FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 16 Nov 2016 17:14:17 +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/2016/Nov/16/t14793164684oo4aoobogxjz2z.htm/, Retrieved Sun, 05 May 2024 08:03:42 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 08:03:42 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
95.31
93.47
98.92
101.21
95.19
90.95
93.09
90.16
91.86
88.82
91.58
94.9
99.85
98.03
93.46
94.15
93.47
88.98
89.26
84.62
82.7
84.37
89.52
89.82
93.08
98.02
97.49
97.35
99.33
96.92
96.42
93.94
89.95
94.38
95.13
96.01
100.37
99.57
100.53
106.51
106.22
106.93
98.63738676
98.81560408
98.99382141
99.17203873
99.35025606
99.52847338
99.70669071
99.88490803
100.0631254
100.2413427
100.41956
100.5977773
100.7759947
100.954212
101.1324293
101.3106466
101.4888639
101.6670813
101.8452986
102.0235159
102.2017332
102.3799506
102.5581679
102.7363852
102.9146025
103.0928199
103.2710372
103.4492545
103.6274718
103.8056892

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
193.78833333333333.5931825177773312.39
290.68583333333335.3332242649832417.15
395.66833333333332.55251331875559.38
4101.2189650353.267853329564948.29261324000001
5100.6868859950.6425716929998671.96039059
6102.8254938750.6425717053545511.9603906

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 93.7883333333333 & 3.59318251777733 & 12.39 \tabularnewline
2 & 90.6858333333333 & 5.33322426498324 & 17.15 \tabularnewline
3 & 95.6683333333333 & 2.5525133187555 & 9.38 \tabularnewline
4 & 101.218965035 & 3.26785332956494 & 8.29261324000001 \tabularnewline
5 & 100.686885995 & 0.642571692999867 & 1.96039059 \tabularnewline
6 & 102.825493875 & 0.642571705354551 & 1.9603906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]93.7883333333333[/C][C]3.59318251777733[/C][C]12.39[/C][/ROW]
[ROW][C]2[/C][C]90.6858333333333[/C][C]5.33322426498324[/C][C]17.15[/C][/ROW]
[ROW][C]3[/C][C]95.6683333333333[/C][C]2.5525133187555[/C][C]9.38[/C][/ROW]
[ROW][C]4[/C][C]101.218965035[/C][C]3.26785332956494[/C][C]8.29261324000001[/C][/ROW]
[ROW][C]5[/C][C]100.686885995[/C][C]0.642571692999867[/C][C]1.96039059[/C][/ROW]
[ROW][C]6[/C][C]102.825493875[/C][C]0.642571705354551[/C][C]1.9603906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
193.78833333333333.5931825177773312.39
290.68583333333335.3332242649832417.15
395.66833333333332.55251331875559.38
4101.2189650353.267853329564948.29261324000001
5100.6868859950.6425716929998671.96039059
6102.8254938750.6425717053545511.9603906






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha33.2787097613066
beta-0.313982824395631
S.D.0.104985563767037
T-STAT-2.99072380172534
p-value0.0403092927216982

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 33.2787097613066 \tabularnewline
beta & -0.313982824395631 \tabularnewline
S.D. & 0.104985563767037 \tabularnewline
T-STAT & -2.99072380172534 \tabularnewline
p-value & 0.0403092927216982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]33.2787097613066[/C][/ROW]
[ROW][C]beta[/C][C]-0.313982824395631[/C][/ROW]
[ROW][C]S.D.[/C][C]0.104985563767037[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.99072380172534[/C][/ROW]
[ROW][C]p-value[/C][C]0.0403092927216982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha33.2787097613066
beta-0.313982824395631
S.D.0.104985563767037
T-STAT-2.99072380172534
p-value0.0403092927216982






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha66.1800160252338
beta-14.3016616665306
S.D.5.78155076138686
T-STAT-2.47367224759953
p-value0.0686755685883203
Lambda15.3016616665306

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 66.1800160252338 \tabularnewline
beta & -14.3016616665306 \tabularnewline
S.D. & 5.78155076138686 \tabularnewline
T-STAT & -2.47367224759953 \tabularnewline
p-value & 0.0686755685883203 \tabularnewline
Lambda & 15.3016616665306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]66.1800160252338[/C][/ROW]
[ROW][C]beta[/C][C]-14.3016616665306[/C][/ROW]
[ROW][C]S.D.[/C][C]5.78155076138686[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.47367224759953[/C][/ROW]
[ROW][C]p-value[/C][C]0.0686755685883203[/C][/ROW]
[ROW][C]Lambda[/C][C]15.3016616665306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha66.1800160252338
beta-14.3016616665306
S.D.5.78155076138686
T-STAT-2.47367224759953
p-value0.0686755685883203
Lambda15.3016616665306


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')