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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 24 Nov 2009 09:43:36 -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/2009/Nov/24/t12590810709dptjho8yrp8fuh.htm/, Retrieved Fri, 26 Apr 2024 14:13:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59159, Retrieved Fri, 26 Apr 2024 14:13:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D          [Standard Deviation-Mean Plot] [Standard deviatio...] [2009-11-24 16:43:36] [2622964eb3e61db9b0dfd11950e3a18c] [Current]
-    D            [Standard Deviation-Mean Plot] [Heteroskedasticity] [2009-12-20 10:58:55] [78314577b456b570897d62c50cdb18d4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5560
3922
3759
4138
4634
3996
4308
4429
5219
4929
5755
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5526
4247
3830
4394
4826
4409
4569
4106
4794
3914
3793
4405
4022
4100
4788
3163
3585
3903
4178
3863
4187

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59159&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59159&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14686.75707.2141407728571996
25169.58333333333562.8604636276661939
34660.91666666667416.2214136148151178
44449470.0255312214431717
53991.75405.922770308031625

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4686.75 & 707.214140772857 & 1996 \tabularnewline
2 & 5169.58333333333 & 562.860463627666 & 1939 \tabularnewline
3 & 4660.91666666667 & 416.221413614815 & 1178 \tabularnewline
4 & 4449 & 470.025531221443 & 1717 \tabularnewline
5 & 3991.75 & 405.92277030803 & 1625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59159&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]4686.75[/C][C]707.214140772857[/C][C]1996[/C][/ROW]
[ROW][C]2[/C][C]5169.58333333333[/C][C]562.860463627666[/C][C]1939[/C][/ROW]
[ROW][C]3[/C][C]4660.91666666667[/C][C]416.221413614815[/C][C]1178[/C][/ROW]
[ROW][C]4[/C][C]4449[/C][C]470.025531221443[/C][C]1717[/C][/ROW]
[ROW][C]5[/C][C]3991.75[/C][C]405.92277030803[/C][C]1625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59159&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
14686.75707.2141407728571996
25169.58333333333562.8604636276661939
34660.91666666667416.2214136148151178
44449470.0255312214431717
53991.75405.922770308031625






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-187.241581492912
beta0.152384886619452
S.D.0.145081746908118
T-STAT1.05033810156669
p-value0.37070691161995

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -187.241581492912 \tabularnewline
beta & 0.152384886619452 \tabularnewline
S.D. & 0.145081746908118 \tabularnewline
T-STAT & 1.05033810156669 \tabularnewline
p-value & 0.37070691161995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59159&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-187.241581492912[/C][/ROW]
[ROW][C]beta[/C][C]0.152384886619452[/C][/ROW]
[ROW][C]S.D.[/C][C]0.145081746908118[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.05033810156669[/C][/ROW]
[ROW][C]p-value[/C][C]0.37070691161995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59159&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-187.241581492912
beta0.152384886619452
S.D.0.145081746908118
T-STAT1.05033810156669
p-value0.37070691161995






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.64188511918604
beta1.40698956938905
S.D.1.1726648667689
T-STAT1.19982239534966
p-value0.316321725105070
Lambda-0.406989569389053

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.64188511918604 \tabularnewline
beta & 1.40698956938905 \tabularnewline
S.D. & 1.1726648667689 \tabularnewline
T-STAT & 1.19982239534966 \tabularnewline
p-value & 0.316321725105070 \tabularnewline
Lambda & -0.406989569389053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59159&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.64188511918604[/C][/ROW]
[ROW][C]beta[/C][C]1.40698956938905[/C][/ROW]
[ROW][C]S.D.[/C][C]1.1726648667689[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.19982239534966[/C][/ROW]
[ROW][C]p-value[/C][C]0.316321725105070[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.406989569389053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59159&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59159&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-5.64188511918604
beta1.40698956938905
S.D.1.1726648667689
T-STAT1.19982239534966
p-value0.316321725105070
Lambda-0.406989569389053


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')