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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 26 Dec 2010 16:31:40 +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/Dec/26/t129338100978kwwx8c9rbb0ol.htm/, Retrieved Tue, 07 May 2024 02:12:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115717, Retrieved Tue, 07 May 2024 02:12:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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] [mean plot bel20] [2008-12-10 18:16:19] [74be16979710d4c4e7c6647856088456]
-  M D  [Standard Deviation-Mean Plot] [bel 20 standard d...] [2009-12-19 09:54:01] [a18c43c8b63fa6800a53bb187b9ddd45]
-    D      [Standard Deviation-Mean Plot] [Werkloosheid vrou...] [2010-12-26 16:31:40] [75888b09f354cf7130ae5528df429303] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
313.737
312.276
309.391
302.950
300.316
304.035
333.476
337.698
335.932
323.931
313.927
314.485
313.218
309.664
302.963
298.989
298.423
301.631
329.765
335.083
327.616
309.119
295.916
291.413
291.542
284.678
276.475
272.566
264.981
263.290
296.806
303.598
286.994
276.427
266.424
267.153
268.381
262.522
255.542
253.158
243.803
250.741
280.445
285.257
270.976
261.076
255.603
260.376
263.903
264.291
263.276
262.572
256.167
264.221
293.860
300.713
287.224
275.902
271.115
277.509
279.681
276.239
271.037
266.148
259.497
266.795
298.305
303.725
289.742
276.444
268.606

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115717&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115717&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115717&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1316.84616666666712.991324201756837.382
2309.48333333333314.323664534502743.67
3279.244513.386150634823440.308
4262.32333333333312.149093272064941.454
5273.39608333333314.007198314751944.546

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 316.846166666667 & 12.9913242017568 & 37.382 \tabularnewline
2 & 309.483333333333 & 14.3236645345027 & 43.67 \tabularnewline
3 & 279.2445 & 13.3861506348234 & 40.308 \tabularnewline
4 & 262.323333333333 & 12.1490932720649 & 41.454 \tabularnewline
5 & 273.396083333333 & 14.0071983147519 & 44.546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115717&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]316.846166666667[/C][C]12.9913242017568[/C][C]37.382[/C][/ROW]
[ROW][C]2[/C][C]309.483333333333[/C][C]14.3236645345027[/C][C]43.67[/C][/ROW]
[ROW][C]3[/C][C]279.2445[/C][C]13.3861506348234[/C][C]40.308[/C][/ROW]
[ROW][C]4[/C][C]262.323333333333[/C][C]12.1490932720649[/C][C]41.454[/C][/ROW]
[ROW][C]5[/C][C]273.396083333333[/C][C]14.0071983147519[/C][C]44.546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115717&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115717&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
1316.84616666666712.991324201756837.382
2309.48333333333314.323664534502743.67
3279.244513.386150634823440.308
4262.32333333333312.149093272064941.454
5273.39608333333314.007198314751944.546






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.32698281861862
beta0.014030811929729
S.D.0.019308971674847
T-STAT0.726647289456969
p-value0.520007812394432

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.32698281861862 \tabularnewline
beta & 0.014030811929729 \tabularnewline
S.D. & 0.019308971674847 \tabularnewline
T-STAT & 0.726647289456969 \tabularnewline
p-value & 0.520007812394432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115717&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.32698281861862[/C][/ROW]
[ROW][C]beta[/C][C]0.014030811929729[/C][/ROW]
[ROW][C]S.D.[/C][C]0.019308971674847[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.726647289456969[/C][/ROW]
[ROW][C]p-value[/C][C]0.520007812394432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115717&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115717&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)
alpha9.32698281861862
beta0.014030811929729
S.D.0.019308971674847
T-STAT0.726647289456969
p-value0.520007812394432






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.747286734337189
beta0.325755588958049
S.D.0.41949243396661
T-STAT0.776546994847534
p-value0.494030560501784
Lambda0.674244411041951

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.747286734337189 \tabularnewline
beta & 0.325755588958049 \tabularnewline
S.D. & 0.41949243396661 \tabularnewline
T-STAT & 0.776546994847534 \tabularnewline
p-value & 0.494030560501784 \tabularnewline
Lambda & 0.674244411041951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115717&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.747286734337189[/C][/ROW]
[ROW][C]beta[/C][C]0.325755588958049[/C][/ROW]
[ROW][C]S.D.[/C][C]0.41949243396661[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.776546994847534[/C][/ROW]
[ROW][C]p-value[/C][C]0.494030560501784[/C][/ROW]
[ROW][C]Lambda[/C][C]0.674244411041951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115717&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115717&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)
alpha0.747286734337189
beta0.325755588958049
S.D.0.41949243396661
T-STAT0.776546994847534
p-value0.494030560501784
Lambda0.674244411041951


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')