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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, 22 Nov 2015 14:31:09 +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/2015/Nov/22/t14482026883exilduji2x3e2b.htm/, Retrieved Wed, 15 May 2024 03:07:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283809, Retrieved Wed, 15 May 2024 03:07:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124

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] [] [2015-11-22 14:31:09] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
173019
173690
172439
171914
171968
169500
173898
172308
171568
164939
161275
160770
162466
160185
154836
154103
150495
142707
149962
149967
144572
143819
141070
144119
145330
143279
139063
139202
133632
134476
141859
140693
138047
138346
140167
146796
152228
155410
159032
160312
157687
160141
167421
167628
164403
163405
163229
171154
173323
172381
168983
165380
161641
161933
172018
168455
164332
161193
157645
161694
163411
161834
159511
156359
154223
151497
160607
159672
155601
154668
153960
157307
165218
165616
162212
159787
157454
156485
165887
166836
163541
163973
164805
167521
174347
173374
172198
171055
168385
167281
177670
177280
174846
174476
174595
178392
185345
183293
181081
177795
173552
170734
179293
178659
175894
174815
173506
175376

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=283809&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=283809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283809&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
11697744726.7596819501113128
2149858.4166666676971.0488901447221396
3140074.1666666673912.3936600903513164
4161837.55447.565286020418926
5165748.1666666675177.6353998068815678
6157387.53621.3840774438211914
7163277.9166666673605.1771223246911036
8173658.253470.8849310435911111
9177445.254308.0574851613314611

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 169774 & 4726.75968195011 & 13128 \tabularnewline
2 & 149858.416666667 & 6971.04889014472 & 21396 \tabularnewline
3 & 140074.166666667 & 3912.39366009035 & 13164 \tabularnewline
4 & 161837.5 & 5447.5652860204 & 18926 \tabularnewline
5 & 165748.166666667 & 5177.63539980688 & 15678 \tabularnewline
6 & 157387.5 & 3621.38407744382 & 11914 \tabularnewline
7 & 163277.916666667 & 3605.17712232469 & 11036 \tabularnewline
8 & 173658.25 & 3470.88493104359 & 11111 \tabularnewline
9 & 177445.25 & 4308.05748516133 & 14611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283809&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]169774[/C][C]4726.75968195011[/C][C]13128[/C][/ROW]
[ROW][C]2[/C][C]149858.416666667[/C][C]6971.04889014472[/C][C]21396[/C][/ROW]
[ROW][C]3[/C][C]140074.166666667[/C][C]3912.39366009035[/C][C]13164[/C][/ROW]
[ROW][C]4[/C][C]161837.5[/C][C]5447.5652860204[/C][C]18926[/C][/ROW]
[ROW][C]5[/C][C]165748.166666667[/C][C]5177.63539980688[/C][C]15678[/C][/ROW]
[ROW][C]6[/C][C]157387.5[/C][C]3621.38407744382[/C][C]11914[/C][/ROW]
[ROW][C]7[/C][C]163277.916666667[/C][C]3605.17712232469[/C][C]11036[/C][/ROW]
[ROW][C]8[/C][C]173658.25[/C][C]3470.88493104359[/C][C]11111[/C][/ROW]
[ROW][C]9[/C][C]177445.25[/C][C]4308.05748516133[/C][C]14611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283809&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
11697744726.7596819501113128
2149858.4166666676971.0488901447221396
3140074.1666666673912.3936600903513164
4161837.55447.565286020418926
5165748.1666666675177.6353998068815678
6157387.53621.3840774438211914
7163277.9166666673605.1771223246911036
8173658.253470.8849310435911111
9177445.254308.0574851613314611






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8283.35859462583
beta-0.0228292833629067
S.D.0.0358475887845386
T-STAT-0.636842926873598
p-value0.544482991216948

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8283.35859462583 \tabularnewline
beta & -0.0228292833629067 \tabularnewline
S.D. & 0.0358475887845386 \tabularnewline
T-STAT & -0.636842926873598 \tabularnewline
p-value & 0.544482991216948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283809&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8283.35859462583[/C][/ROW]
[ROW][C]beta[/C][C]-0.0228292833629067[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0358475887845386[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.636842926873598[/C][/ROW]
[ROW][C]p-value[/C][C]0.544482991216948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283809&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283809&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)
alpha8283.35859462583
beta-0.0228292833629067
S.D.0.0358475887845386
T-STAT-0.636842926873598
p-value0.544482991216948






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha15.5076664878708
beta-0.59222313051581
S.D.1.16804811883155
T-STAT-0.507019463468884
p-value0.627719209367069
Lambda1.59222313051581

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 15.5076664878708 \tabularnewline
beta & -0.59222313051581 \tabularnewline
S.D. & 1.16804811883155 \tabularnewline
T-STAT & -0.507019463468884 \tabularnewline
p-value & 0.627719209367069 \tabularnewline
Lambda & 1.59222313051581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283809&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.5076664878708[/C][/ROW]
[ROW][C]beta[/C][C]-0.59222313051581[/C][/ROW]
[ROW][C]S.D.[/C][C]1.16804811883155[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.507019463468884[/C][/ROW]
[ROW][C]p-value[/C][C]0.627719209367069[/C][/ROW]
[ROW][C]Lambda[/C][C]1.59222313051581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283809&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283809&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)
alpha15.5076664878708
beta-0.59222313051581
S.D.1.16804811883155
T-STAT-0.507019463468884
p-value0.627719209367069
Lambda1.59222313051581


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')