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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 computationFri, 13 May 2011 10:45:26 +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/2011/May/13/t1305283279ydogmted4x0qmbm.htm/, Retrieved Fri, 10 May 2024 08:24:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121539, Retrieved Fri, 10 May 2024 08:24:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160

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] [Jonas Cloots, Sta...] [2011-05-13 10:45:26] [e414a1f4d0a08e5011052e6ef0a3e93e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
193.230
199.068
195.076
191.563
191.067
186.665
185.508
184.371
183.046
175.714
175.768
171.029
170.465
170.102
156.389
124.291
99.360
86.675
85.056
128.236
164.257
162.401
152.779
156.005
153.387
153.190
148.840
144.211
145.953
145.542
150.271
147.489
143.824
134.754
131.736
126.304
125.511
125.495
130.133
126.257
110.323
98.417
105.749
120.665
124.075
127.245
146.731
144.979
148.210
144.670
142.970
142.524
146.142
146.522
148.128
148.798
150.181
152.388
155.694
160.662
155.520
158.262
154.338
158.196
160.371
154.856
150.636
145.899
141.242
140.834
141.119
139.104
134.437
129.425
123.155
119.273
120.472
121.523
121.983
123.658
124.794
124.827
120.382
117.395
115.790
114.283
117.271
117.448
118.764
120.550
123.554
125.412
124.182
119.828
115.361
114.226
115.214
115.864
114.276
113.469

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'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121539&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121539&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'Gwilym Jenkins' @ www.wessa.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1186.008758.5744352915035728.039
2138.00133333333332.282492275460385.409
3143.791758.5402028518062727.083
4123.79833333333314.141691253706248.314
5148.9074166666675.277435990022818.138
6150.0314166666677.92800577307321.267
7123.4436666666674.6564124569991717.042
8118.8890833333333.8810456055584111.186

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 186.00875 & 8.57443529150357 & 28.039 \tabularnewline
2 & 138.001333333333 & 32.2824922754603 & 85.409 \tabularnewline
3 & 143.79175 & 8.54020285180627 & 27.083 \tabularnewline
4 & 123.798333333333 & 14.1416912537062 & 48.314 \tabularnewline
5 & 148.907416666667 & 5.2774359900228 & 18.138 \tabularnewline
6 & 150.031416666667 & 7.928005773073 & 21.267 \tabularnewline
7 & 123.443666666667 & 4.65641245699917 & 17.042 \tabularnewline
8 & 118.889083333333 & 3.88104560555841 & 11.186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121539&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]186.00875[/C][C]8.57443529150357[/C][C]28.039[/C][/ROW]
[ROW][C]2[/C][C]138.001333333333[/C][C]32.2824922754603[/C][C]85.409[/C][/ROW]
[ROW][C]3[/C][C]143.79175[/C][C]8.54020285180627[/C][C]27.083[/C][/ROW]
[ROW][C]4[/C][C]123.798333333333[/C][C]14.1416912537062[/C][C]48.314[/C][/ROW]
[ROW][C]5[/C][C]148.907416666667[/C][C]5.2774359900228[/C][C]18.138[/C][/ROW]
[ROW][C]6[/C][C]150.031416666667[/C][C]7.928005773073[/C][C]21.267[/C][/ROW]
[ROW][C]7[/C][C]123.443666666667[/C][C]4.65641245699917[/C][C]17.042[/C][/ROW]
[ROW][C]8[/C][C]118.889083333333[/C][C]3.88104560555841[/C][C]11.186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121539&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
1186.008758.5744352915035728.039
2138.00133333333332.282492275460385.409
3143.791758.5402028518062727.083
4123.79833333333314.141691253706248.314
5148.9074166666675.277435990022818.138
6150.0314166666677.92800577307321.267
7123.4436666666674.6564124569991717.042
8118.8890833333333.8810456055584111.186






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha12.2360389003197
beta-0.0111279937066377
S.D.0.175642373657178
T-STAT-0.0633559742728001
p-value0.951541002063651

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 12.2360389003197 \tabularnewline
beta & -0.0111279937066377 \tabularnewline
S.D. & 0.175642373657178 \tabularnewline
T-STAT & -0.0633559742728001 \tabularnewline
p-value & 0.951541002063651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121539&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.2360389003197[/C][/ROW]
[ROW][C]beta[/C][C]-0.0111279937066377[/C][/ROW]
[ROW][C]S.D.[/C][C]0.175642373657178[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0633559742728001[/C][/ROW]
[ROW][C]p-value[/C][C]0.951541002063651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121539&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121539&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)
alpha12.2360389003197
beta-0.0111279937066377
S.D.0.175642373657178
T-STAT-0.0633559742728001
p-value0.951541002063651






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.897765662306317
beta0.612607541638625
S.D.1.89669674371493
T-STAT0.322986552103607
p-value0.757664873284216
Lambda0.387392458361375

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.897765662306317 \tabularnewline
beta & 0.612607541638625 \tabularnewline
S.D. & 1.89669674371493 \tabularnewline
T-STAT & 0.322986552103607 \tabularnewline
p-value & 0.757664873284216 \tabularnewline
Lambda & 0.387392458361375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121539&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.897765662306317[/C][/ROW]
[ROW][C]beta[/C][C]0.612607541638625[/C][/ROW]
[ROW][C]S.D.[/C][C]1.89669674371493[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.322986552103607[/C][/ROW]
[ROW][C]p-value[/C][C]0.757664873284216[/C][/ROW]
[ROW][C]Lambda[/C][C]0.387392458361375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121539&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121539&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-0.897765662306317
beta0.612607541638625
S.D.1.89669674371493
T-STAT0.322986552103607
p-value0.757664873284216
Lambda0.387392458361375


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')