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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 computationThu, 19 Aug 2010 16:10:17 +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/Aug/19/t12822342226aexaqie7wt2ned.htm/, Retrieved Fri, 03 May 2024 07:57:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79327, Retrieved Fri, 03 May 2024 07:57:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDieter Van Boxel
Estimated Impact155

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] [TIJDREEKS A - Sta...] [2010-08-19 16:10:17] [f91e4cd4d3d1892f3fcf702e4827e40c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
356
355
354
352
372
371
356
346
347
347
348
350
353
350
343
346
373
363
349
350
353
356
355
346
349
348
342
342
379
375
363
361
363
373
367
360
358
367
357
346
386
383
367
354
363
370
361
354
363
366
353
351
389
385
364
348
347
352
342
338
343
354
329
320
353
345
324
310
314
313
310
301
294
296
274
269
292
287
271
256
260
265
263
256
246
245
220
224
240
238
222
203
209
214
216
214
206
196
169
177
193
183
164
142
141
137
140
146
136
124
105
114
135
123
100
74
64
57
62
64

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=79327&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=79327&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79327&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
1354.58.7230103227560826
2353.0833333333338.2291978326989430
3360.16666666666712.561364527306737
4363.83333333333311.746050271035740
5358.16666666666715.959228355311251
6326.33333333333318.242474579614453
7273.58333333333314.939017451768540
8224.2514.542258171524643
9166.16666666666724.807745613502369
1096.530.5420723235779

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 354.5 & 8.72301032275608 & 26 \tabularnewline
2 & 353.083333333333 & 8.22919783269894 & 30 \tabularnewline
3 & 360.166666666667 & 12.5613645273067 & 37 \tabularnewline
4 & 363.833333333333 & 11.7460502710357 & 40 \tabularnewline
5 & 358.166666666667 & 15.9592283553112 & 51 \tabularnewline
6 & 326.333333333333 & 18.2424745796144 & 53 \tabularnewline
7 & 273.583333333333 & 14.9390174517685 & 40 \tabularnewline
8 & 224.25 & 14.5422581715246 & 43 \tabularnewline
9 & 166.166666666667 & 24.8077456135023 & 69 \tabularnewline
10 & 96.5 & 30.54207232357 & 79 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79327&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]354.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]353.083333333333[/C][C]8.22919783269894[/C][C]30[/C][/ROW]
[ROW][C]3[/C][C]360.166666666667[/C][C]12.5613645273067[/C][C]37[/C][/ROW]
[ROW][C]4[/C][C]363.833333333333[/C][C]11.7460502710357[/C][C]40[/C][/ROW]
[ROW][C]5[/C][C]358.166666666667[/C][C]15.9592283553112[/C][C]51[/C][/ROW]
[ROW][C]6[/C][C]326.333333333333[/C][C]18.2424745796144[/C][C]53[/C][/ROW]
[ROW][C]7[/C][C]273.583333333333[/C][C]14.9390174517685[/C][C]40[/C][/ROW]
[ROW][C]8[/C][C]224.25[/C][C]14.5422581715246[/C][C]43[/C][/ROW]
[ROW][C]9[/C][C]166.166666666667[/C][C]24.8077456135023[/C][C]69[/C][/ROW]
[ROW][C]10[/C][C]96.5[/C][C]30.54207232357[/C][C]79[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79327&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79327&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
1354.58.7230103227560826
2353.0833333333338.2291978326989430
3360.16666666666712.561364527306737
4363.83333333333311.746050271035740
5358.16666666666715.959228355311251
6326.33333333333318.242474579614453
7273.58333333333314.939017451768540
8224.2514.542258171524643
9166.16666666666724.807745613502369
1096.530.5420723235779






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha34.4109955552011
beta-0.063901342253109
S.D.0.0127620527928737
T-STAT-5.00713664879927
p-value0.00104348511100454

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 34.4109955552011 \tabularnewline
beta & -0.063901342253109 \tabularnewline
S.D. & 0.0127620527928737 \tabularnewline
T-STAT & -5.00713664879927 \tabularnewline
p-value & 0.00104348511100454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79327&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]34.4109955552011[/C][/ROW]
[ROW][C]beta[/C][C]-0.063901342253109[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0127620527928737[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.00713664879927[/C][/ROW]
[ROW][C]p-value[/C][C]0.00104348511100454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79327&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79327&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)
alpha34.4109955552011
beta-0.063901342253109
S.D.0.0127620527928737
T-STAT-5.00713664879927
p-value0.00104348511100454






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha6.9759649875315
beta-0.765822041177524
S.D.0.190660114390745
T-STAT-4.01668720080607
p-value0.00385892396282383
Lambda1.76582204117752

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.9759649875315 \tabularnewline
beta & -0.765822041177524 \tabularnewline
S.D. & 0.190660114390745 \tabularnewline
T-STAT & -4.01668720080607 \tabularnewline
p-value & 0.00385892396282383 \tabularnewline
Lambda & 1.76582204117752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79327&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.9759649875315[/C][/ROW]
[ROW][C]beta[/C][C]-0.765822041177524[/C][/ROW]
[ROW][C]S.D.[/C][C]0.190660114390745[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.01668720080607[/C][/ROW]
[ROW][C]p-value[/C][C]0.00385892396282383[/C][/ROW]
[ROW][C]Lambda[/C][C]1.76582204117752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79327&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79327&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)
alpha6.9759649875315
beta-0.765822041177524
S.D.0.190660114390745
T-STAT-4.01668720080607
p-value0.00385892396282383
Lambda1.76582204117752


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')