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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 computationWed, 07 Jul 2010 18:21:53 +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/Jul/07/t1278526935puzrkutpmt4hac2.htm/, Retrieved Sun, 05 May 2024 23:15:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77955, Retrieved Sun, 05 May 2024 23:15:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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] [Kelly Janbroers -...] [2010-07-07 18:21:53] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
33
32
31
29
49
48
33
23
24
24
25
27
24
21
15
21
49
48
35
36
51
50
61
63
61
62
58
65
93
94
86
88
102
107
121
127
125
128
117
127
160
162
153
160
177
178
196
212
212
211
204
216
248
250
240
249
275
277
286
302
290
290
277
285
311
300
291
299
332
337
343
360
353
351
341
348
381
358
353
358
399
409
407
419
418
421
414
424
463
437
430
436
474
489
482
492
502
500
493
504
538
516
502
501
541
571
559
569
576
573
562
570
597
573
562
556
600
630
624
634

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=77955&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=77955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77955&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
131.58.7230103227560826
239.516.451029257659348
388.666666666666723.472743703489369
4157.91666666666729.849496214214895
5247.532.503146700812698
6309.58333333333326.793684239975683
7373.08333333333328.108421039491678
8448.33333333333329.576813195269778
9524.66666666666729.289567901879178
10588.08333333333328.114888754839078

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 31.5 & 8.72301032275608 & 26 \tabularnewline
2 & 39.5 & 16.4510292576593 & 48 \tabularnewline
3 & 88.6666666666667 & 23.4727437034893 & 69 \tabularnewline
4 & 157.916666666667 & 29.8494962142148 & 95 \tabularnewline
5 & 247.5 & 32.5031467008126 & 98 \tabularnewline
6 & 309.583333333333 & 26.7936842399756 & 83 \tabularnewline
7 & 373.083333333333 & 28.1084210394916 & 78 \tabularnewline
8 & 448.333333333333 & 29.5768131952697 & 78 \tabularnewline
9 & 524.666666666667 & 29.2895679018791 & 78 \tabularnewline
10 & 588.083333333333 & 28.1148887548390 & 78 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77955&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]31.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]39.5[/C][C]16.4510292576593[/C][C]48[/C][/ROW]
[ROW][C]3[/C][C]88.6666666666667[/C][C]23.4727437034893[/C][C]69[/C][/ROW]
[ROW][C]4[/C][C]157.916666666667[/C][C]29.8494962142148[/C][C]95[/C][/ROW]
[ROW][C]5[/C][C]247.5[/C][C]32.5031467008126[/C][C]98[/C][/ROW]
[ROW][C]6[/C][C]309.583333333333[/C][C]26.7936842399756[/C][C]83[/C][/ROW]
[ROW][C]7[/C][C]373.083333333333[/C][C]28.1084210394916[/C][C]78[/C][/ROW]
[ROW][C]8[/C][C]448.333333333333[/C][C]29.5768131952697[/C][C]78[/C][/ROW]
[ROW][C]9[/C][C]524.666666666667[/C][C]29.2895679018791[/C][C]78[/C][/ROW]
[ROW][C]10[/C][C]588.083333333333[/C][C]28.1148887548390[/C][C]78[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77955&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
131.58.7230103227560826
239.516.451029257659348
388.666666666666723.472743703489369
4157.91666666666729.849496214214895
5247.532.503146700812698
6309.58333333333326.793684239975683
7373.08333333333328.108421039491678
8448.33333333333329.576813195269778
9524.66666666666729.289567901879178
10588.08333333333328.114888754839078






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha18.6076993246182
beta0.0237841837361437
S.D.0.00970543012622229
T-STAT2.45060583887809
p-value0.0398990129835144

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 18.6076993246182 \tabularnewline
beta & 0.0237841837361437 \tabularnewline
S.D. & 0.00970543012622229 \tabularnewline
T-STAT & 2.45060583887809 \tabularnewline
p-value & 0.0398990129835144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77955&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.6076993246182[/C][/ROW]
[ROW][C]beta[/C][C]0.0237841837361437[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00970543012622229[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.45060583887809[/C][/ROW]
[ROW][C]p-value[/C][C]0.0398990129835144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77955&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)
alpha18.6076993246182
beta0.0237841837361437
S.D.0.00970543012622229
T-STAT2.45060583887809
p-value0.0398990129835144






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.51453524526776
beta0.315270873776792
S.D.0.0742547742126645
T-STAT4.24579937276304
p-value0.00281518068852136
Lambda0.684729126223208

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.51453524526776 \tabularnewline
beta & 0.315270873776792 \tabularnewline
S.D. & 0.0742547742126645 \tabularnewline
T-STAT & 4.24579937276304 \tabularnewline
p-value & 0.00281518068852136 \tabularnewline
Lambda & 0.684729126223208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77955&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.51453524526776[/C][/ROW]
[ROW][C]beta[/C][C]0.315270873776792[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0742547742126645[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.24579937276304[/C][/ROW]
[ROW][C]p-value[/C][C]0.00281518068852136[/C][/ROW]
[ROW][C]Lambda[/C][C]0.684729126223208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77955&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77955&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)
alpha1.51453524526776
beta0.315270873776792
S.D.0.0742547742126645
T-STAT4.24579937276304
p-value0.00281518068852136
Lambda0.684729126223208


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.1 ; par2 = 0.99 ; par3 = 0.01 ;
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')