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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 computationSun, 08 Aug 2010 13:28:02 +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/08/t128127409578guv5m9qkyvkk7.htm/, Retrieved Sat, 04 May 2024 02:33:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78510, Retrieved Sat, 04 May 2024 02:33:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPhilippe De Vocht
Estimated Impact232

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] [Omzet product Y] [2010-08-08 13:28:02] [181f2439255053cc457d7672472fa443] [Current]
-   P     [Standard Deviation-Mean Plot] [Omzet product Y] [2010-08-16 13:50:15] [44f4e89d2978fa9cb7cef84cf6986739]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31
30
29
27
25
24
25
27
28
28
29
31
31
27
25
16
20
21
25
24
28
27
23
36
37
30
27
22
22
25
33
35
35
29
25
34
31
29
21
19
18
25
23
22
20
15
17
25
26
26
23
24
24
42
40
45
47
40
39
49
55
54
48
44
48
62
57
60
56
57
54
62
65
68
69
67
72
82
72
77
79
78
76
79

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=78510&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=78510&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78510&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
129.251.707825127659934
225.251.258305739211793
3291.414213562373103
424.756.3442887702247615
522.52.380476142847625
628.55.4467115461227313
7296.2716292407422615
828.756.2383224240709713
930.754.6457866215887810
10255.887840577551912
11222.943920288775957
1219.254.349329450233310
1324.751.53
1437.759.3941471140279721
1543.754.9916597106239810
1650.255.1881274720911311
1756.756.1846584384264914
1857.253.403429642777028
1967.251.707825127659934
2075.754.7871355387816910
21781.414213562373103

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 29.25 & 1.70782512765993 & 4 \tabularnewline
2 & 25.25 & 1.25830573921179 & 3 \tabularnewline
3 & 29 & 1.41421356237310 & 3 \tabularnewline
4 & 24.75 & 6.34428877022476 & 15 \tabularnewline
5 & 22.5 & 2.38047614284762 & 5 \tabularnewline
6 & 28.5 & 5.44671154612273 & 13 \tabularnewline
7 & 29 & 6.27162924074226 & 15 \tabularnewline
8 & 28.75 & 6.23832242407097 & 13 \tabularnewline
9 & 30.75 & 4.64578662158878 & 10 \tabularnewline
10 & 25 & 5.8878405775519 & 12 \tabularnewline
11 & 22 & 2.94392028877595 & 7 \tabularnewline
12 & 19.25 & 4.3493294502333 & 10 \tabularnewline
13 & 24.75 & 1.5 & 3 \tabularnewline
14 & 37.75 & 9.39414711402797 & 21 \tabularnewline
15 & 43.75 & 4.99165971062398 & 10 \tabularnewline
16 & 50.25 & 5.18812747209113 & 11 \tabularnewline
17 & 56.75 & 6.18465843842649 & 14 \tabularnewline
18 & 57.25 & 3.40342964277702 & 8 \tabularnewline
19 & 67.25 & 1.70782512765993 & 4 \tabularnewline
20 & 75.75 & 4.78713553878169 & 10 \tabularnewline
21 & 78 & 1.41421356237310 & 3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78510&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]29.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]25.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]29[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]24.75[/C][C]6.34428877022476[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]22.5[/C][C]2.38047614284762[/C][C]5[/C][/ROW]
[ROW][C]6[/C][C]28.5[/C][C]5.44671154612273[/C][C]13[/C][/ROW]
[ROW][C]7[/C][C]29[/C][C]6.27162924074226[/C][C]15[/C][/ROW]
[ROW][C]8[/C][C]28.75[/C][C]6.23832242407097[/C][C]13[/C][/ROW]
[ROW][C]9[/C][C]30.75[/C][C]4.64578662158878[/C][C]10[/C][/ROW]
[ROW][C]10[/C][C]25[/C][C]5.8878405775519[/C][C]12[/C][/ROW]
[ROW][C]11[/C][C]22[/C][C]2.94392028877595[/C][C]7[/C][/ROW]
[ROW][C]12[/C][C]19.25[/C][C]4.3493294502333[/C][C]10[/C][/ROW]
[ROW][C]13[/C][C]24.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]14[/C][C]37.75[/C][C]9.39414711402797[/C][C]21[/C][/ROW]
[ROW][C]15[/C][C]43.75[/C][C]4.99165971062398[/C][C]10[/C][/ROW]
[ROW][C]16[/C][C]50.25[/C][C]5.18812747209113[/C][C]11[/C][/ROW]
[ROW][C]17[/C][C]56.75[/C][C]6.18465843842649[/C][C]14[/C][/ROW]
[ROW][C]18[/C][C]57.25[/C][C]3.40342964277702[/C][C]8[/C][/ROW]
[ROW][C]19[/C][C]67.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]20[/C][C]75.75[/C][C]4.78713553878169[/C][C]10[/C][/ROW]
[ROW][C]21[/C][C]78[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78510&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78510&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
129.251.707825127659934
225.251.258305739211793
3291.414213562373103
424.756.3442887702247615
522.52.380476142847625
628.55.4467115461227313
7296.2716292407422615
828.756.2383224240709713
930.754.6457866215887810
10255.887840577551912
11222.943920288775957
1219.254.349329450233310
1324.751.53
1437.759.3941471140279721
1543.754.9916597106239810
1650.255.1881274720911311
1756.756.1846584384264914
1857.253.403429642777028
1967.251.707825127659934
2075.754.7871355387816910
21781.414213562373103






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.51508599987455
beta-0.00913340769609086
S.D.0.0277699350583999
T-STAT-0.328895536733643
p-value0.74583222882182

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.51508599987455 \tabularnewline
beta & -0.00913340769609086 \tabularnewline
S.D. & 0.0277699350583999 \tabularnewline
T-STAT & -0.328895536733643 \tabularnewline
p-value & 0.74583222882182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78510&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.51508599987455[/C][/ROW]
[ROW][C]beta[/C][C]-0.00913340769609086[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0277699350583999[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.328895536733643[/C][/ROW]
[ROW][C]p-value[/C][C]0.74583222882182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78510&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78510&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)
alpha4.51508599987455
beta-0.00913340769609086
S.D.0.0277699350583999
T-STAT-0.328895536733643
p-value0.74583222882182






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.33404305591742
beta-0.0211034225818561
S.D.0.333017001086162
T-STAT-0.0633704060544224
p-value0.950133497054272
Lambda1.02110342258186

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.33404305591742 \tabularnewline
beta & -0.0211034225818561 \tabularnewline
S.D. & 0.333017001086162 \tabularnewline
T-STAT & -0.0633704060544224 \tabularnewline
p-value & 0.950133497054272 \tabularnewline
Lambda & 1.02110342258186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78510&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.33404305591742[/C][/ROW]
[ROW][C]beta[/C][C]-0.0211034225818561[/C][/ROW]
[ROW][C]S.D.[/C][C]0.333017001086162[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0633704060544224[/C][/ROW]
[ROW][C]p-value[/C][C]0.950133497054272[/C][/ROW]
[ROW][C]Lambda[/C][C]1.02110342258186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78510&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78510&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)
alpha1.33404305591742
beta-0.0211034225818561
S.D.0.333017001086162
T-STAT-0.0633704060544224
p-value0.950133497054272
Lambda1.02110342258186


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')