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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 computationMon, 26 Nov 2012 06:00:03 -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/2012/Nov/26/t1353927620gfbuxmz61zzxmya.htm/, Retrieved Tue, 30 Apr 2024 00:14:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=193018, Retrieved Tue, 30 Apr 2024 00:14:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79

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] [] [2012-11-26 11:00:03] [d04b85262060aaf5e7973d5e79a5225e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14
19
16
16
11
13
12
11
6
9
6
15
17
13
12
13
10
14
13
10
11
12
7
11
9
13
12
5
13
11
8
8
8
8
0
3
0
-1
-1
-4
1
-1
0
-1
6
0
-3
-3
4
1
0
-4
-2
3
2
5
6
6
3
4
7
5
6
1
3
6
0
3
4
7
6
6
6
6
2
2
2
3
-1
-4
4
5
3
-1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193018&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]3 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=193018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193018&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
112.33333333333334.0075685971179713
211.91666666666672.4664414311581210
38.166666666666673.9733963794062613
4-0.5833333333333332.5390883594254210
52.333333333333333.1139957766460910
64.52.315952582337647
72.253.0188799849673310

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 12.3333333333333 & 4.00756859711797 & 13 \tabularnewline
2 & 11.9166666666667 & 2.46644143115812 & 10 \tabularnewline
3 & 8.16666666666667 & 3.97339637940626 & 13 \tabularnewline
4 & -0.583333333333333 & 2.53908835942542 & 10 \tabularnewline
5 & 2.33333333333333 & 3.11399577664609 & 10 \tabularnewline
6 & 4.5 & 2.31595258233764 & 7 \tabularnewline
7 & 2.25 & 3.01887998496733 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193018&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]12.3333333333333[/C][C]4.00756859711797[/C][C]13[/C][/ROW]
[ROW][C]2[/C][C]11.9166666666667[/C][C]2.46644143115812[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]8.16666666666667[/C][C]3.97339637940626[/C][C]13[/C][/ROW]
[ROW][C]4[/C][C]-0.583333333333333[/C][C]2.53908835942542[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]2.33333333333333[/C][C]3.11399577664609[/C][C]10[/C][/ROW]
[ROW][C]6[/C][C]4.5[/C][C]2.31595258233764[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]2.25[/C][C]3.01887998496733[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193018&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
112.33333333333334.0075685971179713
211.91666666666672.4664414311581210
38.166666666666673.9733963794062613
4-0.5833333333333332.5390883594254210
52.333333333333333.1139957766460910
64.52.315952582337647
72.253.0188799849673310






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.71882712707038
beta0.0587421561278903
S.D.0.055905992351766
T-STAT1.05073094415853
p-value0.341490318368807

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.71882712707038 \tabularnewline
beta & 0.0587421561278903 \tabularnewline
S.D. & 0.055905992351766 \tabularnewline
T-STAT & 1.05073094415853 \tabularnewline
p-value & 0.341490318368807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193018&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.71882712707038[/C][/ROW]
[ROW][C]beta[/C][C]0.0587421561278903[/C][/ROW]
[ROW][C]S.D.[/C][C]0.055905992351766[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.05073094415853[/C][/ROW]
[ROW][C]p-value[/C][C]0.341490318368807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193018&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)
alpha2.71882712707038
beta0.0587421561278903
S.D.0.055905992351766
T-STAT1.05073094415853
p-value0.341490318368807






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.00639901887012
beta0.0695239505881996
S.D.0.145075498891288
T-STAT0.479225996943132
p-value0.656800431701062
Lambda0.9304760494118

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.00639901887012 \tabularnewline
beta & 0.0695239505881996 \tabularnewline
S.D. & 0.145075498891288 \tabularnewline
T-STAT & 0.479225996943132 \tabularnewline
p-value & 0.656800431701062 \tabularnewline
Lambda & 0.9304760494118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=193018&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.00639901887012[/C][/ROW]
[ROW][C]beta[/C][C]0.0695239505881996[/C][/ROW]
[ROW][C]S.D.[/C][C]0.145075498891288[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.479225996943132[/C][/ROW]
[ROW][C]p-value[/C][C]0.656800431701062[/C][/ROW]
[ROW][C]Lambda[/C][C]0.9304760494118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=193018&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=193018&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)
alpha1.00639901887012
beta0.0695239505881996
S.D.0.145075498891288
T-STAT0.479225996943132
p-value0.656800431701062
Lambda0.9304760494118


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')