FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 May 2009 08:35:39 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/28/t1243521375rqzp52jfrdcqs1b.htm/, Retrieved Mon, 06 May 2024 05:52:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40632, Retrieved Mon, 06 May 2024 05:52:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116

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] [spreidings- en ge...] [2009-05-28 14:35:39] [1a4b490ae86a78f004f9a6b70ce3539b] [Current]
-    D    [Standard Deviation-Mean Plot] [spreidings-en gem...] [2009-06-02 15:35:42] [74be16979710d4c4e7c6647856088456]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18,09
18,13
18
17,72
17,62
17,13
17,39
17,09
17,14
17,38
16,8
16,51
16,01
15,05
13,56
15,22
14,91
15,13
15,25
14,61
14,87
15,1
15,22
15,46
14,96
14
14,2
13,9
13,63
13,32
13,8
14,5
14,12
13,88
14,11
14,26
14,71
14,52
14,32
14,69
15,25
15,04
14,82
14,5
14,72
14,6
14,58
14
14,75
14,41
15,19
14,96
14,83
14,25
14,32
14,93
14,65
15,65
15,65
15,61
15,95
15,83
15,77
16,7
16,69
16,4
16,77
16,78
16,84
16,68
16,67
16,3
16,37
16,6
16,72
16,82
17,5
17,2
17,29
17,2
17,2
17,32
17,16
17,41
17,31
17,3
17,34
17,19
17,05
17,07
17,07
16,81
16,81
16,96
17,05
17
16,77
16,66
16,2
16,26
15,84
15,85
15,71
15,84
15,73
15,77
15,3
15,41
15,4
15,61
15
14,12
14,01
13,46
13,85
13,92
13,59
13,67
13,05
12,87
12,28
11,88
12,49
11,9
10,8
10,99
10,15
10,07
10,05
10,31
9,94
9,65
9,74
9,85
9,96
9,63
9,43
8,77
9,53
9,5
9,78
9,9
9,93
10,35
9,79
9,63
9,02
9,25
9,11
8,95
9,3
9,13
9,75
9,65
9,27
9,59
9,58
9,98
9,57
9,6
9,64
9,46
9,19
9,02
8,9
9,12
8,86
8,94
9
9,23
9,39
9,62
9,9
9,8
9,2
9,87
9,6
9,37
9,21
9,15
8,7
8,2
8,1
6,68
7,7
8,2
7,55
7,53
7,02
6,6
6
3,95
4,91
5,15
5,7
1,93
1,36
1,1
0,98
1
1,1
1,06
1,01
0,93
0,89
0,9
0,88
0,85
0,84
0,94
1
1,1
1,15
1,05
1,06
0,99
0,93
0,84
0,9
0,86
0,78
0,77
0,6
0,57
0,62
0,62
0,58
0,6
0,73
0,75
0,63
0,71
0,68
0,64
0,66
0,69
0,72
0,92
0,85
0,95
1
1,15
1,07
1,01
0,99
0,95
0,92
0,94
0,96
1,05
1,04
1,1
1,14
1,12
1,19
1,35
1,62
1,43
1,45
1,47
1,35
1,15
1,46
1,3
1,3
1,5
1,52
1,63
1,9
1,65
1,5
1,38
1,39

