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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, 28 Nov 2013 08:12:47 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/28/t1385644463o87b5b5l1ajkcye.htm/, Retrieved Thu, 31 Oct 2024 23:02:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229301, Retrieved Thu, 31 Oct 2024 23:02:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

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] [] [2013-11-28 13:12:47] [bc709afd059270defb36fb1011c3ea57] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86.5
86.6
98.8
84.4
91.4
95.7
78.5
81.7
94.3
98.5
95.4
91.7
92.8
90.6
102.2
91.8
95
102
88.9
89.6
97.9
108.6
100.8
95.1
101
100.9
102.5
105.4
98.4
105.3
96.5
88.1
107.9
107.1
92.5
95.7
85.2
85.5
94.7
86.2
88.8
93.4
83.4
82.9
96.7
96.2
92.8
92.8
90.2
95.9
107.5
98
95
108.5
91.8
91.7
108.3
105.1
104.8
103.2
98.6
102.4
121.2
102.6
108.9
105.5
90.8
99.6
111.6
104.7
103.1
101.7
98.8
101.4
114.2
96.9
98.3
104.8
94.4
94.5
102.4
105.5
101.2
99.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229301&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229301&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
190.29166666666676.6740281326311120.3
296.2756.0989007951507919.7
3100.1083333333336.098801422236919.8
489.88333333333335.0957795965847713.8
51006.9717612226362518.3
6104.2257.4658160365032530.4
7100.9916666666675.4613448782134119.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 90.2916666666667 & 6.67402813263111 & 20.3 \tabularnewline
2 & 96.275 & 6.09890079515079 & 19.7 \tabularnewline
3 & 100.108333333333 & 6.0988014222369 & 19.8 \tabularnewline
4 & 89.8833333333333 & 5.09577959658477 & 13.8 \tabularnewline
5 & 100 & 6.97176122263625 & 18.3 \tabularnewline
6 & 104.225 & 7.46581603650325 & 30.4 \tabularnewline
7 & 100.991666666667 & 5.46134487821341 & 19.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229301&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]90.2916666666667[/C][C]6.67402813263111[/C][C]20.3[/C][/ROW]
[ROW][C]2[/C][C]96.275[/C][C]6.09890079515079[/C][C]19.7[/C][/ROW]
[ROW][C]3[/C][C]100.108333333333[/C][C]6.0988014222369[/C][C]19.8[/C][/ROW]
[ROW][C]4[/C][C]89.8833333333333[/C][C]5.09577959658477[/C][C]13.8[/C][/ROW]
[ROW][C]5[/C][C]100[/C][C]6.97176122263625[/C][C]18.3[/C][/ROW]
[ROW][C]6[/C][C]104.225[/C][C]7.46581603650325[/C][C]30.4[/C][/ROW]
[ROW][C]7[/C][C]100.991666666667[/C][C]5.46134487821341[/C][C]19.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229301&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
190.29166666666676.6740281326311120.3
296.2756.0989007951507919.7
3100.1083333333336.098801422236919.8
489.88333333333335.0957795965847713.8
51006.9717612226362518.3
6104.2257.4658160365032530.4
7100.9916666666675.4613448782134119.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.569165049338794
beta0.0701853066324345
S.D.0.0600673886334232
T-STAT1.16844278116964
p-value0.295303033723288

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.569165049338794 \tabularnewline
beta & 0.0701853066324345 \tabularnewline
S.D. & 0.0600673886334232 \tabularnewline
T-STAT & 1.16844278116964 \tabularnewline
p-value & 0.295303033723288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229301&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.569165049338794[/C][/ROW]
[ROW][C]beta[/C][C]0.0701853066324345[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0600673886334232[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16844278116964[/C][/ROW]
[ROW][C]p-value[/C][C]0.295303033723288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229301&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-0.569165049338794
beta0.0701853066324345
S.D.0.0600673886334232
T-STAT1.16844278116964
p-value0.295303033723288






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.06660823587832
beta1.06919755795702
S.D.0.936889743392493
T-STAT1.14122026150637
p-value0.305471410084773
Lambda-0.069197557957019

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.06660823587832 \tabularnewline
beta & 1.06919755795702 \tabularnewline
S.D. & 0.936889743392493 \tabularnewline
T-STAT & 1.14122026150637 \tabularnewline
p-value & 0.305471410084773 \tabularnewline
Lambda & -0.069197557957019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229301&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.06660823587832[/C][/ROW]
[ROW][C]beta[/C][C]1.06919755795702[/C][/ROW]
[ROW][C]S.D.[/C][C]0.936889743392493[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.14122026150637[/C][/ROW]
[ROW][C]p-value[/C][C]0.305471410084773[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.069197557957019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229301&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-3.06660823587832
beta1.06919755795702
S.D.0.936889743392493
T-STAT1.14122026150637
p-value0.305471410084773
Lambda-0.069197557957019


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')