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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, 03 Sep 2015 08:19:07 +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/2015/Sep/03/t1441264775y5ith70tfdju0bx.htm/, Retrieved Thu, 16 May 2024 10:34:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280476, Retrieved Thu, 16 May 2024 10:34:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
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] [Vraag 3] [2015-09-03 07:19:07] [a8f4aacb10d679ebd3f422aa920ff39a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.2
11.5
7.3
5.8
6.4
10
11.2
11.2
5.2
7
16.5
16.5
15.2
17.3
22.5
17.3
13.6
14.5
18.8
15.5
23.6
18.5
33.9
25.5
26.4
32.5
26.7
21.5
23.3
29.5
15.2
21.5
17.6
9.7
14.5
10
8.2
9.4
16.5
9.7
19.7
23.3
23.6
26.4
20
25.2
25.8
21.2
14.5
27.3
25.5
26.4
22.4
24.5
24.8
30.9
26.4
27.3
29.4
23

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=280476&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=280476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280476&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
19.44.1437795659167412.3
219.68333333333335.8327965120956520.3
320.77.4284465523969522.8
419.08333333333336.6529328233129718.2
525.24.1532024883324616.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.4 & 4.14377956591674 & 12.3 \tabularnewline
2 & 19.6833333333333 & 5.83279651209565 & 20.3 \tabularnewline
3 & 20.7 & 7.42844655239695 & 22.8 \tabularnewline
4 & 19.0833333333333 & 6.65293282331297 & 18.2 \tabularnewline
5 & 25.2 & 4.15320248833246 & 16.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280476&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]9.4[/C][C]4.14377956591674[/C][C]12.3[/C][/ROW]
[ROW][C]2[/C][C]19.6833333333333[/C][C]5.83279651209565[/C][C]20.3[/C][/ROW]
[ROW][C]3[/C][C]20.7[/C][C]7.42844655239695[/C][C]22.8[/C][/ROW]
[ROW][C]4[/C][C]19.0833333333333[/C][C]6.65293282331297[/C][C]18.2[/C][/ROW]
[ROW][C]5[/C][C]25.2[/C][C]4.15320248833246[/C][C]16.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280476&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
19.44.1437795659167412.3
219.68333333333335.8327965120956520.3
320.77.4284465523969522.8
419.08333333333336.6529328233129718.2
525.24.1532024883324616.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.46044801068145
beta0.0628162780508238
S.D.0.142785962608576
T-STAT0.439933148211663
p-value0.689750995449744

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.46044801068145 \tabularnewline
beta & 0.0628162780508238 \tabularnewline
S.D. & 0.142785962608576 \tabularnewline
T-STAT & 0.439933148211663 \tabularnewline
p-value & 0.689750995449744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280476&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.46044801068145[/C][/ROW]
[ROW][C]beta[/C][C]0.0628162780508238[/C][/ROW]
[ROW][C]S.D.[/C][C]0.142785962608576[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.439933148211663[/C][/ROW]
[ROW][C]p-value[/C][C]0.689750995449744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280476&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280476&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)
alpha4.46044801068145
beta0.0628162780508238
S.D.0.142785962608576
T-STAT0.439933148211663
p-value0.689750995449744






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.94881216275726
beta0.261002810711062
S.D.0.384033365945596
T-STAT0.679635765679893
p-value0.545478588807804
Lambda0.738997189288938

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.94881216275726 \tabularnewline
beta & 0.261002810711062 \tabularnewline
S.D. & 0.384033365945596 \tabularnewline
T-STAT & 0.679635765679893 \tabularnewline
p-value & 0.545478588807804 \tabularnewline
Lambda & 0.738997189288938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280476&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.94881216275726[/C][/ROW]
[ROW][C]beta[/C][C]0.261002810711062[/C][/ROW]
[ROW][C]S.D.[/C][C]0.384033365945596[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.679635765679893[/C][/ROW]
[ROW][C]p-value[/C][C]0.545478588807804[/C][/ROW]
[ROW][C]Lambda[/C][C]0.738997189288938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280476&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280476&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)
alpha0.94881216275726
beta0.261002810711062
S.D.0.384033365945596
T-STAT0.679635765679893
p-value0.545478588807804
Lambda0.738997189288938


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')