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 computationThu, 15 May 2014 07:58:59 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/15/t14001551467wbdfjiwxocp9sc.htm/, Retrieved Tue, 14 May 2024 16:52:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234876, Retrieved Tue, 14 May 2024 16:52:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

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] [] [2014-05-15 11:58:59] [bc172ccc2f9d668294f33daae64cfa82] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
85
82
92.4
100.3
105.2
104.5
105.1
105
106.5
106
99.4
107.4
89.6
85.3
96.3
107.7
112.7
110.1
110.4
111.6
113.3
109
106.5
113
95.6
93.8
106.4
116.6
119.1
120.9
117.3
117.6
115.3
112.3
107.7
113.4
94.3
97.8
106.6
113
122.4
114.6
115
118.7
110.4
111.6
105.1
107.5
92.9
91
100.2
112.2
116.5
111.2
113.3
112.2
102.2
105.3
96
101.3
86.2
84.4
93.4
104.8
106.2
101.9
105.5
106.4
103.9
108.6
96.4
102.2
90.3
88.5
100.2
111.6
111.5
112.9
110.7
105.5
110.7
108.9
101.3
109.6
94.4
91.4
105.8
112.9
116.1
113.7
112.9
110.7
114.3
109.7
105.7
114

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234876&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234876&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234876&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
199.98.7303025043913525.4
2105.4583333333339.6052503003999528
3111.3333333333338.8824989658759827.1
4109.758.1113276572726628.1
5104.5258.5738635610578925.5
699.99166666666678.0939324450011624.2
7105.1416666666678.3918205125676724.4
8108.4666666666677.9773922981628424.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.9 & 8.73030250439135 & 25.4 \tabularnewline
2 & 105.458333333333 & 9.60525030039995 & 28 \tabularnewline
3 & 111.333333333333 & 8.88249896587598 & 27.1 \tabularnewline
4 & 109.75 & 8.11132765727266 & 28.1 \tabularnewline
5 & 104.525 & 8.57386356105789 & 25.5 \tabularnewline
6 & 99.9916666666667 & 8.09393244500116 & 24.2 \tabularnewline
7 & 105.141666666667 & 8.39182051256767 & 24.4 \tabularnewline
8 & 108.466666666667 & 7.97739229816284 & 24.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234876&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]99.9[/C][C]8.73030250439135[/C][C]25.4[/C][/ROW]
[ROW][C]2[/C][C]105.458333333333[/C][C]9.60525030039995[/C][C]28[/C][/ROW]
[ROW][C]3[/C][C]111.333333333333[/C][C]8.88249896587598[/C][C]27.1[/C][/ROW]
[ROW][C]4[/C][C]109.75[/C][C]8.11132765727266[/C][C]28.1[/C][/ROW]
[ROW][C]5[/C][C]104.525[/C][C]8.57386356105789[/C][C]25.5[/C][/ROW]
[ROW][C]6[/C][C]99.9916666666667[/C][C]8.09393244500116[/C][C]24.2[/C][/ROW]
[ROW][C]7[/C][C]105.141666666667[/C][C]8.39182051256767[/C][C]24.4[/C][/ROW]
[ROW][C]8[/C][C]108.466666666667[/C][C]7.97739229816284[/C][C]24.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234876&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234876&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
199.98.7303025043913525.4
2105.4583333333339.6052503003999528
3111.3333333333338.8824989658759827.1
4109.758.1113276572726628.1
5104.5258.5738635610578925.5
699.99166666666678.0939324450011624.2
7105.1416666666678.3918205125676724.4
8108.4666666666677.9773922981628424.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.65613277200471
beta-0.00104512049331991
S.D.0.0520571107635541
T-STAT-0.0200764214146824
p-value0.984633395464503

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.65613277200471 \tabularnewline
beta & -0.00104512049331991 \tabularnewline
S.D. & 0.0520571107635541 \tabularnewline
T-STAT & -0.0200764214146824 \tabularnewline
p-value & 0.984633395464503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234876&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.65613277200471[/C][/ROW]
[ROW][C]beta[/C][C]-0.00104512049331991[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0520571107635541[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0200764214146824[/C][/ROW]
[ROW][C]p-value[/C][C]0.984633395464503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234876&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234876&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)
alpha8.65613277200471
beta-0.00104512049331991
S.D.0.0520571107635541
T-STAT-0.0200764214146824
p-value0.984633395464503






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.20912611146551
beta-0.0140289655082305
S.D.0.626768282931926
T-STAT-0.0223830176003883
p-value0.982868240133935
Lambda1.01402896550823

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.20912611146551 \tabularnewline
beta & -0.0140289655082305 \tabularnewline
S.D. & 0.626768282931926 \tabularnewline
T-STAT & -0.0223830176003883 \tabularnewline
p-value & 0.982868240133935 \tabularnewline
Lambda & 1.01402896550823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234876&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.20912611146551[/C][/ROW]
[ROW][C]beta[/C][C]-0.0140289655082305[/C][/ROW]
[ROW][C]S.D.[/C][C]0.626768282931926[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0223830176003883[/C][/ROW]
[ROW][C]p-value[/C][C]0.982868240133935[/C][/ROW]
[ROW][C]Lambda[/C][C]1.01402896550823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234876&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234876&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)
alpha2.20912611146551
beta-0.0140289655082305
S.D.0.626768282931926
T-STAT-0.0223830176003883
p-value0.982868240133935
Lambda1.01402896550823


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')