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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, 08 Dec 2013 08:21:25 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/08/t1386508930fma569f1f3t2im2.htm/, Retrieved Fri, 26 Apr 2024 14:20:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231441, Retrieved Fri, 26 Apr 2024 14:20:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111

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] [] [2013-12-08 13:21:25] [3e2b14d12dd0cca2f2b67dfbdf2cdaf9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327
117008
108811
104519
106758
109337
109078
108293
106534
99197
103493
130676
137448
134704
123725
118277
121225
120528
118240
112514
107304
100001
102082
130455
135574
132540
119920
112454
109415
109843
106365
102304
97968
92462
92286
120092
126656
124144
114045
108120
105698
111203
110030
104009
99772
96301
97680
121563
134210
133111
124527
117589
115699

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ yule.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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231441&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231441&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231441&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 time5 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
112637514399.970302999739209
211047611848.35498363337323
3103221.91666666711618.330090134936296
4116832.2512753.499021658938251
5116752.2511650.766663224735573
6108331.91666666711373.572617402734370
7113807.83333333313012.066706319137909

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 126375 & 14399.9703029997 & 39209 \tabularnewline
2 & 110476 & 11848.354983633 & 37323 \tabularnewline
3 & 103221.916666667 & 11618.3300901349 & 36296 \tabularnewline
4 & 116832.25 & 12753.4990216589 & 38251 \tabularnewline
5 & 116752.25 & 11650.7666632247 & 35573 \tabularnewline
6 & 108331.916666667 & 11373.5726174027 & 34370 \tabularnewline
7 & 113807.833333333 & 13012.0667063191 & 37909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231441&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]126375[/C][C]14399.9703029997[/C][C]39209[/C][/ROW]
[ROW][C]2[/C][C]110476[/C][C]11848.354983633[/C][C]37323[/C][/ROW]
[ROW][C]3[/C][C]103221.916666667[/C][C]11618.3300901349[/C][C]36296[/C][/ROW]
[ROW][C]4[/C][C]116832.25[/C][C]12753.4990216589[/C][C]38251[/C][/ROW]
[ROW][C]5[/C][C]116752.25[/C][C]11650.7666632247[/C][C]35573[/C][/ROW]
[ROW][C]6[/C][C]108331.916666667[/C][C]11373.5726174027[/C][C]34370[/C][/ROW]
[ROW][C]7[/C][C]113807.833333333[/C][C]13012.0667063191[/C][C]37909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231441&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231441&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
112637514399.970302999739209
211047611848.35498363337323
3103221.91666666711618.330090134936296
4116832.2512753.499021658938251
5116752.2511650.766663224735573
6108331.91666666711373.572617402734370
7113807.83333333313012.066706319137909






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1351.77288203362
beta0.120783253052055
S.D.0.0368312892103259
T-STAT3.27936533424936
p-value0.0219699239515002

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1351.77288203362 \tabularnewline
beta & 0.120783253052055 \tabularnewline
S.D. & 0.0368312892103259 \tabularnewline
T-STAT & 3.27936533424936 \tabularnewline
p-value & 0.0219699239515002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231441&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1351.77288203362[/C][/ROW]
[ROW][C]beta[/C][C]0.120783253052055[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0368312892103259[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.27936533424936[/C][/ROW]
[ROW][C]p-value[/C][C]0.0219699239515002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231441&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231441&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)
alpha-1351.77288203362
beta0.120783253052055
S.D.0.0368312892103259
T-STAT3.27936533424936
p-value0.0219699239515002






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.95200321156741
beta1.06299951689883
S.D.0.341187149177699
T-STAT3.11559072333404
p-value0.0263834103540221
Lambda-0.0629995168988271

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.95200321156741 \tabularnewline
beta & 1.06299951689883 \tabularnewline
S.D. & 0.341187149177699 \tabularnewline
T-STAT & 3.11559072333404 \tabularnewline
p-value & 0.0263834103540221 \tabularnewline
Lambda & -0.0629995168988271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231441&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.95200321156741[/C][/ROW]
[ROW][C]beta[/C][C]1.06299951689883[/C][/ROW]
[ROW][C]S.D.[/C][C]0.341187149177699[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.11559072333404[/C][/ROW]
[ROW][C]p-value[/C][C]0.0263834103540221[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0629995168988271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231441&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231441&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-2.95200321156741
beta1.06299951689883
S.D.0.341187149177699
T-STAT3.11559072333404
p-value0.0263834103540221
Lambda-0.0629995168988271


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')