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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 19 Dec 2010 18:51:08 +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/Dec/19/t129278457308y6pwhub7f01f8.htm/, Retrieved Sun, 05 May 2024 05:44:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112676, Retrieved Sun, 05 May 2024 05:44:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

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] [] [2010-12-19 18:51:08] [5f45e5b827d1a020c3ecc9d930121b4e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5
4
5
6
6
6
7
8
7
8
7
8
8
9
9
8
9
9
10
11
12
13
13
13
14
14
15
15
16
16
17
18
19
20
22
20
22
25
24
25
28
26
27
26
25
27
28
30
31
32
34
34
33
32
34
36
37
40
38
38
36
40
40
42
44
45
47
49
47
49
52
50
50
57
58
58
58
61
61
64
68
40
34
46
36
34
45
55
50
56
72
76
78
77
90
88
97
93
84
67
72
75
71
75
90
78
73
62
65
61
58
33
39
56
79
82
79
73
87
85
83
82
83
92
95
97
87
84
84
89
103
106
109
106
105
115
120
124
121
131
139
133
119
123
120
128
134
126
115
106
99
100
99
99
100
100
108
109
115
114
108
113
118
122
118
121
118
121
121
112
119
116
110
111
106
108

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112676&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112676&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
150.8164965809277262
26.750.9574271077563382
37.50.5773502691896261
48.50.5773502691896261
59.750.9574271077563382
612.750.51
714.50.5773502691896261
816.750.9574271077563382
920.251.258305739211793
10241.414213562373103
1126.750.9574271077563382
1227.52.081665999466135
1332.751.53
1433.751.707825127659934
1538.251.258305739211793
1639.52.516611478423586
1746.252.217355782608355
1849.52.081665999466135
1955.753.862210075418828
20612.449489742783186
214714.832396974191334
2242.59.6090235369330521
2363.512.476644848141926
2483.256.7019897542943713
2585.2513.326039671760430
2673.252.061552812808834
2775.7511.615363389350628
2854.2514.453949863849232
296420.314198646923543
30816.3245553203367614
31854.6904157598234310
3290.756.2383224240709713
3395.510.661457061146322
34108.754.510
351244.9665548085837811
36128.59.146948489341520
371275.7735026918962614
381057.3484692283495316
3999.50.5773502691896261
40111.53.511884584284257
41115.256.0759087111860614
42119.51.732050807568883
431173.915780041490249
44108.752.217355782608355

