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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 computationWed, 04 Aug 2010 15:24:55 +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/Aug/04/t1280935484bugma2s328e1yaz.htm/, Retrieved Fri, 03 May 2024 12:53:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78341, Retrieved Fri, 03 May 2024 12:53:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBogaerts Yannik
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Tijdreeks B stap 17] [2010-08-04 14:57:12] [f713c1ac4846c73da8c41c71cf7e0185]
- RM      [Standard Deviation-Mean Plot] [Tijdreeks B stap 21] [2010-08-04 15:24:55] [1596366c2ece8f787477cc7d1246d4c7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83
82
81
79
77
76
77
79
80
80
81
83
83
76
77
72
64
70
69
78
84
91
96
101
99
98
98
97
92
106
100
107
111
115
117
120
117
108
111
118
113
129
122
135
146
151
147
151
156
144
151
159
148
170
163
179
184
192
197
199
205
194
200
211
211
230
229
236
239
250
254
254
264
258
264
277
274
284
279
290
287
297
302
294

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78341&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78341&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78341&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
179.83333333333332.329000305762637
280.083333333333311.333444740985437
31059.0553851381374228
412916.381808092015943
5170.16666666666719.58122167854355
6226.08333333333321.381633296459060
7280.83333333333314.037827683107044

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 79.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 80.0833333333333 & 11.3334447409854 & 37 \tabularnewline
3 & 105 & 9.05538513813742 & 28 \tabularnewline
4 & 129 & 16.3818080920159 & 43 \tabularnewline
5 & 170.166666666667 & 19.581221678543 & 55 \tabularnewline
6 & 226.083333333333 & 21.3816332964590 & 60 \tabularnewline
7 & 280.833333333333 & 14.0378276831070 & 44 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78341&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]79.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]80.0833333333333[/C][C]11.3334447409854[/C][C]37[/C][/ROW]
[ROW][C]3[/C][C]105[/C][C]9.05538513813742[/C][C]28[/C][/ROW]
[ROW][C]4[/C][C]129[/C][C]16.3818080920159[/C][C]43[/C][/ROW]
[ROW][C]5[/C][C]170.166666666667[/C][C]19.581221678543[/C][C]55[/C][/ROW]
[ROW][C]6[/C][C]226.083333333333[/C][C]21.3816332964590[/C][C]60[/C][/ROW]
[ROW][C]7[/C][C]280.833333333333[/C][C]14.0378276831070[/C][C]44[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78341&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78341&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
179.83333333333332.329000305762637
280.083333333333311.333444740985437
31059.0553851381374228
412916.381808092015943
5170.16666666666719.58122167854355
6226.08333333333321.381633296459060
7280.83333333333314.037827683107044






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.39544443438983
beta0.0525977683419995
S.D.0.0298826292743926
T-STAT1.76014526228695
p-value0.138697367855206

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.39544443438983 \tabularnewline
beta & 0.0525977683419995 \tabularnewline
S.D. & 0.0298826292743926 \tabularnewline
T-STAT & 1.76014526228695 \tabularnewline
p-value & 0.138697367855206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78341&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.39544443438983[/C][/ROW]
[ROW][C]beta[/C][C]0.0525977683419995[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0298826292743926[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.76014526228695[/C][/ROW]
[ROW][C]p-value[/C][C]0.138697367855206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78341&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78341&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)
alpha5.39544443438983
beta0.0525977683419995
S.D.0.0298826292743926
T-STAT1.76014526228695
p-value0.138697367855206






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.5535416308438
beta1.01027359404696
S.D.0.514190824287418
T-STAT1.96478339621682
p-value0.106633261059233
Lambda-0.0102735940469596

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.5535416308438 \tabularnewline
beta & 1.01027359404696 \tabularnewline
S.D. & 0.514190824287418 \tabularnewline
T-STAT & 1.96478339621682 \tabularnewline
p-value & 0.106633261059233 \tabularnewline
Lambda & -0.0102735940469596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78341&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.5535416308438[/C][/ROW]
[ROW][C]beta[/C][C]1.01027359404696[/C][/ROW]
[ROW][C]S.D.[/C][C]0.514190824287418[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.96478339621682[/C][/ROW]
[ROW][C]p-value[/C][C]0.106633261059233[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0102735940469596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78341&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78341&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-2.5535416308438
beta1.01027359404696
S.D.0.514190824287418
T-STAT1.96478339621682
p-value0.106633261059233
Lambda-0.0102735940469596


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')