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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 computationThu, 01 Feb 2018 09:20:13 +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/2018/Feb/01/t1517473245x0tphkhe8700nkq.htm/, Retrieved Mon, 29 Apr 2024 03:05:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313454, Retrieved Mon, 29 Apr 2024 03:05:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact37

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] [Vraag 4] [2018-02-01 08:20:13] [b4c215a57d838e3992780a1253393c3b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
15
14
14
8
19
17
18
10
15
16
12
13
10
14
15
20
9
12
13
16
12
14
15
19
16
16
14
14
14
13
18
15
15
15
13
14
15
14
19
16
16
12
10
11
13
14
11
11
16
9
16
19
13
15
14
15
11
14
15
17
16
13
15
14
15
14
12
12
15
17
13
5
7
10
15
9
9
15
14
11
18
20
20
16
15
14
13
18
14
12
9
19
13
12
14
6
14
11
11
14
12
19
13
14
17
12
16
15
15
15
16
15
12
13
14
17
14
14
14
15
11
11
16
12
12
19
18
16
16
13
11
10
14
14
14
16
10
16
7
16
15
17
11
11
10
13
14
13
13
12
10
15
6
15
15
11
14
14
16
12
15
20
12
9
13
15
19
11
11
17
15
14
15
11
12
15
16
16

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313454&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=313454&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313454&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1143.4112114616897711
213.58333333333332.8749176536296711
315.16666666666671.850470865548126
413.752.562846428910999
5142.6967994498529710
614.41666666666671.729862492345635
712.755.0113507524056215
814.08333333333332.712205856136410
913.253.3337120996925313
1014.51.314257481345545
1114.16666666666672.855085839605388
1213.33333333333333.1139957766460910
1312.252.667140109487389
1414.16666666666673.1574826950748211

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14 & 3.41121146168977 & 11 \tabularnewline
2 & 13.5833333333333 & 2.87491765362967 & 11 \tabularnewline
3 & 15.1666666666667 & 1.85047086554812 & 6 \tabularnewline
4 & 13.75 & 2.56284642891099 & 9 \tabularnewline
5 & 14 & 2.69679944985297 & 10 \tabularnewline
6 & 14.4166666666667 & 1.72986249234563 & 5 \tabularnewline
7 & 12.75 & 5.01135075240562 & 15 \tabularnewline
8 & 14.0833333333333 & 2.7122058561364 & 10 \tabularnewline
9 & 13.25 & 3.33371209969253 & 13 \tabularnewline
10 & 14.5 & 1.31425748134554 & 5 \tabularnewline
11 & 14.1666666666667 & 2.85508583960538 & 8 \tabularnewline
12 & 13.3333333333333 & 3.11399577664609 & 10 \tabularnewline
13 & 12.25 & 2.66714010948738 & 9 \tabularnewline
14 & 14.1666666666667 & 3.15748269507482 & 11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313454&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]14[/C][C]3.41121146168977[/C][C]11[/C][/ROW]
[ROW][C]2[/C][C]13.5833333333333[/C][C]2.87491765362967[/C][C]11[/C][/ROW]
[ROW][C]3[/C][C]15.1666666666667[/C][C]1.85047086554812[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]13.75[/C][C]2.56284642891099[/C][C]9[/C][/ROW]
[ROW][C]5[/C][C]14[/C][C]2.69679944985297[/C][C]10[/C][/ROW]
[ROW][C]6[/C][C]14.4166666666667[/C][C]1.72986249234563[/C][C]5[/C][/ROW]
[ROW][C]7[/C][C]12.75[/C][C]5.01135075240562[/C][C]15[/C][/ROW]
[ROW][C]8[/C][C]14.0833333333333[/C][C]2.7122058561364[/C][C]10[/C][/ROW]
[ROW][C]9[/C][C]13.25[/C][C]3.33371209969253[/C][C]13[/C][/ROW]
[ROW][C]10[/C][C]14.5[/C][C]1.31425748134554[/C][C]5[/C][/ROW]
[ROW][C]11[/C][C]14.1666666666667[/C][C]2.85508583960538[/C][C]8[/C][/ROW]
[ROW][C]12[/C][C]13.3333333333333[/C][C]3.11399577664609[/C][C]10[/C][/ROW]
[ROW][C]13[/C][C]12.25[/C][C]2.66714010948738[/C][C]9[/C][/ROW]
[ROW][C]14[/C][C]14.1666666666667[/C][C]3.15748269507482[/C][C]11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313454&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313454&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
1143.4112114616897711
213.58333333333332.8749176536296711
315.16666666666671.850470865548126
413.752.562846428910999
5142.6967994498529710
614.41666666666671.729862492345635
712.755.0113507524056215
814.08333333333332.712205856136410
913.253.3337120996925313
1014.51.314257481345545
1114.16666666666672.855085839605388
1213.33333333333333.1139957766460910
1312.252.667140109487389
1414.16666666666673.1574826950748211






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha12.9820985633335
beta-0.736534464063584
S.D.0.267220347701166
T-STAT-2.75628136255273
p-value0.0173986279216564

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 12.9820985633335 \tabularnewline
beta & -0.736534464063584 \tabularnewline
S.D. & 0.267220347701166 \tabularnewline
T-STAT & -2.75628136255273 \tabularnewline
p-value & 0.0173986279216564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313454&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.9820985633335[/C][/ROW]
[ROW][C]beta[/C][C]-0.736534464063584[/C][/ROW]
[ROW][C]S.D.[/C][C]0.267220347701166[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.75628136255273[/C][/ROW]
[ROW][C]p-value[/C][C]0.0173986279216564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313454&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313454&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)
alpha12.9820985633335
beta-0.736534464063584
S.D.0.267220347701166
T-STAT-2.75628136255273
p-value0.0173986279216564






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha10.6357485505514
beta-3.67751088154617
S.D.1.36021215784582
T-STAT-2.70363035673073
p-value0.0191801171407612
Lambda4.67751088154617

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 10.6357485505514 \tabularnewline
beta & -3.67751088154617 \tabularnewline
S.D. & 1.36021215784582 \tabularnewline
T-STAT & -2.70363035673073 \tabularnewline
p-value & 0.0191801171407612 \tabularnewline
Lambda & 4.67751088154617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313454&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.6357485505514[/C][/ROW]
[ROW][C]beta[/C][C]-3.67751088154617[/C][/ROW]
[ROW][C]S.D.[/C][C]1.36021215784582[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.70363035673073[/C][/ROW]
[ROW][C]p-value[/C][C]0.0191801171407612[/C][/ROW]
[ROW][C]Lambda[/C][C]4.67751088154617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313454&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313454&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)
alpha10.6357485505514
beta-3.67751088154617
S.D.1.36021215784582
T-STAT-2.70363035673073
p-value0.0191801171407612
Lambda4.67751088154617


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')