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=40632&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=40632&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40632&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
117.41666666666670.5139567249793651.62000000000000
215.03250.5767010411895332.45
314.05666666666670.418966983583831.64
414.64583333333330.3203821108765231.25
514.93333333333330.5039179827445471.4
616.44833333333330.393881231137541.07
717.06583333333330.3523804331925501.13
817.080.1782745584255320.530000000000001
915.9450.4493935307217331.47
1014.04583333333330.8696023995673732.74
1110.87583333333331.009504453890252.84
129.69750.3843560139435121.58
139.370.2967398615867870.84
149.321666666666670.3624871993560191.12
159.4450.3050335301986560.9
167.185833333333331.286443005368144.75
172.185833333333331.876885516600374.77
180.9708333333333330.1029967637032030.31
190.72250.1373201302861970.36
200.7441666666666670.1063833833003270.32
211.0150.06947857747012910.23
221.335833333333330.1591145004153430.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 17.4166666666667 & 0.513956724979365 & 1.62000000000000 \tabularnewline
2 & 15.0325 & 0.576701041189533 & 2.45 \tabularnewline
3 & 14.0566666666667 & 0.41896698358383 & 1.64 \tabularnewline
4 & 14.6458333333333 & 0.320382110876523 & 1.25 \tabularnewline
5 & 14.9333333333333 & 0.503917982744547 & 1.4 \tabularnewline
6 & 16.4483333333333 & 0.39388123113754 & 1.07 \tabularnewline
7 & 17.0658333333333 & 0.352380433192550 & 1.13 \tabularnewline
8 & 17.08 & 0.178274558425532 & 0.530000000000001 \tabularnewline
9 & 15.945 & 0.449393530721733 & 1.47 \tabularnewline
10 & 14.0458333333333 & 0.869602399567373 & 2.74 \tabularnewline
11 & 10.8758333333333 & 1.00950445389025 & 2.84 \tabularnewline
12 & 9.6975 & 0.384356013943512 & 1.58 \tabularnewline
13 & 9.37 & 0.296739861586787 & 0.84 \tabularnewline
14 & 9.32166666666667 & 0.362487199356019 & 1.12 \tabularnewline
15 & 9.445 & 0.305033530198656 & 0.9 \tabularnewline
16 & 7.18583333333333 & 1.28644300536814 & 4.75 \tabularnewline
17 & 2.18583333333333 & 1.87688551660037 & 4.77 \tabularnewline
18 & 0.970833333333333 & 0.102996763703203 & 0.31 \tabularnewline
19 & 0.7225 & 0.137320130286197 & 0.36 \tabularnewline
20 & 0.744166666666667 & 0.106383383300327 & 0.32 \tabularnewline
21 & 1.015 & 0.0694785774701291 & 0.23 \tabularnewline
22 & 1.33583333333333 & 0.159114500415343 & 0.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40632&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]17.4166666666667[/C][C]0.513956724979365[/C][C]1.62000000000000[/C][/ROW]
[ROW][C]2[/C][C]15.0325[/C][C]0.576701041189533[/C][C]2.45[/C][/ROW]
[ROW][C]3[/C][C]14.0566666666667[/C][C]0.41896698358383[/C][C]1.64[/C][/ROW]
[ROW][C]4[/C][C]14.6458333333333[/C][C]0.320382110876523[/C][C]1.25[/C][/ROW]
[ROW][C]5[/C][C]14.9333333333333[/C][C]0.503917982744547[/C][C]1.4[/C][/ROW]
[ROW][C]6[/C][C]16.4483333333333[/C][C]0.39388123113754[/C][C]1.07[/C][/ROW]
[ROW][C]7[/C][C]17.0658333333333[/C][C]0.352380433192550[/C][C]1.13[/C][/ROW]
[ROW][C]8[/C][C]17.08[/C][C]0.178274558425532[/C][C]0.530000000000001[/C][/ROW]
[ROW][C]9[/C][C]15.945[/C][C]0.449393530721733[/C][C]1.47[/C][/ROW]
[ROW][C]10[/C][C]14.0458333333333[/C][C]0.869602399567373[/C][C]2.74[/C][/ROW]
[ROW][C]11[/C][C]10.8758333333333[/C][C]1.00950445389025[/C][C]2.84[/C][/ROW]
[ROW][C]12[/C][C]9.6975[/C][C]0.384356013943512[/C][C]1.58[/C][/ROW]
[ROW][C]13[/C][C]9.37[/C][C]0.296739861586787[/C][C]0.84[/C][/ROW]
[ROW][C]14[/C][C]9.32166666666667[/C][C]0.362487199356019[/C][C]1.12[/C][/ROW]
[ROW][C]15[/C][C]9.445[/C][C]0.305033530198656[/C][C]0.9[/C][/ROW]
[ROW][C]16[/C][C]7.18583333333333[/C][C]1.28644300536814[/C][C]4.75[/C][/ROW]
[ROW][C]17[/C][C]2.18583333333333[/C][C]1.87688551660037[/C][C]4.77[/C][/ROW]
[ROW][C]18[/C][C]0.970833333333333[/C][C]0.102996763703203[/C][C]0.31[/C][/ROW]
[ROW][C]19[/C][C]0.7225[/C][C]0.137320130286197[/C][C]0.36[/C][/ROW]
[ROW][C]20[/C][C]0.744166666666667[/C][C]0.106383383300327[/C][C]0.32[/C][/ROW]
[ROW][C]21[/C][C]1.015[/C][C]0.0694785774701291[/C][C]0.23[/C][/ROW]
[ROW][C]22[/C][C]1.33583333333333[/C][C]0.159114500415343[/C][C]0.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40632&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40632&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
117.41666666666670.5139567249793651.62000000000000
215.03250.5767010411895332.45
314.05666666666670.418966983583831.64
414.64583333333330.3203821108765231.25
514.93333333333330.5039179827445471.4
616.44833333333330.393881231137541.07
717.06583333333330.3523804331925501.13
817.080.1782745584255320.530000000000001
915.9450.4493935307217331.47
1014.04583333333330.8696023995673732.74
1110.87583333333331.009504453890252.84
129.69750.3843560139435121.58
139.370.2967398615867870.84
149.321666666666670.3624871993560191.12
159.4450.3050335301986560.9
167.185833333333331.286443005368144.75
172.185833333333331.876885516600374.77
180.9708333333333330.1029967637032030.31
190.72250.1373201302861970.36
200.7441666666666670.1063833833003270.32
211.0150.06947857747012910.23
221.335833333333330.1591145004153430.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.463415225176544
beta0.00218213072175222
S.D.0.0155427068656950
T-STAT0.140395797244848
p-value0.889751628047624

