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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 computationFri, 06 Aug 2010 12:13:02 +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/Aug/06/t1281096765a7qtja80gghum74.htm/, Retrieved Tue, 07 May 2024 03:30:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78469, Retrieved Tue, 07 May 2024 03:30:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

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] [] [2010-08-06 12:13:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94
93
92
90
88
87
88
90
91
91
92
94
88
90
82
83
88
83
85
81
79
71
70
85
88
84
81
93
99
96
90
95
93
86
77
89
90
84
76
96
104
101
95
101
95
90
88
99
81
79
70
95
100
105
107
106
99
86
81
95
82
78
68
96
98
107
102
98
93
69
65
90
87
80
67
85
85
92
87
85
79
58
47
67

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78469&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]1 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=78469&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78469&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 time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
190.83333333333332.329000305762637
282.08333333333336.2589330100459220
389.256.4684549230020222
493.258.0580281819945428
59212.254869162166437
687.166666666666714.357977404617842
776.583333333333313.780475868108345

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 90.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 82.0833333333333 & 6.25893301004592 & 20 \tabularnewline
3 & 89.25 & 6.46845492300202 & 22 \tabularnewline
4 & 93.25 & 8.05802818199454 & 28 \tabularnewline
5 & 92 & 12.2548691621664 & 37 \tabularnewline
6 & 87.1666666666667 & 14.3579774046178 & 42 \tabularnewline
7 & 76.5833333333333 & 13.7804758681083 & 45 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78469&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]90.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]82.0833333333333[/C][C]6.25893301004592[/C][C]20[/C][/ROW]
[ROW][C]3[/C][C]89.25[/C][C]6.46845492300202[/C][C]22[/C][/ROW]
[ROW][C]4[/C][C]93.25[/C][C]8.05802818199454[/C][C]28[/C][/ROW]
[ROW][C]5[/C][C]92[/C][C]12.2548691621664[/C][C]37[/C][/ROW]
[ROW][C]6[/C][C]87.1666666666667[/C][C]14.3579774046178[/C][C]42[/C][/ROW]
[ROW][C]7[/C][C]76.5833333333333[/C][C]13.7804758681083[/C][C]45[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78469&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78469&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
190.83333333333332.329000305762637
282.08333333333336.2589330100459220
389.256.4684549230020222
493.258.0580281819945428
59212.254869162166437
687.166666666666714.357977404617842
776.583333333333313.780475868108345






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha31.911396397988
beta-0.261585005612574
S.D.0.314363151480299
T-STAT-0.832110902250475
p-value0.443260480661788

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 31.911396397988 \tabularnewline
beta & -0.261585005612574 \tabularnewline
S.D. & 0.314363151480299 \tabularnewline
T-STAT & -0.832110902250475 \tabularnewline
p-value & 0.443260480661788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78469&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]31.911396397988[/C][/ROW]
[ROW][C]beta[/C][C]-0.261585005612574[/C][/ROW]
[ROW][C]S.D.[/C][C]0.314363151480299[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.832110902250475[/C][/ROW]
[ROW][C]p-value[/C][C]0.443260480661788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78469&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78469&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)
alpha31.911396397988
beta-0.261585005612574
S.D.0.314363151480299
T-STAT-0.832110902250475
p-value0.443260480661788






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha15.1388818313029
beta-2.92744843609259
S.D.3.81366869403575
T-STAT-0.76762001918805
p-value0.477377979445344
Lambda3.92744843609259

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 15.1388818313029 \tabularnewline
beta & -2.92744843609259 \tabularnewline
S.D. & 3.81366869403575 \tabularnewline
T-STAT & -0.76762001918805 \tabularnewline
p-value & 0.477377979445344 \tabularnewline
Lambda & 3.92744843609259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78469&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.1388818313029[/C][/ROW]
[ROW][C]beta[/C][C]-2.92744843609259[/C][/ROW]
[ROW][C]S.D.[/C][C]3.81366869403575[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.76762001918805[/C][/ROW]
[ROW][C]p-value[/C][C]0.477377979445344[/C][/ROW]
[ROW][C]Lambda[/C][C]3.92744843609259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78469&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78469&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)
alpha15.1388818313029
beta-2.92744843609259
S.D.3.81366869403575
T-STAT-0.76762001918805
p-value0.477377979445344
Lambda3.92744843609259


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')