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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 computationWed, 11 Aug 2010 13:23:20 +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/2010/Aug/11/t1281533047ygse8oxhkr7xj5c.htm/, Retrieved Mon, 06 May 2024 04:14:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78632, Retrieved Mon, 06 May 2024 04:14:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJacobs Jeff
Estimated Impact173

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] [Tijdreeks A - Sta...] [2010-08-11 13:23:20] [03859715711bd3369851d387eaa83ba4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
130
129
128
126
146
145
130
120
121
121
122
124
123
125
120
124
146
149
138
133
135
149
146
141
139
141
138
139
166
179
167
154
151
162
148
143
145
143
148
139
169
186
174
161
151
158
144
135
139
137
149
136
169
185
177
164
145
147
142
126
130
136
139
120
151
166
156
150
141
141
130
110
110
123
133
108
136
148
146
142
132
128
116
90
94
112
130
106
124
139
140
129
113
110
102
78
79
94
121
99
126
137
141
119
96
96
88
64
66
92
120
101
135
146
149
134
101
100
91
70

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78632&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78632&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78632&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1128.58.7230103227560826
2135.7510.729102309309829
3152.2513.505049560677841
4154.41666666666715.506352559418051
5151.33333333333318.217540664941259
6139.16666666666715.561218305502856
712617.357209662636758
8114.7518.587018930621362
910523.698868404132077
10108.7527.932141798554383

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 128.5 & 8.72301032275608 & 26 \tabularnewline
2 & 135.75 & 10.7291023093098 & 29 \tabularnewline
3 & 152.25 & 13.5050495606778 & 41 \tabularnewline
4 & 154.416666666667 & 15.5063525594180 & 51 \tabularnewline
5 & 151.333333333333 & 18.2175406649412 & 59 \tabularnewline
6 & 139.166666666667 & 15.5612183055028 & 56 \tabularnewline
7 & 126 & 17.3572096626367 & 58 \tabularnewline
8 & 114.75 & 18.5870189306213 & 62 \tabularnewline
9 & 105 & 23.6988684041320 & 77 \tabularnewline
10 & 108.75 & 27.9321417985543 & 83 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78632&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]128.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]135.75[/C][C]10.7291023093098[/C][C]29[/C][/ROW]
[ROW][C]3[/C][C]152.25[/C][C]13.5050495606778[/C][C]41[/C][/ROW]
[ROW][C]4[/C][C]154.416666666667[/C][C]15.5063525594180[/C][C]51[/C][/ROW]
[ROW][C]5[/C][C]151.333333333333[/C][C]18.2175406649412[/C][C]59[/C][/ROW]
[ROW][C]6[/C][C]139.166666666667[/C][C]15.5612183055028[/C][C]56[/C][/ROW]
[ROW][C]7[/C][C]126[/C][C]17.3572096626367[/C][C]58[/C][/ROW]
[ROW][C]8[/C][C]114.75[/C][C]18.5870189306213[/C][C]62[/C][/ROW]
[ROW][C]9[/C][C]105[/C][C]23.6988684041320[/C][C]77[/C][/ROW]
[ROW][C]10[/C][C]108.75[/C][C]27.9321417985543[/C][C]83[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78632&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78632&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
1128.58.7230103227560826
2135.7510.729102309309829
3152.2513.505049560677841
4154.41666666666715.506352559418051
5151.33333333333318.217540664941259
6139.16666666666715.561218305502856
712617.357209662636758
8114.7518.587018930621362
910523.698868404132077
10108.7527.932141798554383






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha41.3970300481064
beta-0.185538183493773
S.D.0.0896744827297925
T-STAT-2.06901872021763
p-value0.072339298003533

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 41.3970300481064 \tabularnewline
beta & -0.185538183493773 \tabularnewline
S.D. & 0.0896744827297925 \tabularnewline
T-STAT & -2.06901872021763 \tabularnewline
p-value & 0.072339298003533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78632&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]41.3970300481064[/C][/ROW]
[ROW][C]beta[/C][C]-0.185538183493773[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0896744827297925[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.06901872021763[/C][/ROW]
[ROW][C]p-value[/C][C]0.072339298003533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78632&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78632&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)
alpha41.3970300481064
beta-0.185538183493773
S.D.0.0896744827297925
T-STAT-2.06901872021763
p-value0.072339298003533






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.0512043180526
beta-1.28743754811647
S.D.0.736264850466333
T-STAT-1.74860656094208
p-value0.118483677000635
Lambda2.28743754811647

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.0512043180526 \tabularnewline
beta & -1.28743754811647 \tabularnewline
S.D. & 0.736264850466333 \tabularnewline
T-STAT & -1.74860656094208 \tabularnewline
p-value & 0.118483677000635 \tabularnewline
Lambda & 2.28743754811647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78632&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.0512043180526[/C][/ROW]
[ROW][C]beta[/C][C]-1.28743754811647[/C][/ROW]
[ROW][C]S.D.[/C][C]0.736264850466333[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.74860656094208[/C][/ROW]
[ROW][C]p-value[/C][C]0.118483677000635[/C][/ROW]
[ROW][C]Lambda[/C][C]2.28743754811647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78632&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78632&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)
alpha9.0512043180526
beta-1.28743754811647
S.D.0.736264850466333
T-STAT-1.74860656094208
p-value0.118483677000635
Lambda2.28743754811647


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')