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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, 30 Dec 2014 12:19:40 +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/2014/Dec/30/t14199420144tcyzkjnojp67v5.htm/, Retrieved Fri, 17 May 2024 18:35:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271732, Retrieved Fri, 17 May 2024 18:35:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

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] [] [2014-12-30 12:19:40] [bdca4dcc63d0690a1e5c4820657ce42d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
55,7
59,2
59,8
61,6
65,8
64,2
67
62,8
65,5
75,2
80,9
83,2
83,7
86,4
85,9
80,4
81,8
87,5
83,7
87
99,7
101,4
101,9
115,7
123,2
136,9
146,8
149,6
146,5
157
147,9
133,6
128,7
100,8
91,8
89,3
96,7
91,6
93,3
93,3
101
100,4
86,9
83,9
80,3
87,7
92,7
95,5
92
87,4
86,8
83,7
85
81,7
90,9
101,5
113,8
120,1
122,1
132,5
140
149,4
144,3
154,4
151,4
145,5
136,8
146,6
145,1
133,6
131,4
127,5
130,1
131,1
132,3
128,6
125,1
128,7
156,1
163,2
159,8
157,4
156,2
152,5
149,4
145,9
144,8
135,9
137,6
136
117,7
111,5
107,8
107,3
102,6
101
98,3
102,7
110,8
112,8
113,4
104,3
93,8
90,5

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'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271732&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271732&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271732&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'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
166.74166666666678.6381246211024927.5
291.258333333333310.833236596304735.3
3129.34166666666723.470928181411467.7
491.94166666666676.3021581200170620.7
599.791666666666717.700100581806350.8
6142.1666666666678.3615280610156126.9
7143.42515.034331922757238.1
8124.79166666666718.450644646699748.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 66.7416666666667 & 8.63812462110249 & 27.5 \tabularnewline
2 & 91.2583333333333 & 10.8332365963047 & 35.3 \tabularnewline
3 & 129.341666666667 & 23.4709281814114 & 67.7 \tabularnewline
4 & 91.9416666666667 & 6.30215812001706 & 20.7 \tabularnewline
5 & 99.7916666666667 & 17.7001005818063 & 50.8 \tabularnewline
6 & 142.166666666667 & 8.36152806101561 & 26.9 \tabularnewline
7 & 143.425 & 15.0343319227572 & 38.1 \tabularnewline
8 & 124.791666666667 & 18.4506446466997 & 48.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271732&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]66.7416666666667[/C][C]8.63812462110249[/C][C]27.5[/C][/ROW]
[ROW][C]2[/C][C]91.2583333333333[/C][C]10.8332365963047[/C][C]35.3[/C][/ROW]
[ROW][C]3[/C][C]129.341666666667[/C][C]23.4709281814114[/C][C]67.7[/C][/ROW]
[ROW][C]4[/C][C]91.9416666666667[/C][C]6.30215812001706[/C][C]20.7[/C][/ROW]
[ROW][C]5[/C][C]99.7916666666667[/C][C]17.7001005818063[/C][C]50.8[/C][/ROW]
[ROW][C]6[/C][C]142.166666666667[/C][C]8.36152806101561[/C][C]26.9[/C][/ROW]
[ROW][C]7[/C][C]143.425[/C][C]15.0343319227572[/C][C]38.1[/C][/ROW]
[ROW][C]8[/C][C]124.791666666667[/C][C]18.4506446466997[/C][C]48.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271732&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271732&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
166.74166666666678.6381246211024927.5
291.258333333333310.833236596304735.3
3129.34166666666723.470928181411467.7
491.94166666666676.3021581200170620.7
599.791666666666717.700100581806350.8
6142.1666666666678.3615280610156126.9
7143.42515.034331922757238.1
8124.79166666666718.450644646699748.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.30840013129516
beta0.0925550400683035
S.D.0.0799658535997098
T-STAT1.15743202757032
p-value0.29108646423781

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.30840013129516 \tabularnewline
beta & 0.0925550400683035 \tabularnewline
S.D. & 0.0799658535997098 \tabularnewline
T-STAT & 1.15743202757032 \tabularnewline
p-value & 0.29108646423781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271732&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.30840013129516[/C][/ROW]
[ROW][C]beta[/C][C]0.0925550400683035[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0799658535997098[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.15743202757032[/C][/ROW]
[ROW][C]p-value[/C][C]0.29108646423781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271732&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271732&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)
alpha3.30840013129516
beta0.0925550400683035
S.D.0.0799658535997098
T-STAT1.15743202757032
p-value0.29108646423781






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.17974654992809
beta0.790268162118057
S.D.0.625570267052572
T-STAT1.26327641152364
p-value0.253357691833676
Lambda0.209731837881943

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.17974654992809 \tabularnewline
beta & 0.790268162118057 \tabularnewline
S.D. & 0.625570267052572 \tabularnewline
T-STAT & 1.26327641152364 \tabularnewline
p-value & 0.253357691833676 \tabularnewline
Lambda & 0.209731837881943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271732&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.17974654992809[/C][/ROW]
[ROW][C]beta[/C][C]0.790268162118057[/C][/ROW]
[ROW][C]S.D.[/C][C]0.625570267052572[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.26327641152364[/C][/ROW]
[ROW][C]p-value[/C][C]0.253357691833676[/C][/ROW]
[ROW][C]Lambda[/C][C]0.209731837881943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271732&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271732&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-1.17974654992809
beta0.790268162118057
S.D.0.625570267052572
T-STAT1.26327641152364
p-value0.253357691833676
Lambda0.209731837881943


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 <- '12'
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')