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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, 29 Nov 2007 08:04:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/29/t1196348130j9i3ldv7nkb00mf.htm/, Retrieved Fri, 03 May 2024 09:18:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7505, Retrieved Fri, 03 May 2024 09:18:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208

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] [tijdreeks-goud] [2007-11-29 15:04:54] [6c82e325b196f1aec5740f38b2795d46] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10.137
9.984
9.732
9.103
9.155
9.308
9.394
9.948
10.177
10.002
9.728
10.002
10.063
10.018
9.960
10.236
10.893
10.756
10.940
10.997
10.827
10.166
10.186
10.457
10.368
10.244
10.511
10.812
10.738
10.171
9.721
9.897
9.828
9.924
10.371
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7505&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7505&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7505&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.72250.3860679403232740.113999999999999
210.458250.3980859032465681.013
310.28591666666670.3914421955081521.114
410.541250.1780562347329431.769
510.93250.4832329571843082.809
614.92008333333331.294968196052667.756
715.77483333333330.4230755001035617.044

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.7225 & 0.386067940323274 & 0.113999999999999 \tabularnewline
2 & 10.45825 & 0.398085903246568 & 1.013 \tabularnewline
3 & 10.2859166666667 & 0.391442195508152 & 1.114 \tabularnewline
4 & 10.54125 & 0.178056234732943 & 1.769 \tabularnewline
5 & 10.9325 & 0.483232957184308 & 2.809 \tabularnewline
6 & 14.9200833333333 & 1.29496819605266 & 7.756 \tabularnewline
7 & 15.7748333333333 & 0.423075500103561 & 7.044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7505&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]9.7225[/C][C]0.386067940323274[/C][C]0.113999999999999[/C][/ROW]
[ROW][C]2[/C][C]10.45825[/C][C]0.398085903246568[/C][C]1.013[/C][/ROW]
[ROW][C]3[/C][C]10.2859166666667[/C][C]0.391442195508152[/C][C]1.114[/C][/ROW]
[ROW][C]4[/C][C]10.54125[/C][C]0.178056234732943[/C][C]1.769[/C][/ROW]
[ROW][C]5[/C][C]10.9325[/C][C]0.483232957184308[/C][C]2.809[/C][/ROW]
[ROW][C]6[/C][C]14.9200833333333[/C][C]1.29496819605266[/C][C]7.756[/C][/ROW]
[ROW][C]7[/C][C]15.7748333333333[/C][C]0.423075500103561[/C][C]7.044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7505&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7505&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
19.72250.3860679403232740.113999999999999
210.458250.3980859032465681.013
310.28591666666670.3914421955081521.114
410.541250.1780562347329431.769
510.93250.4832329571843082.809
614.92008333333331.294968196052667.756
715.77483333333330.4230755001035617.044






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.511246192532357
beta0.0863269014248703
S.D.0.0528240598824175
T-STAT1.63423450634100
p-value0.163137469796574

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.511246192532357 \tabularnewline
beta & 0.0863269014248703 \tabularnewline
S.D. & 0.0528240598824175 \tabularnewline
T-STAT & 1.63423450634100 \tabularnewline
p-value & 0.163137469796574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7505&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.511246192532357[/C][/ROW]
[ROW][C]beta[/C][C]0.0863269014248703[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0528240598824175[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.63423450634100[/C][/ROW]
[ROW][C]p-value[/C][C]0.163137469796574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7505&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7505&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-0.511246192532357
beta0.0863269014248703
S.D.0.0528240598824175
T-STAT1.63423450634100
p-value0.163137469796574






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.03302417763293
beta1.71121646228132
S.D.1.09827735665320
T-STAT1.55809136181770
p-value0.179948577058701
Lambda-0.711216462281317

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.03302417763293 \tabularnewline
beta & 1.71121646228132 \tabularnewline
S.D. & 1.09827735665320 \tabularnewline
T-STAT & 1.55809136181770 \tabularnewline
p-value & 0.179948577058701 \tabularnewline
Lambda & -0.711216462281317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7505&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.03302417763293[/C][/ROW]
[ROW][C]beta[/C][C]1.71121646228132[/C][/ROW]
[ROW][C]S.D.[/C][C]1.09827735665320[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.55809136181770[/C][/ROW]
[ROW][C]p-value[/C][C]0.179948577058701[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.711216462281317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7505&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7505&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-5.03302417763293
beta1.71121646228132
S.D.1.09827735665320
T-STAT1.55809136181770
p-value0.179948577058701
Lambda-0.711216462281317


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')