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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 computationSat, 06 Dec 2008 12:53:03 -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/2008/Dec/06/t1228593226pocmp3lfwkdqlrx.htm/, Retrieved Sat, 25 May 2024 21:00:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29807, Retrieved Sat, 25 May 2024 21:00:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [] [2008-12-06 19:53:03] [19ef54504342c1b076371d395a2ab19f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86,7
87,9
89,8
103
102,7
156,3
95
84,6
106,5
98,7
103,5
110,7
96,2
89,2
97,1
104,8
132,5
154,8
83,6
82,4
103,9
87
93,2
110,5
96,4
76,3
94
103,4
137
150,1
112,6
81,4
113,6
99,6
98,2
118,6
86,8
79,3
98,4
93,6
101
161,2
92,5
99,8
104,1
90,2
99,2
116,5
98,4
90,6
130,5
107,4
106
196,5
107,8
90,5
123,8
114,7
115,3
197
88,4
93,8
111,3
105,9
123,6
171
97
99,2
126,6
103,4
121,3
129,6
110,8
98,9
122,8
120,9
133,1
203,1
110,2
119,5
135,1
113,9
137,4
157,1
126,4
112,2
128,8
136,8
156,5
215,2
146,7
130,8
133,1
154,4
160,4
175,1
145,3

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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29807&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29807&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29807&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' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1102.11666666666719.051119429449671.7
2102.93333333333321.400906239661672.4
3106.76666666666721.300462365162373.8
4101.88333333333320.872244873530281.9
5123.20833333333336.3535282352555106.5
6114.25833333333322.467085352631482.6
7130.23333333333327.6335544824283104.2
8148.03333333333327.434263027805103

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.116666666667 & 19.0511194294496 & 71.7 \tabularnewline
2 & 102.933333333333 & 21.4009062396616 & 72.4 \tabularnewline
3 & 106.766666666667 & 21.3004623651623 & 73.8 \tabularnewline
4 & 101.883333333333 & 20.8722448735302 & 81.9 \tabularnewline
5 & 123.208333333333 & 36.3535282352555 & 106.5 \tabularnewline
6 & 114.258333333333 & 22.4670853526314 & 82.6 \tabularnewline
7 & 130.233333333333 & 27.6335544824283 & 104.2 \tabularnewline
8 & 148.033333333333 & 27.434263027805 & 103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29807&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]102.116666666667[/C][C]19.0511194294496[/C][C]71.7[/C][/ROW]
[ROW][C]2[/C][C]102.933333333333[/C][C]21.4009062396616[/C][C]72.4[/C][/ROW]
[ROW][C]3[/C][C]106.766666666667[/C][C]21.3004623651623[/C][C]73.8[/C][/ROW]
[ROW][C]4[/C][C]101.883333333333[/C][C]20.8722448735302[/C][C]81.9[/C][/ROW]
[ROW][C]5[/C][C]123.208333333333[/C][C]36.3535282352555[/C][C]106.5[/C][/ROW]
[ROW][C]6[/C][C]114.258333333333[/C][C]22.4670853526314[/C][C]82.6[/C][/ROW]
[ROW][C]7[/C][C]130.233333333333[/C][C]27.6335544824283[/C][C]104.2[/C][/ROW]
[ROW][C]8[/C][C]148.033333333333[/C][C]27.434263027805[/C][C]103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29807&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29807&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
1102.11666666666719.051119429449671.7
2102.93333333333321.400906239661672.4
3106.76666666666721.300462365162373.8
4101.88333333333320.872244873530281.9
5123.20833333333336.3535282352555106.5
6114.25833333333322.467085352631482.6
7130.23333333333327.6335544824283104.2
8148.03333333333327.434263027805103






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.962818591215035
beta0.219720667864624
S.D.0.106919351428934
T-STAT2.05501310032418
p-value0.0856456007450454

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.962818591215035 \tabularnewline
beta & 0.219720667864624 \tabularnewline
S.D. & 0.106919351428934 \tabularnewline
T-STAT & 2.05501310032418 \tabularnewline
p-value & 0.0856456007450454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29807&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.962818591215035[/C][/ROW]
[ROW][C]beta[/C][C]0.219720667864624[/C][/ROW]
[ROW][C]S.D.[/C][C]0.106919351428934[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.05501310032418[/C][/ROW]
[ROW][C]p-value[/C][C]0.0856456007450454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29807&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29807&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-0.962818591215035
beta0.219720667864624
S.D.0.106919351428934
T-STAT2.05501310032418
p-value0.0856456007450454






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.13518211266471
beta1.11986050082377
S.D.0.438871180193382
T-STAT2.55168384565677
p-value0.0433920444475969
Lambda-0.119860500823774

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.13518211266471 \tabularnewline
beta & 1.11986050082377 \tabularnewline
S.D. & 0.438871180193382 \tabularnewline
T-STAT & 2.55168384565677 \tabularnewline
p-value & 0.0433920444475969 \tabularnewline
Lambda & -0.119860500823774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29807&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.13518211266471[/C][/ROW]
[ROW][C]beta[/C][C]1.11986050082377[/C][/ROW]
[ROW][C]S.D.[/C][C]0.438871180193382[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.55168384565677[/C][/ROW]
[ROW][C]p-value[/C][C]0.0433920444475969[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.119860500823774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29807&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29807&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-2.13518211266471
beta1.11986050082377
S.D.0.438871180193382
T-STAT2.55168384565677
p-value0.0433920444475969
Lambda-0.119860500823774


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')