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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 computationMon, 08 Dec 2008 04:16:44 -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/2008/Dec/08/t1228735056w150w1oysxvp57b.htm/, Retrieved Thu, 16 May 2024 12:49:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30375, Retrieved Thu, 16 May 2024 12:49:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [ARIMA Backward Selection] [ARIMA Backward Se...] [2008-12-08 10:48:08] [58bf45a666dc5198906262e8815a9722]
- RMPD      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-08 11:16:44] [63db34dadd44fb018112addcdefe949f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101
104
99
105
107
111
117
119
127
128
135
132
136
143
142
153
145
138
148
152
169
169
161
174
179
191
190
182
175
181
197
194
197
216
221
218
230
227
204
197
199
208
191
202
211
224
224
231
244
235
250
266
288
283
295
312
334
348
383
407

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30375&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30375&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1115.41666666666712.695441797127136
2152.512.929880826280638
3195.08333333333315.715992626697946
4212.33333333333314.182789399533340
5303.7554.9778881171165172

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 115.416666666667 & 12.6954417971271 & 36 \tabularnewline
2 & 152.5 & 12.9298808262806 & 38 \tabularnewline
3 & 195.083333333333 & 15.7159926266979 & 46 \tabularnewline
4 & 212.333333333333 & 14.1827893995333 & 40 \tabularnewline
5 & 303.75 & 54.9778881171165 & 172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30375&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]115.416666666667[/C][C]12.6954417971271[/C][C]36[/C][/ROW]
[ROW][C]2[/C][C]152.5[/C][C]12.9298808262806[/C][C]38[/C][/ROW]
[ROW][C]3[/C][C]195.083333333333[/C][C]15.7159926266979[/C][C]46[/C][/ROW]
[ROW][C]4[/C][C]212.333333333333[/C][C]14.1827893995333[/C][C]40[/C][/ROW]
[ROW][C]5[/C][C]303.75[/C][C]54.9778881171165[/C][C]172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30375&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
1115.41666666666712.695441797127136
2152.512.929880826280638
3195.08333333333315.715992626697946
4212.33333333333314.182789399533340
5303.7554.9778881171165172






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-22.1188444511570
beta0.225819608500339
S.D.0.0729611005460954
T-STAT3.09506856133113
p-value0.0535012232569148

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -22.1188444511570 \tabularnewline
beta & 0.225819608500339 \tabularnewline
S.D. & 0.0729611005460954 \tabularnewline
T-STAT & 3.09506856133113 \tabularnewline
p-value & 0.0535012232569148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30375&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-22.1188444511570[/C][/ROW]
[ROW][C]beta[/C][C]0.225819608500339[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0729611005460954[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.09506856133113[/C][/ROW]
[ROW][C]p-value[/C][C]0.0535012232569148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30375&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-22.1188444511570
beta0.225819608500339
S.D.0.0729611005460954
T-STAT3.09506856133113
p-value0.0535012232569148






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.44595886834948
beta1.40655784533844
S.D.0.567060711473542
T-STAT2.48043607479597
p-value0.0892355134597415
Lambda-0.406557845338445

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.44595886834948 \tabularnewline
beta & 1.40655784533844 \tabularnewline
S.D. & 0.567060711473542 \tabularnewline
T-STAT & 2.48043607479597 \tabularnewline
p-value & 0.0892355134597415 \tabularnewline
Lambda & -0.406557845338445 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30375&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.44595886834948[/C][/ROW]
[ROW][C]beta[/C][C]1.40655784533844[/C][/ROW]
[ROW][C]S.D.[/C][C]0.567060711473542[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.48043607479597[/C][/ROW]
[ROW][C]p-value[/C][C]0.0892355134597415[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.406557845338445[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30375&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30375&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-4.44595886834948
beta1.40655784533844
S.D.0.567060711473542
T-STAT2.48043607479597
p-value0.0892355134597415
Lambda-0.406557845338445


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')