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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 computationMon, 28 Apr 2014 11:30:48 -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/2014/Apr/28/t1398699071ac7zm9hjhf69eyh.htm/, Retrieved Fri, 17 May 2024 04:50:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234692, Retrieved Fri, 17 May 2024 04:50:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

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] [] [2014-04-28 15:30:48] [0eca9a6fc90a8387c91ea907ab097326] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
449
446
447
451
465
460
433
431
437
442
449
450
435
431
434
439
455
452
426
428
433
438
442
446
442
436
444
454
469
471
443
437
444
451
457
460
454
439
441
446
459
456
433
424
430
428
424
419
409
397
397
401
413
413
390
385
397
398
406
412
409
404
412
418
434
431
406
416
424
427
438
444
442
443
453
471
476
476
461
462
460
463
467
468

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234692&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234692&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1446.66666666666710.012113874823134
2438.259.0867035727034629
3450.66666666666711.726685444538535
4437.7513.605647223253940
5401.59.1899154215120728
6421.91666666666713.124981962469640
7461.83333333333311.207410968018534

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 446.666666666667 & 10.0121138748231 & 34 \tabularnewline
2 & 438.25 & 9.08670357270346 & 29 \tabularnewline
3 & 450.666666666667 & 11.7266854445385 & 35 \tabularnewline
4 & 437.75 & 13.6056472232539 & 40 \tabularnewline
5 & 401.5 & 9.18991542151207 & 28 \tabularnewline
6 & 421.916666666667 & 13.1249819624696 & 40 \tabularnewline
7 & 461.833333333333 & 11.2074109680185 & 34 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234692&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]446.666666666667[/C][C]10.0121138748231[/C][C]34[/C][/ROW]
[ROW][C]2[/C][C]438.25[/C][C]9.08670357270346[/C][C]29[/C][/ROW]
[ROW][C]3[/C][C]450.666666666667[/C][C]11.7266854445385[/C][C]35[/C][/ROW]
[ROW][C]4[/C][C]437.75[/C][C]13.6056472232539[/C][C]40[/C][/ROW]
[ROW][C]5[/C][C]401.5[/C][C]9.18991542151207[/C][C]28[/C][/ROW]
[ROW][C]6[/C][C]421.916666666667[/C][C]13.1249819624696[/C][C]40[/C][/ROW]
[ROW][C]7[/C][C]461.833333333333[/C][C]11.2074109680185[/C][C]34[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234692&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
1446.66666666666710.012113874823134
2438.259.0867035727034629
3450.66666666666711.726685444538535
4437.7513.605647223253940
5401.59.1899154215120728
6421.91666666666713.124981962469640
7461.83333333333311.207410968018534






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.29716411275376
beta0.0156521187950988
S.D.0.0399793316686507
T-STAT0.391505263890448
p-value0.711552436002077

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.29716411275376 \tabularnewline
beta & 0.0156521187950988 \tabularnewline
S.D. & 0.0399793316686507 \tabularnewline
T-STAT & 0.391505263890448 \tabularnewline
p-value & 0.711552436002077 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234692&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.29716411275376[/C][/ROW]
[ROW][C]beta[/C][C]0.0156521187950988[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0399793316686507[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.391505263890448[/C][/ROW]
[ROW][C]p-value[/C][C]0.711552436002077[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234692&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)
alpha4.29716411275376
beta0.0156521187950988
S.D.0.0399793316686507
T-STAT0.391505263890448
p-value0.711552436002077






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.21929922463465
beta0.759708213327991
S.D.1.53057013545334
T-STAT0.496356354884041
p-value0.640690993111409
Lambda0.240291786672009

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.21929922463465 \tabularnewline
beta & 0.759708213327991 \tabularnewline
S.D. & 1.53057013545334 \tabularnewline
T-STAT & 0.496356354884041 \tabularnewline
p-value & 0.640690993111409 \tabularnewline
Lambda & 0.240291786672009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234692&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.21929922463465[/C][/ROW]
[ROW][C]beta[/C][C]0.759708213327991[/C][/ROW]
[ROW][C]S.D.[/C][C]1.53057013545334[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.496356354884041[/C][/ROW]
[ROW][C]p-value[/C][C]0.640690993111409[/C][/ROW]
[ROW][C]Lambda[/C][C]0.240291786672009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234692&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234692&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-2.21929922463465
beta0.759708213327991
S.D.1.53057013545334
T-STAT0.496356354884041
p-value0.640690993111409
Lambda0.240291786672009


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')