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.463415225176544 \tabularnewline
beta & 0.00218213072175222 \tabularnewline
S.D. & 0.0155427068656950 \tabularnewline
T-STAT & 0.140395797244848 \tabularnewline
p-value & 0.889751628047624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40632&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.463415225176544[/C][/ROW]
[ROW][C]beta[/C][C]0.00218213072175222[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0155427068656950[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.140395797244848[/C][/ROW]
[ROW][C]p-value[/C][C]0.889751628047624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40632&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40632&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)
alpha0.463415225176544
beta0.00218213072175222
S.D.0.0155427068656950
T-STAT0.140395797244848
p-value0.889751628047624






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.79786034585081
beta0.400274714088788
S.D.0.131776448096118
T-STAT3.03752848002723
p-value0.0065019142133407
Lambda0.599725285911212

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.79786034585081 \tabularnewline
beta & 0.400274714088788 \tabularnewline
S.D. & 0.131776448096118 \tabularnewline
T-STAT & 3.03752848002723 \tabularnewline
p-value & 0.0065019142133407 \tabularnewline
Lambda & 0.599725285911212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40632&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.79786034585081[/C][/ROW]
[ROW][C]beta[/C][C]0.400274714088788[/C][/ROW]
[ROW][C]S.D.[/C][C]0.131776448096118[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.03752848002723[/C][/ROW]
[ROW][C]p-value[/C][C]0.0065019142133407[/C][/ROW]
[ROW][C]Lambda[/C][C]0.599725285911212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40632&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40632&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-1.79786034585081
beta0.400274714088788
S.D.0.131776448096118
T-STAT3.03752848002723
p-value0.0065019142133407
Lambda0.599725285911212


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')