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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 computationTue, 27 Nov 2007 02:47:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/27/t1196156232qc4ztrpq72rkwf7.htm/, Retrieved Sun, 05 May 2024 14:51:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6763, Retrieved Sun, 05 May 2024 14:51:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234

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] [statistiek opdrac...] [2007-11-27 09:47:03] [0d8f90662bd29255b957138f6acc6b00] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104
85
110
106
142
138
115
118
118
128
119
114
108
130
109
127
121
131
111
108
122
134
144
125
118
93
106
109
121
137
153
140
135
124
137
113
97
105
101
120
117
123
133
104
136
116
110
91
99
67
102
101
107
114
129
112
97
100
105
81
104
80
97
90
99
103
111
110
88
97
87
97

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6763&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6763&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1116.41666666666715.270043956198845
2122.511.626771614761377
3123.83333333333317.140241503195956
4112.7513.948769903406646
5101.16666666666715.677623505744730
696.91666666666679.404624909956258

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 116.416666666667 & 15.2700439561988 & 45 \tabularnewline
2 & 122.5 & 11.6267716147613 & 77 \tabularnewline
3 & 123.833333333333 & 17.1402415031959 & 56 \tabularnewline
4 & 112.75 & 13.9487699034066 & 46 \tabularnewline
5 & 101.166666666667 & 15.6776235057447 & 30 \tabularnewline
6 & 96.9166666666667 & 9.40462490995625 & 8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6763&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]116.416666666667[/C][C]15.2700439561988[/C][C]45[/C][/ROW]
[ROW][C]2[/C][C]122.5[/C][C]11.6267716147613[/C][C]77[/C][/ROW]
[ROW][C]3[/C][C]123.833333333333[/C][C]17.1402415031959[/C][C]56[/C][/ROW]
[ROW][C]4[/C][C]112.75[/C][C]13.9487699034066[/C][C]46[/C][/ROW]
[ROW][C]5[/C][C]101.166666666667[/C][C]15.6776235057447[/C][C]30[/C][/ROW]
[ROW][C]6[/C][C]96.9166666666667[/C][C]9.40462490995625[/C][C]8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6763&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
1116.41666666666715.270043956198845
2122.511.626771614761377
3123.83333333333317.140241503195956
4112.7513.948769903406646
5101.16666666666715.677623505744730
696.91666666666679.404624909956258






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.20913103622834
beta0.112552204640693
S.D.0.116029792756769
T-STAT0.970028489808937
p-value0.386962061836247

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.20913103622834 \tabularnewline
beta & 0.112552204640693 \tabularnewline
S.D. & 0.116029792756769 \tabularnewline
T-STAT & 0.970028489808937 \tabularnewline
p-value & 0.386962061836247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6763&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.20913103622834[/C][/ROW]
[ROW][C]beta[/C][C]0.112552204640693[/C][/ROW]
[ROW][C]S.D.[/C][C]0.116029792756769[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.970028489808937[/C][/ROW]
[ROW][C]p-value[/C][C]0.386962061836247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6763&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6763&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)
alpha1.20913103622834
beta0.112552204640693
S.D.0.116029792756769
T-STAT0.970028489808937
p-value0.386962061836247






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.27533280084978
beta1.03538652883102
S.D.0.975625076604462
T-STAT1.06125452662057
p-value0.348401317555441
Lambda-0.0353865288310249

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.27533280084978 \tabularnewline
beta & 1.03538652883102 \tabularnewline
S.D. & 0.975625076604462 \tabularnewline
T-STAT & 1.06125452662057 \tabularnewline
p-value & 0.348401317555441 \tabularnewline
Lambda & -0.0353865288310249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6763&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.27533280084978[/C][/ROW]
[ROW][C]beta[/C][C]1.03538652883102[/C][/ROW]
[ROW][C]S.D.[/C][C]0.975625076604462[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.06125452662057[/C][/ROW]
[ROW][C]p-value[/C][C]0.348401317555441[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0353865288310249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6763&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6763&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-2.27533280084978
beta1.03538652883102
S.D.0.975625076604462
T-STAT1.06125452662057
p-value0.348401317555441
Lambda-0.0353865288310249


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')