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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 computationSun, 01 Jun 2008 03:07:45 -0600
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/Jun/01/t1212311408813l1chjxt7rvwd.htm/, Retrieved Sat, 18 May 2024 14:47:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13640, Retrieved Sat, 18 May 2024 14:47:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact267

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] [Spreidings- en ge...] [2008-05-10 09:21:51] [0e940a1545270f585c264b36ea1585a8]
-   PD    [Standard Deviation-Mean Plot] [Spreidings- en ge...] [2008-06-01 09:07:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
492.865
480.961
461.935
456.608
441.977
439.148
488.180
520.564
501.492
485.025
464.196
460.170
467.037
460.070
447.988
442.867
436.087
431.328
484.015
509.673
512.927
502.831
470.984
471.067
476.049
474.605
470.439
461.251
454.724
455.626
516.847
525.192
522.975
518.585
509.239
512.238
519.164
517.009
509.933
509.127
500.857
506.971
569.323
579.714
577.992
565.464
547.344
554.788
562.325
560.854
555.332
543.599
536.662
542.722
593.530
610.763
612.613
611.324
594.167
595.454
590.865
589.379
584.428
573.100
567.456
569.028
620.735
628.884
628.232
612.117
595.404
597.141
593.408
590.072
579.799
574.205
572.775
572.942
619.567
625.809
619.916
587.625
565.742
557.274
560.576
548.854
531.673
525.919
511.038
498.662
555.362
564.591
541.657
527.070
509.846
514.258
516.922

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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13640&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13640&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' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1474.4267524.540069612129981.416
2469.739528.068080740487981.599
3491.48083333333328.234064982291270.468
4538.140530.455563407275078.857
5576.61208333333329.164685309021375.951
6596.39741666666721.872304573502561.428
7588.26116666666722.629620286989768.535
8532.45883333333321.778072975246365.929

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 474.42675 & 24.5400696121299 & 81.416 \tabularnewline
2 & 469.7395 & 28.0680807404879 & 81.599 \tabularnewline
3 & 491.480833333333 & 28.2340649822912 & 70.468 \tabularnewline
4 & 538.1405 & 30.4555634072750 & 78.857 \tabularnewline
5 & 576.612083333333 & 29.1646853090213 & 75.951 \tabularnewline
6 & 596.397416666667 & 21.8723045735025 & 61.428 \tabularnewline
7 & 588.261166666667 & 22.6296202869897 & 68.535 \tabularnewline
8 & 532.458833333333 & 21.7780729752463 & 65.929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13640&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]474.42675[/C][C]24.5400696121299[/C][C]81.416[/C][/ROW]
[ROW][C]2[/C][C]469.7395[/C][C]28.0680807404879[/C][C]81.599[/C][/ROW]
[ROW][C]3[/C][C]491.480833333333[/C][C]28.2340649822912[/C][C]70.468[/C][/ROW]
[ROW][C]4[/C][C]538.1405[/C][C]30.4555634072750[/C][C]78.857[/C][/ROW]
[ROW][C]5[/C][C]576.612083333333[/C][C]29.1646853090213[/C][C]75.951[/C][/ROW]
[ROW][C]6[/C][C]596.397416666667[/C][C]21.8723045735025[/C][C]61.428[/C][/ROW]
[ROW][C]7[/C][C]588.261166666667[/C][C]22.6296202869897[/C][C]68.535[/C][/ROW]
[ROW][C]8[/C][C]532.458833333333[/C][C]21.7780729752463[/C][C]65.929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13640&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
1474.4267524.540069612129981.416
2469.739528.068080740487981.599
3491.48083333333328.234064982291270.468
4538.140530.455563407275078.857
5576.61208333333329.164685309021375.951
6596.39741666666721.872304573502561.428
7588.26116666666722.629620286989768.535
8532.45883333333321.778072975246365.929






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha38.2483024108651
beta-0.0232556672795924
S.D.0.0266670887398313
T-STAT-0.87207372002541
p-value0.416695736342381

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 38.2483024108651 \tabularnewline
beta & -0.0232556672795924 \tabularnewline
S.D. & 0.0266670887398313 \tabularnewline
T-STAT & -0.87207372002541 \tabularnewline
p-value & 0.416695736342381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13640&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]38.2483024108651[/C][/ROW]
[ROW][C]beta[/C][C]-0.0232556672795924[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0266670887398313[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.87207372002541[/C][/ROW]
[ROW][C]p-value[/C][C]0.416695736342381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13640&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13640&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)
alpha38.2483024108651
beta-0.0232556672795924
S.D.0.0266670887398313
T-STAT-0.87207372002541
p-value0.416695736342381






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha6.38743517343744
beta-0.500958301908456
S.D.0.548950482151329
T-STAT-0.912574664194133
p-value0.39665190188296
Lambda1.50095830190846

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.38743517343744 \tabularnewline
beta & -0.500958301908456 \tabularnewline
S.D. & 0.548950482151329 \tabularnewline
T-STAT & -0.912574664194133 \tabularnewline
p-value & 0.39665190188296 \tabularnewline
Lambda & 1.50095830190846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13640&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.38743517343744[/C][/ROW]
[ROW][C]beta[/C][C]-0.500958301908456[/C][/ROW]
[ROW][C]S.D.[/C][C]0.548950482151329[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.912574664194133[/C][/ROW]
[ROW][C]p-value[/C][C]0.39665190188296[/C][/ROW]
[ROW][C]Lambda[/C][C]1.50095830190846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13640&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13640&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)
alpha6.38743517343744
beta-0.500958301908456
S.D.0.548950482151329
T-STAT-0.912574664194133
p-value0.39665190188296
Lambda1.50095830190846


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')