/C][/ROW]
[ROW][C]p-value[/C][C]0.0130129832672958[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.108822364876789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76013&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-2.56112991196893
beta1.10882236487679
S.D.0.260047985611106
T-STAT4.26391445513829
p-value0.0130129832672958
Lambda-0.108822364876789


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')