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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 27 Dec 2010 23:46:33 +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/Dec/28/t12934934618fyabzph6sg3bkx.htm/, Retrieved Sun, 05 May 2024 07:22:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116188, Retrieved Sun, 05 May 2024 07:22:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Standard Deviation-Mean Plot] [] [2010-12-14 14:15:51] [c91278f1cd2d8b4eeb874e50bb706c21]
-    D    [Standard Deviation-Mean Plot] [] [2010-12-19 14:23:46] [c91278f1cd2d8b4eeb874e50bb706c21]
-    D      [Standard Deviation-Mean Plot] [] [2010-12-21 16:16:49] [c91278f1cd2d8b4eeb874e50bb706c21]
-               [Standard Deviation-Mean Plot] [] [2010-12-27 23:46:33] [4dbe485270073769796ed1462cddce37] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
224
215
196
159
187
208
131
93
210
228
176
195
188
188
190
188
176
225
93
79
235
247
195
197
211
156
209
180
185
303
129
85
249
231
212
240
234
217
287
221
208
241
156
96
320
242
227
200
215
238
279
208
262
259
167
123
302
246
235

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116188&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116188&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1185.16666666666740.210431331668135
2183.41666666666750.4443137318646168
3199.16666666666757.7893247979768218
4220.7556.9515344194278224

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 185.166666666667 & 40.210431331668 & 135 \tabularnewline
2 & 183.416666666667 & 50.4443137318646 & 168 \tabularnewline
3 & 199.166666666667 & 57.7893247979768 & 218 \tabularnewline
4 & 220.75 & 56.9515344194278 & 224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116188&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]185.166666666667[/C][C]40.210431331668[/C][C]135[/C][/ROW]
[ROW][C]2[/C][C]183.416666666667[/C][C]50.4443137318646[/C][C]168[/C][/ROW]
[ROW][C]3[/C][C]199.166666666667[/C][C]57.7893247979768[/C][C]218[/C][/ROW]
[ROW][C]4[/C][C]220.75[/C][C]56.9515344194278[/C][C]224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116188&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
1185.16666666666740.210431331668135
2183.41666666666750.4443137318646168
3199.16666666666757.7893247979768218
4220.7556.9515344194278224






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-12.8954483369324
beta0.325906655204397
S.D.0.239974198678583
T-STAT1.35809039888038
p-value0.307349971731885

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -12.8954483369324 \tabularnewline
beta & 0.325906655204397 \tabularnewline
S.D. & 0.239974198678583 \tabularnewline
T-STAT & 1.35809039888038 \tabularnewline
p-value & 0.307349971731885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116188&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.8954483369324[/C][/ROW]
[ROW][C]beta[/C][C]0.325906655204397[/C][/ROW]
[ROW][C]S.D.[/C][C]0.239974198678583[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.35809039888038[/C][/ROW]
[ROW][C]p-value[/C][C]0.307349971731885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116188&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116188&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-12.8954483369324
beta0.325906655204397
S.D.0.239974198678583
T-STAT1.35809039888038
p-value0.307349971731885






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.13143021120543
beta1.33684285995822
S.D.1.01202338277423
T-STAT1.32096044687581
p-value0.317397955569378
Lambda-0.336842859958223

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.13143021120543 \tabularnewline
beta & 1.33684285995822 \tabularnewline
S.D. & 1.01202338277423 \tabularnewline
T-STAT & 1.32096044687581 \tabularnewline
p-value & 0.317397955569378 \tabularnewline
Lambda & -0.336842859958223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116188&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.13143021120543[/C][/ROW]
[ROW][C]beta[/C][C]1.33684285995822[/C][/ROW]
[ROW][C]S.D.[/C][C]1.01202338277423[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.32096044687581[/C][/ROW]
[ROW][C]p-value[/C][C]0.317397955569378[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.336842859958223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116188&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116188&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-3.13143021120543
beta1.33684285995822
S.D.1.01202338277423
T-STAT1.32096044687581
p-value0.317397955569378
Lambda-0.336842859958223


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')