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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 computationMon, 07 Jun 2010 06:45:43 +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/Jun/07/t1275893151ji3emycrg6h54m8.htm/, Retrieved Fri, 03 May 2024 19:42:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77845, Retrieved Fri, 03 May 2024 19:42:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198

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] [] [2010-06-07 06:45:43] [aec95ccba2c38285ca49e8d90cbfedc9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77845&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77845&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1136.516.654237789933148
2132.91666666666716.345465500384045
3125.83333333333314.577899420532139
4109.58333333333311.618624025349337
5103.58333333333311.781791292524536
6117.7512.650008983108638

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 136.5 & 16.6542377899331 & 48 \tabularnewline
2 & 132.916666666667 & 16.3454655003840 & 45 \tabularnewline
3 & 125.833333333333 & 14.5778994205321 & 39 \tabularnewline
4 & 109.583333333333 & 11.6186240253493 & 37 \tabularnewline
5 & 103.583333333333 & 11.7817912925245 & 36 \tabularnewline
6 & 117.75 & 12.6500089831086 & 38 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77845&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]136.5[/C][C]16.6542377899331[/C][C]48[/C][/ROW]
[ROW][C]2[/C][C]132.916666666667[/C][C]16.3454655003840[/C][C]45[/C][/ROW]
[ROW][C]3[/C][C]125.833333333333[/C][C]14.5778994205321[/C][C]39[/C][/ROW]
[ROW][C]4[/C][C]109.583333333333[/C][C]11.6186240253493[/C][C]37[/C][/ROW]
[ROW][C]5[/C][C]103.583333333333[/C][C]11.7817912925245[/C][C]36[/C][/ROW]
[ROW][C]6[/C][C]117.75[/C][C]12.6500089831086[/C][C]38[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77845&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
1136.516.654237789933148
2132.91666666666716.345465500384045
3125.83333333333314.577899420532139
4109.58333333333311.618624025349337
5103.58333333333311.781791292524536
6117.7512.650008983108638






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-6.29883308936518
beta0.167208205941734
S.D.0.0210771830099776
T-STAT7.93313821218806
p-value0.00136682155417223

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -6.29883308936518 \tabularnewline
beta & 0.167208205941734 \tabularnewline
S.D. & 0.0210771830099776 \tabularnewline
T-STAT & 7.93313821218806 \tabularnewline
p-value & 0.00136682155417223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77845&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.29883308936518[/C][/ROW]
[ROW][C]beta[/C][C]0.167208205941734[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0210771830099776[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.93313821218806[/C][/ROW]
[ROW][C]p-value[/C][C]0.00136682155417223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77845&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77845&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-6.29883308936518
beta0.167208205941734
S.D.0.0210771830099776
T-STAT7.93313821218806
p-value0.00136682155417223






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.19812607455587
beta1.42387819934898
S.D.0.190184103299379
T-STAT7.48684130086085
p-value0.00170212566778900
Lambda-0.423878199348977

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.19812607455587 \tabularnewline
beta & 1.42387819934898 \tabularnewline
S.D. & 0.190184103299379 \tabularnewline
T-STAT & 7.48684130086085 \tabularnewline
p-value & 0.00170212566778900 \tabularnewline
Lambda & -0.423878199348977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77845&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.19812607455587[/C][/ROW]
[ROW][C]beta[/C][C]1.42387819934898[/C][/ROW]
[ROW][C]S.D.[/C][C]0.190184103299379[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.48684130086085[/C][/ROW]
[ROW][C]p-value[/C][C]0.00170212566778900[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.423878199348977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77845&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77845&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-4.19812607455587
beta1.42387819934898
S.D.0.190184103299379
T-STAT7.48684130086085
p-value0.00170212566778900
Lambda-0.423878199348977


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')