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5 & 0.816496580927726 & 2 \tabularnewline
2 & 6.75 & 0.957427107756338 & 2 \tabularnewline
3 & 7.5 & 0.577350269189626 & 1 \tabularnewline
4 & 8.5 & 0.577350269189626 & 1 \tabularnewline
5 & 9.75 & 0.957427107756338 & 2 \tabularnewline
6 & 12.75 & 0.5 & 1 \tabularnewline
7 & 14.5 & 0.577350269189626 & 1 \tabularnewline
8 & 16.75 & 0.957427107756338 & 2 \tabularnewline
9 & 20.25 & 1.25830573921179 & 3 \tabularnewline
10 & 24 & 1.41421356237310 & 3 \tabularnewline
11 & 26.75 & 0.957427107756338 & 2 \tabularnewline
12 & 27.5 & 2.08166599946613 & 5 \tabularnewline
13 & 32.75 & 1.5 & 3 \tabularnewline
14 & 33.75 & 1.70782512765993 & 4 \tabularnewline
15 & 38.25 & 1.25830573921179 & 3 \tabularnewline
16 & 39.5 & 2.51661147842358 & 6 \tabularnewline
17 & 46.25 & 2.21735578260835 & 5 \tabularnewline
18 & 49.5 & 2.08166599946613 & 5 \tabularnewline
19 & 55.75 & 3.86221007541882 & 8 \tabularnewline
20 & 61 & 2.44948974278318 & 6 \tabularnewline
21 & 47 & 14.8323969741913 & 34 \tabularnewline
22 & 42.5 & 9.60902353693305 & 21 \tabularnewline
23 & 63.5 & 12.4766448481419 & 26 \tabularnewline
24 & 83.25 & 6.70198975429437 & 13 \tabularnewline
25 & 85.25 & 13.3260396717604 & 30 \tabularnewline
26 & 73.25 & 2.06155281280883 & 4 \tabularnewline
27 & 75.75 & 11.6153633893506 & 28 \tabularnewline
28 & 54.25 & 14.4539498638492 & 32 \tabularnewline
29 & 64 & 20.3141986469235 & 43 \tabularnewline
30 & 81 & 6.32455532033676 & 14 \tabularnewline
31 & 85 & 4.69041575982343 & 10 \tabularnewline
32 & 90.75 & 6.23832242407097 & 13 \tabularnewline
33 & 95.5 & 10.6614570611463 & 22 \tabularnewline
34 & 108.75 & 4.5 & 10 \tabularnewline
35 & 124 & 4.96655480858378 & 11 \tabularnewline
36 & 128.5 & 9.1469484893415 & 20 \tabularnewline
37 & 127 & 5.77350269189626 & 14 \tabularnewline
38 & 105 & 7.34846922834953 & 16 \tabularnewline
39 & 99.5 & 0.577350269189626 & 1 \tabularnewline
40 & 111.5 & 3.51188458428425 & 7 \tabularnewline
41 & 115.25 & 6.07590871118606 & 14 \tabularnewline
42 & 119.5 & 1.73205080756888 & 3 \tabularnewline
43 & 117 & 3.91578004149024 & 9 \tabularnewline
44 & 108.75 & 2.21735578260835 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112676&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]5[/C][C]0.816496580927726[/C][C]2[/C][/ROW]
[ROW][C]2[/C][C]6.75[/C][C]0.957427107756338[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]7.5[/C][C]0.577350269189626[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]0.577350269189626[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]9.75[/C][C]0.957427107756338[/C][C]2[/C][/ROW]
[ROW][C]6[/C][C]12.75[/C][C]0.5[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]14.5[/C][C]0.577350269189626[/C][C]1[/C][/ROW]
[ROW][C]8[/C][C]16.75[/C][C]0.957427107756338[/C][C]2[/C][/ROW]
[ROW][C]9[/C][C]20.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]10[/C][C]24[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]11[/C][C]26.75[/C][C]0.957427107756338[/C][C]2[/C][/ROW]
[ROW][C]12[/C][C]27.5[/C][C]2.08166599946613[/C][C]5[/C][/ROW]
[ROW][C]13[/C][C]32.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]14[/C][C]33.75[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]15[/C][C]38.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]16[/C][C]39.5[/C][C]2.51661147842358[/C][C]6[/C][/ROW]
[ROW][C]17[/C][C]46.25[/C][C]2.21735578260835[/C][C]5[/C][/ROW]
[ROW][C]18[/C][C]49.5[/C][C]2.08166599946613[/C][C]5[/C][/ROW]
[ROW][C]19[/C][C]55.75[/C][C]3.86221007541882[/C][C]8[/C][/ROW]
[ROW][C]20[/C][C]61[/C][C]2.44948974278318[/C][C]6[/C][/ROW]
[ROW][C]21[/C][C]47[/C][C]14.8323969741913[/C][C]34[/C][/ROW]
[ROW][C]22[/C][C]42.5[/C][C]9.60902353693305[/C][C]21[/C][/ROW]
[ROW][C]23[/C][C]63.5[/C][C]12.4766448481419[/C][C]26[/C][/ROW]
[ROW][C]24[/C][C]83.25[/C][C]6.70198975429437[/C][C]13[/C][/ROW]
[ROW][C]25[/C][C]85.25[/C][C]13.3260396717604[/C][C]30[/C][/ROW]
[ROW][C]26[/C][C]73.25[/C][C]2.06155281280883[/C][C]4[/C][/ROW]
[ROW][C]27[/C][C]75.75[/C][C]11.6153633893506[/C][C]28[/C][/ROW]
[ROW][C]28[/C][C]54.25[/C][C]14.4539498638492[/C][C]32[/C][/ROW]
[ROW][C]29[/C][C]64[/C][C]20.3141986469235[/C][C]43[/C][/ROW]
[ROW][C]30[/C][C]81[/C][C]6.32455532033676[/C][C]14[/C][/ROW]
[ROW][C]31[/C][C]85[/C][C]4.69041575982343[/C][C]10[/C][/ROW]
[ROW][C]32[/C][C]90.75[/C][C]6.23832242407097[/C][C]13[/C][/ROW]
[ROW][C]33[/C][C]95.5[/C][C]10.6614570611463[/C][C]22[/C][/ROW]
[ROW][C]34[/C][C]108.75[/C][C]4.5[/C][C]10[/C][/ROW]
[ROW][C]35[/C][C]124[/C][C]4.96655480858378[/C][C]11[/C][/ROW]
[ROW][C]36[/C][C]128.5[/C][C]9.1469484893415[/C][C]20[/C][/ROW]
[ROW][C]37[/C][C]127[/C][C]5.77350269189626[/C][C]14[/C][/ROW]
[ROW][C]38[/C][C]105[/C][C]7.34846922834953[/C][C]16[/C][/ROW]
[ROW][C]39[/C][C]99.5[/C][C]0.577350269189626[/C][C]1[/C][/ROW]
[ROW][C]40[/C][C]111.5[/C][C]3.51188458428425[/C][C]7[/C][/ROW]
[ROW][C]41[/C][C]115.25[/C][C]6.07590871118606[/C][C]14[/C][/ROW]
[ROW][C]42[/C][C]119.5[/C][C]1.73205080756888[/C][C]3[/C][/ROW]
[ROW][C]43[/C][C]117[/C][C]3.91578004149024[/C][C]9[/C][/ROW]
[ROW][C]44[/C][C]108.75[/C][C]2.21735578260835[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112676&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
150.8164965809277262
26.750.9574271077563382
37.50.5773502691896261
48.50.5773502691896261
59.750.9574271077563382
612.750.51
714.50.5773502691896261
816.750.9574271077563382
920.251.258305739211793
10241.414213562373103
1126.750.9574271077563382
1227.52.081665999466135
1332.751.53
1433.751.707825127659934
1538.251.258305739211793
1639.52.516611478423586
1746.252.217355782608355
1849.52.081665999466135
1955.753.862210075418828
20612.449489742783186
214714.832396974191334
2242.59.6090235369330521
2363.512.476644848141926
2483.256.7019897542943713
2585.2513.326039671760430
2673.252.061552812808834
2775.7511.615363389350628
2854.2514.453949863849232
296420.314198646923543
30816.3245553203367614
31854.6904157598234310
3290.756.2383224240709713
3395.510.661457061146322
34108.754.510
351244.9665548085837811
36128.59.146948489341520
371275.7735026918962614
381057.3484692283495316
3999.50.5773502691896261
40111.53.511884584284257
41115.256.0759087111860614
42119.51.732050807568883
431173.915780041490249
44108.752.217355782608355






