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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 computationTue, 02 Dec 2008 16:37:24 -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/03/t1228261130gzqlehry6slt8ss.htm/, Retrieved Fri, 17 May 2024 19:08:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28536, Retrieved Fri, 17 May 2024 19:08:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact215

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] [Gilliam Schoorel] [2008-12-02 23:37:24] [4a7b7ae341cb1fe8993cedd56bcfa583] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
119,5
125
145
105,3
116,9
120,1
88,9
78,4
114,6
113,3
117
99,6
99,4
101,9
115,2
108,5
113,8
121
92,2
90,2
101,5
126,6
93,9
89,8
93,4
101,5
110,4
105,9
108,4
113,9
86,1
69,4
101,2
100,5
98
106,6
90,1
96,9
125,9
112
100
123,9
79,8
83,4
113,6
112,9
104
109,9
99
106,3
128,9
111,1
102,9
130
87
87,5
117,6
103,4
110,8
112,6
102,5
112,4
135,6
105,1
127,7
137
91
90,5
122,4
123,3
124,3
120
118,1
119
142,7
123,6
129,6
151,6
110,4
99,2
130,5
136,2
129,7
128
121,6
135,8
143,8
147,5
136,2
156,6
123,3
104,5
143,6

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28536&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28536&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28536&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1111.96666666666717.316641146771566.6
2104.512.444933251583336.8
399.608333333333312.171237207100844.5
4104.36666666666714.813405067605846.1
5108.09166666666713.630811243338243
6115.98333333333315.755104992774046.5
7126.5514.027019381439352.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 111.966666666667 & 17.3166411467715 & 66.6 \tabularnewline
2 & 104.5 & 12.4449332515833 & 36.8 \tabularnewline
3 & 99.6083333333333 & 12.1712372071008 & 44.5 \tabularnewline
4 & 104.366666666667 & 14.8134050676058 & 46.1 \tabularnewline
5 & 108.091666666667 & 13.6308112433382 & 43 \tabularnewline
6 & 115.983333333333 & 15.7551049927740 & 46.5 \tabularnewline
7 & 126.55 & 14.0270193814393 & 52.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28536&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]111.966666666667[/C][C]17.3166411467715[/C][C]66.6[/C][/ROW]
[ROW][C]2[/C][C]104.5[/C][C]12.4449332515833[/C][C]36.8[/C][/ROW]
[ROW][C]3[/C][C]99.6083333333333[/C][C]12.1712372071008[/C][C]44.5[/C][/ROW]
[ROW][C]4[/C][C]104.366666666667[/C][C]14.8134050676058[/C][C]46.1[/C][/ROW]
[ROW][C]5[/C][C]108.091666666667[/C][C]13.6308112433382[/C][C]43[/C][/ROW]
[ROW][C]6[/C][C]115.983333333333[/C][C]15.7551049927740[/C][C]46.5[/C][/ROW]
[ROW][C]7[/C][C]126.55[/C][C]14.0270193814393[/C][C]52.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28536&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28536&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
1111.96666666666717.316641146771566.6
2104.512.444933251583336.8
399.608333333333312.171237207100844.5
4104.36666666666714.813405067605846.1
5108.09166666666713.630811243338243
6115.98333333333315.755104992774046.5
7126.5514.027019381439352.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.07564012459102
beta0.0838185259620557
S.D.0.0824508460438442
T-STAT1.01658782151834
p-value0.355989781435845

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.07564012459102 \tabularnewline
beta & 0.0838185259620557 \tabularnewline
S.D. & 0.0824508460438442 \tabularnewline
T-STAT & 1.01658782151834 \tabularnewline
p-value & 0.355989781435845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28536&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.07564012459102[/C][/ROW]
[ROW][C]beta[/C][C]0.0838185259620557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0824508460438442[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.01658782151834[/C][/ROW]
[ROW][C]p-value[/C][C]0.355989781435845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28536&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28536&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)
alpha5.07564012459102
beta0.0838185259620557
S.D.0.0824508460438442
T-STAT1.01658782151834
p-value0.355989781435845






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.765400820990676
beta0.72767566062631
S.D.0.624467719642049
T-STAT1.16527346048155
p-value0.296471321212962
Lambda0.27232433937369

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.765400820990676 \tabularnewline
beta & 0.72767566062631 \tabularnewline
S.D. & 0.624467719642049 \tabularnewline
T-STAT & 1.16527346048155 \tabularnewline
p-value & 0.296471321212962 \tabularnewline
Lambda & 0.27232433937369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28536&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.765400820990676[/C][/ROW]
[ROW][C]beta[/C][C]0.72767566062631[/C][/ROW]
[ROW][C]S.D.[/C][C]0.624467719642049[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16527346048155[/C][/ROW]
[ROW][C]p-value[/C][C]0.296471321212962[/C][/ROW]
[ROW][C]Lambda[/C][C]0.27232433937369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28536&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28536&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-0.765400820990676
beta0.72767566062631
S.D.0.624467719642049
T-STAT1.16527346048155
p-value0.296471321212962
Lambda0.27232433937369


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')