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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, 19 Aug 2010 15:30:20 +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/19/t12822318501zcyxa693ghvsmy.htm/, Retrieved Fri, 03 May 2024 12:54:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79318, Retrieved Fri, 03 May 2024 12:54:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGregory Goris
Estimated Impact120

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...] [2010-08-19 15:30:20] [4069dbe0e58b4004934f5f5b0dc60f40] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
159
158
157
155
175
174
159
149
150
150
151
153
146
156
154
151
171
167
144
138
138
132
132
132
125
131
129
131
145
156
126
123
127
116
114
114
109
110
113
114
138
155
126
123
124
124
134
131
126
128
128
124
148
174
146
137
152
159
170
166
165
168
175
180
199
228
206
193
201
214
225
224
215
222
238
248
262
288
261
240
248
260
266
268
256
261
287
295
304
331
299
275
293
309
311
311
289
298
319
325
331
348
320
305
322
337
346
343
321
331
343
345
347
363
322
304
323
340
352
351

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=79318&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=79318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79318&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
1157.58.7230103227560826
2146.7513.376539843390739
3128.08333333333312.310072249498742
4125.08333333333313.27648867416246
5146.518.037839015903150
6198.16666666666722.364067500155663
7251.33333333333320.513114799753873
8294.33333333333321.827144623707575
9323.58333333333318.937496874687259
10336.83333333333316.808187038320159

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 157.5 & 8.72301032275608 & 26 \tabularnewline
2 & 146.75 & 13.3765398433907 & 39 \tabularnewline
3 & 128.083333333333 & 12.3100722494987 & 42 \tabularnewline
4 & 125.083333333333 & 13.276488674162 & 46 \tabularnewline
5 & 146.5 & 18.0378390159031 & 50 \tabularnewline
6 & 198.166666666667 & 22.3640675001556 & 63 \tabularnewline
7 & 251.333333333333 & 20.5131147997538 & 73 \tabularnewline
8 & 294.333333333333 & 21.8271446237075 & 75 \tabularnewline
9 & 323.583333333333 & 18.9374968746872 & 59 \tabularnewline
10 & 336.833333333333 & 16.8081870383201 & 59 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79318&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]157.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]146.75[/C][C]13.3765398433907[/C][C]39[/C][/ROW]
[ROW][C]3[/C][C]128.083333333333[/C][C]12.3100722494987[/C][C]42[/C][/ROW]
[ROW][C]4[/C][C]125.083333333333[/C][C]13.276488674162[/C][C]46[/C][/ROW]
[ROW][C]5[/C][C]146.5[/C][C]18.0378390159031[/C][C]50[/C][/ROW]
[ROW][C]6[/C][C]198.166666666667[/C][C]22.3640675001556[/C][C]63[/C][/ROW]
[ROW][C]7[/C][C]251.333333333333[/C][C]20.5131147997538[/C][C]73[/C][/ROW]
[ROW][C]8[/C][C]294.333333333333[/C][C]21.8271446237075[/C][C]75[/C][/ROW]
[ROW][C]9[/C][C]323.583333333333[/C][C]18.9374968746872[/C][C]59[/C][/ROW]
[ROW][C]10[/C][C]336.833333333333[/C][C]16.8081870383201[/C][C]59[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79318&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
1157.58.7230103227560826
2146.7513.376539843390739
3128.08333333333312.310072249498742
4125.08333333333313.27648867416246
5146.518.037839015903150
6198.16666666666722.364067500155663
7251.33333333333320.513114799753873
8294.33333333333321.827144623707575
9323.58333333333318.937496874687259
10336.83333333333316.808187038320159






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.93514009362885
beta0.0316970005562715
S.D.0.0156253016047095
T-STAT2.02856887874202
p-value0.077028057773607

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.93514009362885 \tabularnewline
beta & 0.0316970005562715 \tabularnewline
S.D. & 0.0156253016047095 \tabularnewline
T-STAT & 2.02856887874202 \tabularnewline
p-value & 0.077028057773607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79318&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.93514009362885[/C][/ROW]
[ROW][C]beta[/C][C]0.0316970005562715[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0156253016047095[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.02856887874202[/C][/ROW]
[ROW][C]p-value[/C][C]0.077028057773607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79318&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79318&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)
alpha9.93514009362885
beta0.0316970005562715
S.D.0.0156253016047095
T-STAT2.02856887874202
p-value0.077028057773607






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.275899906756028
beta0.472656111841922
S.D.0.216278151855789
T-STAT2.18540850190491
p-value0.0603514639473668
Lambda0.527343888158078

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.275899906756028 \tabularnewline
beta & 0.472656111841922 \tabularnewline
S.D. & 0.216278151855789 \tabularnewline
T-STAT & 2.18540850190491 \tabularnewline
p-value & 0.0603514639473668 \tabularnewline
Lambda & 0.527343888158078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79318&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.275899906756028[/C][/ROW]
[ROW][C]beta[/C][C]0.472656111841922[/C][/ROW]
[ROW][C]S.D.[/C][C]0.216278151855789[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.18540850190491[/C][/ROW]
[ROW][C]p-value[/C][C]0.0603514639473668[/C][/ROW]
[ROW][C]Lambda[/C][C]0.527343888158078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79318&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79318&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)
alpha0.275899906756028
beta0.472656111841922
S.D.0.216278151855789
T-STAT2.18540850190491
p-value0.0603514639473668
Lambda0.527343888158078


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')