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.18246687026624
beta0.0423952883327472
S.D.0.0175591399422823
T-STAT2.41442852395404
p-value0.0201951800080296

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.18246687026624 \tabularnewline
beta & 0.0423952883327472 \tabularnewline
S.D. & 0.0175591399422823 \tabularnewline
T-STAT & 2.41442852395404 \tabularnewline
p-value & 0.0201951800080296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112676&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.18246687026624[/C][/ROW]
[ROW][C]beta[/C][C]0.0423952883327472[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0175591399422823[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.41442852395404[/C][/ROW]
[ROW][C]p-value[/C][C]0.0201951800080296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112676&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112676&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)
alpha2.18246687026624
beta0.0423952883327472
S.D.0.0175591399422823
T-STAT2.41442852395404
p-value0.0201951800080296






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.96607958072566
beta0.793692118958827
S.D.0.130903559933309
T-STAT6.06318208124507
p-value3.22180606847752e-07
Lambda0.206307881041173

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.96607958072566 \tabularnewline
beta & 0.793692118958827 \tabularnewline
S.D. & 0.130903559933309 \tabularnewline
T-STAT & 6.06318208124507 \tabularnewline
p-value & 3.22180606847752e-07 \tabularnewline
Lambda & 0.206307881041173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112676&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.96607958072566[/C][/ROW]
[ROW][C]beta[/C][C]0.793692118958827[/C][/ROW]
[ROW][C]S.D.[/C][C]0.130903559933309[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.06318208124507[/C][/ROW]
[ROW][C]p-value[/C][C]3.22180606847752e-07[/C][/ROW]
[ROW][C]Lambda[/C][C]0.206307881041173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112676&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112676&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-1.96607958072566
beta0.793692118958827
S.D.0.130903559933309
T-STAT6.06318208124507
p-value3.22180606847752e-07
Lambda0.206307881041173


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')