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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 computationFri, 29 Nov 2013 12:23:11 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/29/t1385745832ojljlage2ey6jmu.htm/, Retrieved Sun, 05 May 2024 23:09:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229578, Retrieved Sun, 05 May 2024 23:09:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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] [] [2013-11-29 17:23:11] [27a1831061bd99e933e6c6e7cff94cc2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
339
139
186
155
153
222
102
107
188
162
185
24
394
209
248
254
202
258
215
309
240
258
276
48
455
345
311
346
310
297
300
274
292
304
186
14
321
206
160
217
204
246
234
175
364
328
158
40
556
193
221
278
230
253
240
252
228
306
206
48
557
279
399
364
306
471
293
333
316
329
265
61
679
428
394
352
387
590
177
199
203
255
261
115

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 Maurice George Kendall' @ kendall.wessa.net

\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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229578&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229578&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 Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1163.575.6853534527832315
2242.58333333333380.0539117587566346
3286.166666666667105.16120381528441
4221.08333333333388.3119042045999324
5250.916666666667114.959643775412508
6331.083333333333120.095006582541496
7336.666666666667170.456783823687564

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 163.5 & 75.6853534527832 & 315 \tabularnewline
2 & 242.583333333333 & 80.0539117587566 & 346 \tabularnewline
3 & 286.166666666667 & 105.16120381528 & 441 \tabularnewline
4 & 221.083333333333 & 88.3119042045999 & 324 \tabularnewline
5 & 250.916666666667 & 114.959643775412 & 508 \tabularnewline
6 & 331.083333333333 & 120.095006582541 & 496 \tabularnewline
7 & 336.666666666667 & 170.456783823687 & 564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229578&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]163.5[/C][C]75.6853534527832[/C][C]315[/C][/ROW]
[ROW][C]2[/C][C]242.583333333333[/C][C]80.0539117587566[/C][C]346[/C][/ROW]
[ROW][C]3[/C][C]286.166666666667[/C][C]105.16120381528[/C][C]441[/C][/ROW]
[ROW][C]4[/C][C]221.083333333333[/C][C]88.3119042045999[/C][C]324[/C][/ROW]
[ROW][C]5[/C][C]250.916666666667[/C][C]114.959643775412[/C][C]508[/C][/ROW]
[ROW][C]6[/C][C]331.083333333333[/C][C]120.095006582541[/C][C]496[/C][/ROW]
[ROW][C]7[/C][C]336.666666666667[/C][C]170.456783823687[/C][C]564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229578&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
1163.575.6853534527832315
2242.58333333333380.0539117587566346
3286.166666666667105.16120381528441
4221.08333333333388.3119042045999324
5250.916666666667114.959643775412508
6331.083333333333120.095006582541496
7336.666666666667170.456783823687564






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.60215526657136
beta0.433372758885949
S.D.0.133511827234482
T-STAT3.24595032412246
p-value0.0227981111454496

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.60215526657136 \tabularnewline
beta & 0.433372758885949 \tabularnewline
S.D. & 0.133511827234482 \tabularnewline
T-STAT & 3.24595032412246 \tabularnewline
p-value & 0.0227981111454496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229578&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.60215526657136[/C][/ROW]
[ROW][C]beta[/C][C]0.433372758885949[/C][/ROW]
[ROW][C]S.D.[/C][C]0.133511827234482[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.24595032412246[/C][/ROW]
[ROW][C]p-value[/C][C]0.0227981111454496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229578&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229578&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-5.60215526657136
beta0.433372758885949
S.D.0.133511827234482
T-STAT3.24595032412246
p-value0.0227981111454496






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.499277829157951
beta0.928385621866054
S.D.0.275803138323907
T-STAT3.36611696120639
p-value0.0199741171710988
Lambda0.0716143781339457

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.499277829157951 \tabularnewline
beta & 0.928385621866054 \tabularnewline
S.D. & 0.275803138323907 \tabularnewline
T-STAT & 3.36611696120639 \tabularnewline
p-value & 0.0199741171710988 \tabularnewline
Lambda & 0.0716143781339457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229578&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.499277829157951[/C][/ROW]
[ROW][C]beta[/C][C]0.928385621866054[/C][/ROW]
[ROW][C]S.D.[/C][C]0.275803138323907[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.36611696120639[/C][/ROW]
[ROW][C]p-value[/C][C]0.0199741171710988[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0716143781339457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229578&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229578&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-0.499277829157951
beta0.928385621866054
S.D.0.275803138323907
T-STAT3.36611696120639
p-value0.0199741171710988
Lambda0.0716143781339457


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')