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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, 01 Jul 2010 16:17:55 +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/Jul/01/t1278001094g5uq0ta0p97dau4.htm/, Retrieved Fri, 03 May 2024 16:09:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77900, Retrieved Fri, 03 May 2024 16:09:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSteffi Poppe
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] [Tijdreeks1-Stap26] [2010-07-01 16:17:55] [b37bab310ab56201887748d7a7c0dc58] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
300
299
298
296
316
315
300
290
291
291
292
294
302
296
282
282
298
300
289
275
270
269
268
260
271
269
260
262
285
286
272
248
240
234
231
222
233
236
226
232
248
253
233
216
209
202
204
193
201
201
188
198
220
225
215
198
195
183
180
170
175
180
161
174
195
198
188
173
162
149
140
129
132
133
116
128
148
154
152
141
136
119
114
100
108
115
101
116
131
133
135
124
131
113
118
99
107
112
106
121
138
134
132
121
132
113
112
91
96
99
99
110
127
122
124
114
129
113
115
94

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77900&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]3 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=77900&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77900&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1298.58.7230103227560826
2282.58333333333314.342931951651242
3256.66666666666721.368342486165464
4223.7518.887826767524160
5197.83333333333316.408608235996955
6168.66666666666721.381101822673169
7131.08333333333316.560952614966154
8118.66666666666712.323911224882636
9118.2514.000811664783147
10111.83333333333312.408452642037935

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 298.5 & 8.72301032275608 & 26 \tabularnewline
2 & 282.583333333333 & 14.3429319516512 & 42 \tabularnewline
3 & 256.666666666667 & 21.3683424861654 & 64 \tabularnewline
4 & 223.75 & 18.8878267675241 & 60 \tabularnewline
5 & 197.833333333333 & 16.4086082359969 & 55 \tabularnewline
6 & 168.666666666667 & 21.3811018226731 & 69 \tabularnewline
7 & 131.083333333333 & 16.5609526149661 & 54 \tabularnewline
8 & 118.666666666667 & 12.3239112248826 & 36 \tabularnewline
9 & 118.25 & 14.0008116647831 & 47 \tabularnewline
10 & 111.833333333333 & 12.4084526420379 & 35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77900&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]298.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]282.583333333333[/C][C]14.3429319516512[/C][C]42[/C][/ROW]
[ROW][C]3[/C][C]256.666666666667[/C][C]21.3683424861654[/C][C]64[/C][/ROW]
[ROW][C]4[/C][C]223.75[/C][C]18.8878267675241[/C][C]60[/C][/ROW]
[ROW][C]5[/C][C]197.833333333333[/C][C]16.4086082359969[/C][C]55[/C][/ROW]
[ROW][C]6[/C][C]168.666666666667[/C][C]21.3811018226731[/C][C]69[/C][/ROW]
[ROW][C]7[/C][C]131.083333333333[/C][C]16.5609526149661[/C][C]54[/C][/ROW]
[ROW][C]8[/C][C]118.666666666667[/C][C]12.3239112248826[/C][C]36[/C][/ROW]
[ROW][C]9[/C][C]118.25[/C][C]14.0008116647831[/C][C]47[/C][/ROW]
[ROW][C]10[/C][C]111.833333333333[/C][C]12.4084526420379[/C][C]35[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77900&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77900&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
1298.58.7230103227560826
2282.58333333333314.342931951651242
3256.66666666666721.368342486165464
4223.7518.887826767524160
5197.83333333333316.408608235996955
6168.66666666666721.381101822673169
7131.08333333333316.560952614966154
8118.66666666666712.323911224882636
9118.2514.000811664783147
10111.83333333333312.408452642037935






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha15.4056523410459
beta0.00123146308533785
S.D.0.0202235344696562
T-STAT0.0608925747962385
p-value0.952938518271976

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15.4056523410459 \tabularnewline
beta & 0.00123146308533785 \tabularnewline
S.D. & 0.0202235344696562 \tabularnewline
T-STAT & 0.0608925747962385 \tabularnewline
p-value & 0.952938518271976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77900&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.4056523410459[/C][/ROW]
[ROW][C]beta[/C][C]0.00123146308533785[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0202235344696562[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0608925747962385[/C][/ROW]
[ROW][C]p-value[/C][C]0.952938518271976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77900&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77900&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)
alpha15.4056523410459
beta0.00123146308533785
S.D.0.0202235344696562
T-STAT0.0608925747962385
p-value0.952938518271976






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.57127888407905
beta0.0280235756735517
S.D.0.256363371874761
T-STAT0.109311932779702
p-value0.91564731131296
Lambda0.971976424326448

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.57127888407905 \tabularnewline
beta & 0.0280235756735517 \tabularnewline
S.D. & 0.256363371874761 \tabularnewline
T-STAT & 0.109311932779702 \tabularnewline
p-value & 0.91564731131296 \tabularnewline
Lambda & 0.971976424326448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77900&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.57127888407905[/C][/ROW]
[ROW][C]beta[/C][C]0.0280235756735517[/C][/ROW]
[ROW][C]S.D.[/C][C]0.256363371874761[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.109311932779702[/C][/ROW]
[ROW][C]p-value[/C][C]0.91564731131296[/C][/ROW]
[ROW][C]Lambda[/C][C]0.971976424326448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77900&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77900&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)
alpha2.57127888407905
beta0.0280235756735517
S.D.0.256363371874761
T-STAT0.109311932779702
p-value0.91564731131296
Lambda0.971976424326448


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')