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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 computationSun, 01 Jun 2008 05:51:53 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jun/01/t12123211707znfytvakcv3rh9.htm/, Retrieved Sat, 18 May 2024 16:21:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13655, Retrieved Sat, 18 May 2024 16:21:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact258

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] [S.D.-meanplot eig...] [2008-06-01 11:51:53] [27c64ea554ef4b85171a9127abe82aee] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
42.3
50.8
54.1
38.2
48.4
61.1
54.1
61.4
64.3
57.4
71.7
55.3
55.1
66.8
59.4
64.9
59.2
77.4
75.8
38.3
54
61.8
61.3
104.3
39.7
62.6
50.2
90.9
56.2
50.2
52.8
45.6
69
81.9
73.9
54.9
55.4
64.6
49.6
55.8
44.6
61.5
40.5
48.3
50.9
65.3
56.5
53.2
56.9
79.5
94
68.4
65.9
85.5
77.5
114.8
87.4
107.5
151.7
94.4
67.5
95.2
96.2
70.6
80.1
83.4
115.4
61.5
80.6
94.3
82.6
107.7
79.1
102.8
125.2
106.4
62.3
107.4
67.9
88
76.5
130.5
100.9
85.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13655&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13655&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13655&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
154.9259.3209563496846933.5
264.858333333333316.064441723221866
360.658333333333315.415485622246851.2
453.857.6288328667687424.8
590.291666666666725.582325515634494.8
686.258333333333316.107505779115653.9
794.383333333333321.496758036052968.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 54.925 & 9.32095634968469 & 33.5 \tabularnewline
2 & 64.8583333333333 & 16.0644417232218 & 66 \tabularnewline
3 & 60.6583333333333 & 15.4154856222468 & 51.2 \tabularnewline
4 & 53.85 & 7.62883286676874 & 24.8 \tabularnewline
5 & 90.2916666666667 & 25.5823255156344 & 94.8 \tabularnewline
6 & 86.2583333333333 & 16.1075057791156 & 53.9 \tabularnewline
7 & 94.3833333333333 & 21.4967580360529 & 68.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13655&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]54.925[/C][C]9.32095634968469[/C][C]33.5[/C][/ROW]
[ROW][C]2[/C][C]64.8583333333333[/C][C]16.0644417232218[/C][C]66[/C][/ROW]
[ROW][C]3[/C][C]60.6583333333333[/C][C]15.4154856222468[/C][C]51.2[/C][/ROW]
[ROW][C]4[/C][C]53.85[/C][C]7.62883286676874[/C][C]24.8[/C][/ROW]
[ROW][C]5[/C][C]90.2916666666667[/C][C]25.5823255156344[/C][C]94.8[/C][/ROW]
[ROW][C]6[/C][C]86.2583333333333[/C][C]16.1075057791156[/C][C]53.9[/C][/ROW]
[ROW][C]7[/C][C]94.3833333333333[/C][C]21.4967580360529[/C][C]68.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13655&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13655&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
154.9259.3209563496846933.5
264.858333333333316.064441723221866
360.658333333333315.415485622246851.2
453.857.6288328667687424.8
590.291666666666725.582325515634494.8
686.258333333333316.107505779115653.9
794.383333333333321.496758036052968.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.50284286955878
beta0.311022229659333
S.D.0.0801872378771892
T-STAT3.87869987660230
p-value0.011657222123183

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6.50284286955878 \tabularnewline
beta & 0.311022229659333 \tabularnewline
S.D. & 0.0801872378771892 \tabularnewline
T-STAT & 3.87869987660230 \tabularnewline
p-value & 0.011657222123183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13655&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.50284286955878[/C][/ROW]
[ROW][C]beta[/C][C]0.311022229659333[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0801872378771892[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.87869987660230[/C][/ROW]
[ROW][C]p-value[/C][C]0.011657222123183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13655&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13655&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-6.50284286955878
beta0.311022229659333
S.D.0.0801872378771892
T-STAT3.87869987660230
p-value0.011657222123183






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.86942069863953
beta1.54315792320640
S.D.0.392195965879166
T-STAT3.93466036741908
p-value0.0110186893912023
Lambda-0.543157923206397

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.86942069863953 \tabularnewline
beta & 1.54315792320640 \tabularnewline
S.D. & 0.392195965879166 \tabularnewline
T-STAT & 3.93466036741908 \tabularnewline
p-value & 0.0110186893912023 \tabularnewline
Lambda & -0.543157923206397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13655&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.86942069863953[/C][/ROW]
[ROW][C]beta[/C][C]1.54315792320640[/C][/ROW]
[ROW][C]S.D.[/C][C]0.392195965879166[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.93466036741908[/C][/ROW]
[ROW][C]p-value[/C][C]0.0110186893912023[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.543157923206397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13655&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13655&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-3.86942069863953
beta1.54315792320640
S.D.0.392195965879166
T-STAT3.93466036741908
p-value0.0110186893912023
Lambda-0.543157923206397


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')