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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 computationThu, 20 Nov 2014 15:43:09 +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/2014/Nov/20/t14164982453qh2hbv1ajuu4b9.htm/, Retrieved Sun, 19 May 2024 14:11:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257211, Retrieved Sun, 19 May 2024 14:11:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsEline Van Loon
Estimated Impact59

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] [] [2014-11-20 15:43:09] [9adebd9d8505f0d6c7bd6ecbde218cd8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22943
21413
20631
19775
17506
20688
32631
34062
29159
25871
23719
25638
27596
28006
27662
26655
25213
28434
40388
42758
37956
33490
31578
34766
32324
32046
29565
28284
26366
27530
39728
41528
36458
32301
28985
29118
29249
28036
26326
24942
23280
23969
35948
37639
34327
30133
27549
27990
30437
30464
28471
26882
25806
26465
36416
42870
40489
36645
33841
33496
34504
34699
33322
32160
30173
30782
43062
46223
45191
40671
37251
36870

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257211&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257211&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257211&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1245035185.0467517836216556
232041.83333333335824.0038529166417545
332019.41666666674856.3790000806415162
429115.66666666674653.1601838932714359
532690.16666666675589.4407726994617064
637075.66666666675527.9524786362516050

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 24503 & 5185.04675178362 & 16556 \tabularnewline
2 & 32041.8333333333 & 5824.00385291664 & 17545 \tabularnewline
3 & 32019.4166666667 & 4856.37900008064 & 15162 \tabularnewline
4 & 29115.6666666667 & 4653.16018389327 & 14359 \tabularnewline
5 & 32690.1666666667 & 5589.44077269946 & 17064 \tabularnewline
6 & 37075.6666666667 & 5527.95247863625 & 16050 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257211&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]24503[/C][C]5185.04675178362[/C][C]16556[/C][/ROW]
[ROW][C]2[/C][C]32041.8333333333[/C][C]5824.00385291664[/C][C]17545[/C][/ROW]
[ROW][C]3[/C][C]32019.4166666667[/C][C]4856.37900008064[/C][C]15162[/C][/ROW]
[ROW][C]4[/C][C]29115.6666666667[/C][C]4653.16018389327[/C][C]14359[/C][/ROW]
[ROW][C]5[/C][C]32690.1666666667[/C][C]5589.44077269946[/C][C]17064[/C][/ROW]
[ROW][C]6[/C][C]37075.6666666667[/C][C]5527.95247863625[/C][C]16050[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257211&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257211&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
1245035185.0467517836216556
232041.83333333335824.0038529166417545
332019.41666666674856.3790000806415162
429115.66666666674653.1601838932714359
532690.16666666675589.4407726994617064
637075.66666666675527.9524786362516050






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3850.99989242342
beta0.0455064128446195
S.D.0.0494345861235338
T-STAT0.920537955570255
p-value0.409384539414723

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3850.99989242342 \tabularnewline
beta & 0.0455064128446195 \tabularnewline
S.D. & 0.0494345861235338 \tabularnewline
T-STAT & 0.920537955570255 \tabularnewline
p-value & 0.409384539414723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257211&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3850.99989242342[/C][/ROW]
[ROW][C]beta[/C][C]0.0455064128446195[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0494345861235338[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.920537955570255[/C][/ROW]
[ROW][C]p-value[/C][C]0.409384539414723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257211&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257211&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)
alpha3850.99989242342
beta0.0455064128446195
S.D.0.0494345861235338
T-STAT0.920537955570255
p-value0.409384539414723






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.99198110810261
beta0.249007935440745
S.D.0.289086142937111
T-STAT0.861362405374496
p-value0.437611624480626
Lambda0.750992064559255

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.99198110810261 \tabularnewline
beta & 0.249007935440745 \tabularnewline
S.D. & 0.289086142937111 \tabularnewline
T-STAT & 0.861362405374496 \tabularnewline
p-value & 0.437611624480626 \tabularnewline
Lambda & 0.750992064559255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257211&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.99198110810261[/C][/ROW]
[ROW][C]beta[/C][C]0.249007935440745[/C][/ROW]
[ROW][C]S.D.[/C][C]0.289086142937111[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.861362405374496[/C][/ROW]
[ROW][C]p-value[/C][C]0.437611624480626[/C][/ROW]
[ROW][C]Lambda[/C][C]0.750992064559255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257211&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257211&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)
alpha5.99198110810261
beta0.249007935440745
S.D.0.289086142937111
T-STAT0.861362405374496
p-value0.437611624480626
Lambda0.750992064559255


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')