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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, 05 Jul 2013 10:12:40 -0400
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/Jul/05/t1373033701ur63ioz2na4ermi.htm/, Retrieved Thu, 31 Oct 2024 23:00:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210785, Retrieved Thu, 31 Oct 2024 23:00:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJeroen Biesemans
Estimated Impact225

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 1 stap 26] [2013-07-05 14:12:40] [09688f513f3d2798cb35a3603f8bd204] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1155168
1144638
1133976
1111920
1330188
1318626
1155168
1046484
1056978
1056978
1068672
1089696
1155168
1133976
1166694
1220472
1526400
1526400
1461096
1395624
1449402
1514838
1526400
1559118
1657302
1591836
1591836
1690020
1962198
1984254
1929480
1798572
1896726
1896726
1907256
1962198
2005446
2027502
2027502
2092938
2344086
2409390
2419884
2256426
2344086
2311368
2245902
2387334
2419884
2365110
2376672
2452638
2736510
2877744
2877744
2812440
2910492
2812440
2757528
2965434
2997984
2920992
3117198
3194196
3423126
3575052
3554034
3542334
3629994
3619332
3488592
3684768
3750240
3684768
3956946
4087854
4392612
4512858
4480272
4414800
4469610
4535046
4316646
4490766
4600518
4556238
4839942
4937958
5352606
5428566
5330544
5385324
5418042
5450760
5242854
5439066
5547744
5439066
5755650
5853708
6278808
6344280
6365304
6475020
6475020
6518268
6322056
6420246
6485550
6365304
6714474
6779916
7215582
7292580
7401258
7499448
7509942
7521504
7325298
7521504

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210785&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210785&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1113904195118.5063438809283704
21386299167264.20928144425142
31822367149747.710659083392418
42239322158622.61015264414438
52697053226458.290370334600324
63395633.5265993.43257665763776
74257701.5307809.55762363850278
85165201.5337627.331456256894522
96149597.5388664.8345223331079202
107136030429348.0646112831156200

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1139041 & 95118.5063438809 & 283704 \tabularnewline
2 & 1386299 & 167264.20928144 & 425142 \tabularnewline
3 & 1822367 & 149747.710659083 & 392418 \tabularnewline
4 & 2239322 & 158622.61015264 & 414438 \tabularnewline
5 & 2697053 & 226458.290370334 & 600324 \tabularnewline
6 & 3395633.5 & 265993.43257665 & 763776 \tabularnewline
7 & 4257701.5 & 307809.55762363 & 850278 \tabularnewline
8 & 5165201.5 & 337627.331456256 & 894522 \tabularnewline
9 & 6149597.5 & 388664.834522333 & 1079202 \tabularnewline
10 & 7136030 & 429348.064611283 & 1156200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210785&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]1139041[/C][C]95118.5063438809[/C][C]283704[/C][/ROW]
[ROW][C]2[/C][C]1386299[/C][C]167264.20928144[/C][C]425142[/C][/ROW]
[ROW][C]3[/C][C]1822367[/C][C]149747.710659083[/C][C]392418[/C][/ROW]
[ROW][C]4[/C][C]2239322[/C][C]158622.61015264[/C][C]414438[/C][/ROW]
[ROW][C]5[/C][C]2697053[/C][C]226458.290370334[/C][C]600324[/C][/ROW]
[ROW][C]6[/C][C]3395633.5[/C][C]265993.43257665[/C][C]763776[/C][/ROW]
[ROW][C]7[/C][C]4257701.5[/C][C]307809.55762363[/C][C]850278[/C][/ROW]
[ROW][C]8[/C][C]5165201.5[/C][C]337627.331456256[/C][C]894522[/C][/ROW]
[ROW][C]9[/C][C]6149597.5[/C][C]388664.834522333[/C][C]1079202[/C][/ROW]
[ROW][C]10[/C][C]7136030[/C][C]429348.064611283[/C][C]1156200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210785&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
1113904195118.5063438809283704
21386299167264.20928144425142
31822367149747.710659083392418
42239322158622.61015264414438
52697053226458.290370334600324
63395633.5265993.43257665763776
74257701.5307809.55762363850278
85165201.5337627.331456256894522
96149597.5388664.8345223331079202
107136030429348.0646112831156200






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha65141.1099928001
beta0.052990573414391
S.D.0.00349978787465951
T-STAT15.1410814918451
p-value3.58359764182104e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 65141.1099928001 \tabularnewline
beta & 0.052990573414391 \tabularnewline
S.D. & 0.00349978787465951 \tabularnewline
T-STAT & 15.1410814918451 \tabularnewline
p-value & 3.58359764182104e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210785&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]65141.1099928001[/C][/ROW]
[ROW][C]beta[/C][C]0.052990573414391[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00349978787465951[/C][/ROW]
[ROW][C]T-STAT[/C][C]15.1410814918451[/C][/ROW]
[ROW][C]p-value[/C][C]3.58359764182104e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210785&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)
alpha65141.1099928001
beta0.052990573414391
S.D.0.00349978787465951
T-STAT15.1410814918451
p-value3.58359764182104e-07






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.21069868773581
beta0.74647467514631
S.D.0.0667776731902774
T-STAT11.1785068194768
p-value3.67346936710801e-06
Lambda0.25352532485369

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.21069868773581 \tabularnewline
beta & 0.74647467514631 \tabularnewline
S.D. & 0.0667776731902774 \tabularnewline
T-STAT & 11.1785068194768 \tabularnewline
p-value & 3.67346936710801e-06 \tabularnewline
Lambda & 0.25352532485369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210785&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.21069868773581[/C][/ROW]
[ROW][C]beta[/C][C]0.74647467514631[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0667776731902774[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.1785068194768[/C][/ROW]
[ROW][C]p-value[/C][C]3.67346936710801e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.25352532485369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210785&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210785&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)
alpha1.21069868773581
beta0.74647467514631
S.D.0.0667776731902774
T-STAT11.1785068194768
p-value3.67346936710801e-06
Lambda0.25352532485369


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')