FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 12 Aug 2016 21:03:27 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/12/t147103222380qzx3pijt4c3wq.htm/, Retrieved Sun, 05 May 2024 09:10:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296472, Retrieved Sun, 05 May 2024 09:10:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

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] [] [2016-08-12 20:03:27] [517bf63cbd197750110a40d4d2cd39d6] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
465
455
444
424
630
620
465
362
372
372
382
403
434
424
362
372
661
723
558
465
486
496
548
599
610
506
517
382
765
878
620
537
589
651
744
858
858
785
754
568
878
1023
899
765
785
858
961
1085
1002
951
951
785
1023
1178
1054
920
961
1126
1199
1302
1219
1085
1054
806
971
1147
951
837
951
1064
1126
1292
1209
1002
1023
827
992
1137
971
858
961
1085
1064
1312
1271
1106
1116
899
1033
1240
1085
992
1147
1240
1168
1498
1416
1230
1178
940
1075
1199
1044
1044
1219
1312
1261
1622
1529
1354
1281
1023
1116
1281
1157
1126
1271
1395
1261
1581

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'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296472&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296472&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296472&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1449.590.0651279504297268
2510.666666666667111.498335359228361
3638.083333333333149.193259860755496
4851.583333333333136.572630249744517
51037.66666666667142.617309502378517
61041.91666666667145.761610068279486
71036.75137.497190053933485
81149.58333333333154.109440648423599
91211.66666666667184.147832575961682
101281.25166.11010860817558

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 449.5 & 90.0651279504297 & 268 \tabularnewline
2 & 510.666666666667 & 111.498335359228 & 361 \tabularnewline
3 & 638.083333333333 & 149.193259860755 & 496 \tabularnewline
4 & 851.583333333333 & 136.572630249744 & 517 \tabularnewline
5 & 1037.66666666667 & 142.617309502378 & 517 \tabularnewline
6 & 1041.91666666667 & 145.761610068279 & 486 \tabularnewline
7 & 1036.75 & 137.497190053933 & 485 \tabularnewline
8 & 1149.58333333333 & 154.109440648423 & 599 \tabularnewline
9 & 1211.66666666667 & 184.147832575961 & 682 \tabularnewline
10 & 1281.25 & 166.11010860817 & 558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296472&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]449.5[/C][C]90.0651279504297[/C][C]268[/C][/ROW]
[ROW][C]2[/C][C]510.666666666667[/C][C]111.498335359228[/C][C]361[/C][/ROW]
[ROW][C]3[/C][C]638.083333333333[/C][C]149.193259860755[/C][C]496[/C][/ROW]
[ROW][C]4[/C][C]851.583333333333[/C][C]136.572630249744[/C][C]517[/C][/ROW]
[ROW][C]5[/C][C]1037.66666666667[/C][C]142.617309502378[/C][C]517[/C][/ROW]
[ROW][C]6[/C][C]1041.91666666667[/C][C]145.761610068279[/C][C]486[/C][/ROW]
[ROW][C]7[/C][C]1036.75[/C][C]137.497190053933[/C][C]485[/C][/ROW]
[ROW][C]8[/C][C]1149.58333333333[/C][C]154.109440648423[/C][C]599[/C][/ROW]
[ROW][C]9[/C][C]1211.66666666667[/C][C]184.147832575961[/C][C]682[/C][/ROW]
[ROW][C]10[/C][C]1281.25[/C][C]166.11010860817[/C][C]558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296472&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296472&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
1449.590.0651279504297268
2510.666666666667111.498335359228361
3638.083333333333149.193259860755496
4851.583333333333136.572630249744517
51037.66666666667142.617309502378517
61041.91666666667145.761610068279486
71036.75137.497190053933485
81149.58333333333154.109440648423599
91211.66666666667184.147832575961682
101281.25166.11010860817558






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha72.3658932730713
beta0.0753544391674422
S.D.0.0169315322288635
T-STAT4.45053868420627
p-value0.00213776864531764

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 72.3658932730713 \tabularnewline
beta & 0.0753544391674422 \tabularnewline
S.D. & 0.0169315322288635 \tabularnewline
T-STAT & 4.45053868420627 \tabularnewline
p-value & 0.00213776864531764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296472&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]72.3658932730713[/C][/ROW]
[ROW][C]beta[/C][C]0.0753544391674422[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0169315322288635[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.45053868420627[/C][/ROW]
[ROW][C]p-value[/C][C]0.00213776864531764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296472&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296472&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)
alpha72.3658932730713
beta0.0753544391674422
S.D.0.0169315322288635
T-STAT4.45053868420627
p-value0.00213776864531764






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.76660083999266
beta0.468352042900411
S.D.0.0964844284387386
T-STAT4.85417233100764
p-value0.00126513009037642
Lambda0.531647957099589

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.76660083999266 \tabularnewline
beta & 0.468352042900411 \tabularnewline
S.D. & 0.0964844284387386 \tabularnewline
T-STAT & 4.85417233100764 \tabularnewline
p-value & 0.00126513009037642 \tabularnewline
Lambda & 0.531647957099589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296472&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.76660083999266[/C][/ROW]
[ROW][C]beta[/C][C]0.468352042900411[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0964844284387386[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.85417233100764[/C][/ROW]
[ROW][C]p-value[/C][C]0.00126513009037642[/C][/ROW]
[ROW][C]Lambda[/C][C]0.531647957099589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296472&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296472&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)
alpha1.76660083999266
beta0.468352042900411
S.D.0.0964844284387386
T-STAT4.85417233100764
p-value0.00126513009037642
Lambda0.531647957099589


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')