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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, 12 Mar 2015 14:06:59 +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/2015/Mar/12/t1426169245h5hgpxj0k3a7mf7.htm/, Retrieved Fri, 17 May 2024 16:22:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278273, Retrieved Fri, 17 May 2024 16:22:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

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] [] [2015-03-12 14:06:59] [006461bb825a57cb671d1f8ff85b37cb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
299.81
299.01
296.82
296.67
296.95
296.80
296.80
295.93
293.77
291.02
288.61
284.55
284.55
278.14
273.28
270.14
268.36
267.15
267.15
265.47
261.75
256.51
252.98
251.17
251.17
244.27
240.54
238.92
237.47
235.91
235.91
231.41
224.94
222.19
219.06
217.83
217.83
216.89
213.84
212.90
213.98
215.31
215.31
214.09
213.71
211.54
209.40
207.33
207.33
202.75
200.26
198.99
198.82
198.43
198.43
195.68
195.45
193.65
191.38
189.71
189.71
185.49
183.01
182.38
181.60
182.13
182.13
180.81
180.25
179.84
178.50
178.11
178.11
178.10
177.52
177.34
175.53
176.01
175.94
175.47
175.48
173.76
173.74
173.65
172.00
171.50
170.41
171.50
171.43
170.69
170.40
169.90
170.21
170.55
169.98
169.34

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278273&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278273&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1294.7283333333334.5021930682993215.26
2266.38759.8437133837702833.38
3233.30166666666710.41714132251933.34
4213.5108333333332.9635741883234410.5
5197.5733333333334.8421695613233217.62
6181.9966666666673.1552073360293411.6
7175.88751.630388269428764.46000000000001
8170.6591666666670.7935931901895022.66

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 294.728333333333 & 4.50219306829932 & 15.26 \tabularnewline
2 & 266.3875 & 9.84371338377028 & 33.38 \tabularnewline
3 & 233.301666666667 & 10.417141322519 & 33.34 \tabularnewline
4 & 213.510833333333 & 2.96357418832344 & 10.5 \tabularnewline
5 & 197.573333333333 & 4.84216956132332 & 17.62 \tabularnewline
6 & 181.996666666667 & 3.15520733602934 & 11.6 \tabularnewline
7 & 175.8875 & 1.63038826942876 & 4.46000000000001 \tabularnewline
8 & 170.659166666667 & 0.793593190189502 & 2.66 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278273&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]294.728333333333[/C][C]4.50219306829932[/C][C]15.26[/C][/ROW]
[ROW][C]2[/C][C]266.3875[/C][C]9.84371338377028[/C][C]33.38[/C][/ROW]
[ROW][C]3[/C][C]233.301666666667[/C][C]10.417141322519[/C][C]33.34[/C][/ROW]
[ROW][C]4[/C][C]213.510833333333[/C][C]2.96357418832344[/C][C]10.5[/C][/ROW]
[ROW][C]5[/C][C]197.573333333333[/C][C]4.84216956132332[/C][C]17.62[/C][/ROW]
[ROW][C]6[/C][C]181.996666666667[/C][C]3.15520733602934[/C][C]11.6[/C][/ROW]
[ROW][C]7[/C][C]175.8875[/C][C]1.63038826942876[/C][C]4.46000000000001[/C][/ROW]
[ROW][C]8[/C][C]170.659166666667[/C][C]0.793593190189502[/C][C]2.66[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278273&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
1294.7283333333334.5021930682993215.26
2266.38759.8437133837702833.38
3233.30166666666710.41714132251933.34
4213.5108333333332.9635741883234410.5
5197.5733333333334.8421695613233217.62
6181.9966666666673.1552073360293411.6
7175.88751.630388269428764.46000000000001
8170.6591666666670.7935931901895022.66






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.86560620636867
beta0.0490603357876136
S.D.0.0254259435599881
T-STAT1.92953845240253
p-value0.101909401583965

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.86560620636867 \tabularnewline
beta & 0.0490603357876136 \tabularnewline
S.D. & 0.0254259435599881 \tabularnewline
T-STAT & 1.92953845240253 \tabularnewline
p-value & 0.101909401583965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278273&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.86560620636867[/C][/ROW]
[ROW][C]beta[/C][C]0.0490603357876136[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0254259435599881[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.92953845240253[/C][/ROW]
[ROW][C]p-value[/C][C]0.101909401583965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278273&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278273&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-5.86560620636867
beta0.0490603357876136
S.D.0.0254259435599881
T-STAT1.92953845240253
p-value0.101909401583965






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.5579271361877
beta3.14010898183931
S.D.1.2168545660022
T-STAT2.58051296315195
p-value0.0417406610443756
Lambda-2.14010898183931

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.5579271361877 \tabularnewline
beta & 3.14010898183931 \tabularnewline
S.D. & 1.2168545660022 \tabularnewline
T-STAT & 2.58051296315195 \tabularnewline
p-value & 0.0417406610443756 \tabularnewline
Lambda & -2.14010898183931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278273&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.5579271361877[/C][/ROW]
[ROW][C]beta[/C][C]3.14010898183931[/C][/ROW]
[ROW][C]S.D.[/C][C]1.2168545660022[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.58051296315195[/C][/ROW]
[ROW][C]p-value[/C][C]0.0417406610443756[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.14010898183931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278273&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278273&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-15.5579271361877
beta3.14010898183931
S.D.1.2168545660022
T-STAT2.58051296315195
p-value0.0417406610443756
Lambda-2.14010898183931


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')