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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 Nov 2015 09:40:54 +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/Nov/19/t1447926094s0h9di1gd2h5b2q.htm/, Retrieved Mon, 13 May 2024 20:34:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283582, Retrieved Mon, 13 May 2024 20:34:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

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] [] [2015-11-19 09:40:54] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
464
675
703
887
1139
1077
1318
1260
1120
963
996
960
530
883
894
1045
1199
1287
1565
1577
1076
918
1008
1063
544
635
804
980
1018
1064
1404
1286
1104
999
996
1015
615
722
832
977
1270
1437
1520
1708
1151
934
1159
1209
699
830
996
1124
1458
1270
1753
2258
1208
1241
1265
1828

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283582&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283582&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283582&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1963.5250.321792898661854
21087.08333333333293.4907334245171047
3987.416666666667240.938867513707860
41127.83333333333328.8848467537571093
51327.5440.7853528336981559

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 963.5 & 250.321792898661 & 854 \tabularnewline
2 & 1087.08333333333 & 293.490733424517 & 1047 \tabularnewline
3 & 987.416666666667 & 240.938867513707 & 860 \tabularnewline
4 & 1127.83333333333 & 328.884846753757 & 1093 \tabularnewline
5 & 1327.5 & 440.785352833698 & 1559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283582&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]963.5[/C][C]250.321792898661[/C][C]854[/C][/ROW]
[ROW][C]2[/C][C]1087.08333333333[/C][C]293.490733424517[/C][C]1047[/C][/ROW]
[ROW][C]3[/C][C]987.416666666667[/C][C]240.938867513707[/C][C]860[/C][/ROW]
[ROW][C]4[/C][C]1127.83333333333[/C][C]328.884846753757[/C][C]1093[/C][/ROW]
[ROW][C]5[/C][C]1327.5[/C][C]440.785352833698[/C][C]1559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283582&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283582&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
1963.5250.321792898661854
21087.08333333333293.4907334245171047
3987.416666666667240.938867513707860
41127.83333333333328.8848467537571093
51327.5440.7853528336981559






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-296.282959471823
beta0.552640119681454
S.D.0.0402216704642983
T-STAT13.7398599635982
p-value0.000834263968701658

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -296.282959471823 \tabularnewline
beta & 0.552640119681454 \tabularnewline
S.D. & 0.0402216704642983 \tabularnewline
T-STAT & 13.7398599635982 \tabularnewline
p-value & 0.000834263968701658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283582&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-296.282959471823[/C][/ROW]
[ROW][C]beta[/C][C]0.552640119681454[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0402216704642983[/C][/ROW]
[ROW][C]T-STAT[/C][C]13.7398599635982[/C][/ROW]
[ROW][C]p-value[/C][C]0.000834263968701658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283582&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283582&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-296.282959471823
beta0.552640119681454
S.D.0.0402216704642983
T-STAT13.7398599635982
p-value0.000834263968701658






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.51834567301883
beta1.89172816155358
S.D.0.153475128991573
T-STAT12.3259590917656
p-value0.00115030353923804
Lambda-0.891728161553583

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.51834567301883 \tabularnewline
beta & 1.89172816155358 \tabularnewline
S.D. & 0.153475128991573 \tabularnewline
T-STAT & 12.3259590917656 \tabularnewline
p-value & 0.00115030353923804 \tabularnewline
Lambda & -0.891728161553583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283582&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.51834567301883[/C][/ROW]
[ROW][C]beta[/C][C]1.89172816155358[/C][/ROW]
[ROW][C]S.D.[/C][C]0.153475128991573[/C][/ROW]
[ROW][C]T-STAT[/C][C]12.3259590917656[/C][/ROW]
[ROW][C]p-value[/C][C]0.00115030353923804[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.891728161553583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283582&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283582&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-7.51834567301883
beta1.89172816155358
S.D.0.153475128991573
T-STAT12.3259590917656
p-value0.00115030353923804
Lambda-0.891728161553583


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')