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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, 26 May 2010 19:08:03 +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/May/26/t1274900949m9rrthzbho1wknk.htm/, Retrieved Fri, 03 May 2024 11:52:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76542, Retrieved Fri, 03 May 2024 11:52:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact129

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] [] [2010-05-26 19:08:03] [ac302f869d0778eba7cafda3b14e71eb] [Current]
-   P     [Standard Deviation-Mean Plot] [] [2010-05-26 19:11:09] [5a3034bcadf7735f2909fd8cdba599d5]
- RMPD    [Central Tendency] [] [2010-05-26 19:21:42] [5a3034bcadf7735f2909fd8cdba599d5]
- RMPD    [Mean versus Median] [] [2010-05-26 19:29:38] [5a3034bcadf7735f2909fd8cdba599d5]
- RMPD    [Central Tendency] [] [2010-05-26 19:38:37] [5a3034bcadf7735f2909fd8cdba599d5]
- RMP     [Mean versus Median] [] [2010-05-26 19:46:12] [5a3034bcadf7735f2909fd8cdba599d5]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
70.5
70.65
70.71
15.80
170.99
15.26
17.21
16.97
16.80
18.37
18.53
18.708
18.73
18.63
19.15
19.76
20.02
20.26
20.32
20.52
20.81
21.26
22.15
23.05
270.01
270.69
70.38
26.33
27.36
28.55
30.10
32.20
36.28
700.91
7070.66
707.83
709.97
52.20
55.67
59.92
65.15
70.17
770.6
78.23
79.27
80.707
81.701
83.97
86.83
89.61
91.79
970.32
96.56
97.98
100.00
101.63
102.60
103.75
106.39
109.02
110.81
112.57
1170.93
118.13
120.7
122.707
127.97
127.87

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=76542&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=76542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76542&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
156.91527.410142283468754.91
255.107577.2598784945977155.73
318.1020.8789099309182181.90800000000000
419.06750.5137038705973191.13000000000000
520.280.205912602819740.5
621.81750.9925514260396462.24
7159.3525129.424640202964244.36
829.55252.091337291463694.84
92128.923309.513848759867034.38
10219.44327.035238570199657.77
11246.0375349.749833774085705.45
1281.4121.975860487652584.7
13309.6375440.459677259641883.49
1499.04252.228876772427465.06999999999999
15105.442.865926260972776.42
16378.11528.555873552331060.12
17124.811753.681661615357947.27

