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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 computationThu, 20 Nov 2014 14:50:18 +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/Nov/20/t1416495039czybav3uuhtstj7.htm/, Retrieved Fri, 17 May 2024 03:44:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257174, Retrieved Fri, 17 May 2024 03:44:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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] [] [2014-11-20 14:50:18] [959220cfe8d8b51f3b8cc01ba011fecd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
123
146
156
127
128
147
128
139
130
118
147
98
141
138
130
145
123
116
90
110
102
109
111
93
120
81
84
87
110
90
108
101
87
118
82
86
103
93
83
91
69
95
96
105
121
101
111
130
134
161
186
244
145
170
164
124
154
126
173
140
142
129
171
107
98
185
142
135
126
126
134
119
134
133
129
96
150
113
99
164
127
148
166
115
199
141
149
131
171
178
181
129
112
186
153
116
190
169
165
160
202
155
257
171
168
202
189
132

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257174&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257174&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1132.2515.852301238162758
2117.33333333333318.302177383297855
396.166666666666714.42115449503639
499.833333333333316.286264895378161
5160.08333333333332.7621131889575120
6134.524.306751774315387
7131.16666666666723.013171459102770
8153.83333333333328.919428302325387
918031.5911379978626125

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 132.25 & 15.8523012381627 & 58 \tabularnewline
2 & 117.333333333333 & 18.3021773832978 & 55 \tabularnewline
3 & 96.1666666666667 & 14.421154495036 & 39 \tabularnewline
4 & 99.8333333333333 & 16.2862648953781 & 61 \tabularnewline
5 & 160.083333333333 & 32.7621131889575 & 120 \tabularnewline
6 & 134.5 & 24.3067517743153 & 87 \tabularnewline
7 & 131.166666666667 & 23.0131714591027 & 70 \tabularnewline
8 & 153.833333333333 & 28.9194283023253 & 87 \tabularnewline
9 & 180 & 31.5911379978626 & 125 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257174&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]132.25[/C][C]15.8523012381627[/C][C]58[/C][/ROW]
[ROW][C]2[/C][C]117.333333333333[/C][C]18.3021773832978[/C][C]55[/C][/ROW]
[ROW][C]3[/C][C]96.1666666666667[/C][C]14.421154495036[/C][C]39[/C][/ROW]
[ROW][C]4[/C][C]99.8333333333333[/C][C]16.2862648953781[/C][C]61[/C][/ROW]
[ROW][C]5[/C][C]160.083333333333[/C][C]32.7621131889575[/C][C]120[/C][/ROW]
[ROW][C]6[/C][C]134.5[/C][C]24.3067517743153[/C][C]87[/C][/ROW]
[ROW][C]7[/C][C]131.166666666667[/C][C]23.0131714591027[/C][C]70[/C][/ROW]
[ROW][C]8[/C][C]153.833333333333[/C][C]28.9194283023253[/C][C]87[/C][/ROW]
[ROW][C]9[/C][C]180[/C][C]31.5911379978626[/C][C]125[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257174&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
1132.2515.852301238162758
2117.33333333333318.302177383297855
396.166666666666714.42115449503639
499.833333333333316.286264895378161
5160.08333333333332.7621131889575120
6134.524.306751774315387
7131.16666666666723.013171459102770
8153.83333333333328.919428302325387
918031.5911379978626125






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8.29292261427188
beta0.232408356462081
S.D.0.0403175027664463
T-STAT5.76445316587167
p-value0.000688127995285119

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -8.29292261427188 \tabularnewline
beta & 0.232408356462081 \tabularnewline
S.D. & 0.0403175027664463 \tabularnewline
T-STAT & 5.76445316587167 \tabularnewline
p-value & 0.000688127995285119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257174&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.29292261427188[/C][/ROW]
[ROW][C]beta[/C][C]0.232408356462081[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0403175027664463[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.76445316587167[/C][/ROW]
[ROW][C]p-value[/C][C]0.000688127995285119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257174&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-8.29292261427188
beta0.232408356462081
S.D.0.0403175027664463
T-STAT5.76445316587167
p-value0.000688127995285119






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.4947541422584
beta1.34881836466882
S.D.0.248263290139071
T-STAT5.43301574676321
p-value0.000973476679285362
Lambda-0.348818364668817

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.4947541422584 \tabularnewline
beta & 1.34881836466882 \tabularnewline
S.D. & 0.248263290139071 \tabularnewline
T-STAT & 5.43301574676321 \tabularnewline
p-value & 0.000973476679285362 \tabularnewline
Lambda & -0.348818364668817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257174&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.4947541422584[/C][/ROW]
[ROW][C]beta[/C][C]1.34881836466882[/C][/ROW]
[ROW][C]S.D.[/C][C]0.248263290139071[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.43301574676321[/C][/ROW]
[ROW][C]p-value[/C][C]0.000973476679285362[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.348818364668817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257174&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257174&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-3.4947541422584
beta1.34881836466882
S.D.0.248263290139071
T-STAT5.43301574676321
p-value0.000973476679285362
Lambda-0.348818364668817


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')