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 56.915 & 27.4101422834687 & 54.91 \tabularnewline
2 & 55.1075 & 77.2598784945977 & 155.73 \tabularnewline
3 & 18.102 & 0.878909930918218 & 1.90800000000000 \tabularnewline
4 & 19.0675 & 0.513703870597319 & 1.13000000000000 \tabularnewline
5 & 20.28 & 0.20591260281974 & 0.5 \tabularnewline
6 & 21.8175 & 0.992551426039646 & 2.24 \tabularnewline
7 & 159.3525 & 129.424640202964 & 244.36 \tabularnewline
8 & 29.5525 & 2.09133729146369 & 4.84 \tabularnewline
9 & 2128.92 & 3309.51384875986 & 7034.38 \tabularnewline
10 & 219.44 & 327.035238570199 & 657.77 \tabularnewline
11 & 246.0375 & 349.749833774085 & 705.45 \tabularnewline
12 & 81.412 & 1.97586048765258 & 4.7 \tabularnewline
13 & 309.6375 & 440.459677259641 & 883.49 \tabularnewline
14 & 99.0425 & 2.22887677242746 & 5.06999999999999 \tabularnewline
15 & 105.44 & 2.86592626097277 & 6.42 \tabularnewline
16 & 378.11 & 528.55587355233 & 1060.12 \tabularnewline
17 & 124.81175 & 3.68166161535794 & 7.27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76542&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]56.915[/C][C]27.4101422834687[/C][C]54.91[/C][/ROW]
[ROW][C]2[/C][C]55.1075[/C][C]77.2598784945977[/C][C]155.73[/C][/ROW]
[ROW][C]3[/C][C]18.102[/C][C]0.878909930918218[/C][C]1.90800000000000[/C][/ROW]
[ROW][C]4[/C][C]19.0675[/C][C]0.513703870597319[/C][C]1.13000000000000[/C][/ROW]
[ROW][C]5[/C][C]20.28[/C][C]0.20591260281974[/C][C]0.5[/C][/ROW]
[ROW][C]6[/C][C]21.8175[/C][C]0.992551426039646[/C][C]2.24[/C][/ROW]
[ROW][C]7[/C][C]159.3525[/C][C]129.424640202964[/C][C]244.36[/C][/ROW]
[ROW][C]8[/C][C]29.5525[/C][C]2.09133729146369[/C][C]4.84[/C][/ROW]
[ROW][C]9[/C][C]2128.92[/C][C]3309.51384875986[/C][C]7034.38[/C][/ROW]
[ROW][C]10[/C][C]219.44[/C][C]327.035238570199[/C][C]657.77[/C][/ROW]
[ROW][C]11[/C][C]246.0375[/C][C]349.749833774085[/C][C]705.45[/C][/ROW]
[ROW][C]12[/C][C]81.412[/C][C]1.97586048765258[/C][C]4.7[/C][/ROW]
[ROW][C]13[/C][C]309.6375[/C][C]440.459677259641[/C][C]883.49[/C][/ROW]
[ROW][C]14[/C][C]99.0425[/C][C]2.22887677242746[/C][C]5.06999999999999[/C][/ROW]
[ROW][C]15[/C][C]105.44[/C][C]2.86592626097277[/C][C]6.42[/C][/ROW]
[ROW][C]16[/C][C]378.11[/C][C]528.55587355233[/C][C]1060.12[/C][/ROW]
[ROW][C]17[/C][C]124.81175[/C][C]3.68166161535794[/C][C]7.27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76542&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
156.91527.410142283468754.91
255.107577.2598784945977155.73
318.1020.8789099309182181.90800000000000
419.06750.5137038705973191.13000000000000
520.280.205912602819740.5
621.81750.9925514260396462.24
7159.3525129.424640202964244.36
829.55252.091337291463694.84
92128.923309.513848759867034.38
10219.44327.035238570199657.77
11246.0375349.749833774085705.45
1281.4121.975860487652584.7
13309.6375440.459677259641883.49
1499.04252.228876772427465.06999999999999
15105.442.865926260972776.42
16378.11528.555873552331060.12
17124.811753.681661615357947.27






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-74.1964777614502
beta1.58755496303965
S.D.0.0293656047429775
T-STAT54.061715293614
p-value1.31312186768654e-18

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -74.1964777614502 \tabularnewline
beta & 1.58755496303965 \tabularnewline
S.D. & 0.0293656047429775 \tabularnewline
T-STAT & 54.061715293614 \tabularnewline
p-value & 1.31312186768654e-18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76542&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-74.1964777614502[/C][/ROW]
[ROW][C]beta[/C][C]1.58755496303965[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0293656047429775[/C][/ROW]
[ROW][C]T-STAT[/C][C]54.061715293614[/C][/ROW]
[ROW][C]p-value[/C][C]1.31312186768654e-18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76542&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76542&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-74.1964777614502
beta1.58755496303965
S.D.0.0293656047429775
T-STAT54.061715293614
p-value1.31312186768654e-18






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.39190563402268
beta2.01525418370514
S.D.0.28760825680658
T-STAT7.00694133778092
p-value4.23082022788061e-06
Lambda-1.01525418370514

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.39190563402268 \tabularnewline
beta & 2.01525418370514 \tabularnewline
S.D. & 0.28760825680658 \tabularnewline
T-STAT & 7.00694133778092 \tabularnewline
p-value & 4.23082022788061e-06 \tabularnewline
Lambda & -1.01525418370514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76542&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.39190563402268[/C][/ROW]
[ROW][C]beta[/C][C]2.01525418370514[/C][/ROW]
[ROW][C]S.D.[/C][C]0.28760825680658[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.00694133778092[/C][/ROW]
[ROW][C]p-value[/C][C]4.23082022788061e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.01525418370514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76542&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76542&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-6.39190563402268
beta2.01525418370514
S.D.0.28760825680658
T-STAT7.00694133778092
p-value4.23082022788061e-06
Lambda-1.01525418370514


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')