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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 computationFri, 03 Jul 2009 14:49:54 -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/Jul/03/t1246654279w0lnwpau8k7akm4.htm/, Retrieved Sat, 18 May 2024 16:45:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42334, Retrieved Sat, 18 May 2024 16:45:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

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] [Opgave 8, oefenin...] [2009-07-03 20:49:54] [564a720da86171cdf215ca3dfe587c26] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,26
9,29
9,28
9,31
9,27
9,27
9,28
9,25
9,32
9,33
9,31
9,3
9,29
9,33
9,35
9,35
9,37
9,37
9,35
9,33
9,34
9,37
9,33
9,31
9,26
9,27
9,29
9,27
9,29
9,31
9,33
9,35
9,34
9,35
9,38
9,43
9,47
9,5
9,55
9,58
9,61
9,57
9,61
9,65
9,62
9,63
9,62
9,63
9,65
9,72
9,75
9,77
9,78
9,82
9,84
9,9
9,94
9,96
10,03
10,03
10,12
10,12
10,05
10,14
10,17
10,2
10,2
10,35
10,43
10,52
10,57
10,57
10,57
10,65
10,57
10,61
10,63
10,71
10,72
10,77
10,79
10,82
10,9
10,83
10,92
10,91
10,88
10,87
11
10,99
11,03
11,04
10,99
10,9
11
10,99
10,92
10,98
11,15
11,19
11,33
11,38
11,4
11,45
11,56
11,61
11,82
11,77
11,85
11,82
11,92
11,86
11,87
11,94
11,86
11,92
11,83
11,91
11,93
11,99
11,96
12,12
11,85
12,01
12,1
12,21
12,31
12,31
12,39
12,35
12,41
12,51

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42334&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]5 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=42334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42334&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.2850.02081665999466160.0500000000000007
29.26750.01258305739211760.0299999999999994
39.3150.01290994448735780.0299999999999994
49.330.02828427124746210.0600000000000005
59.3550.01914854215512640.0399999999999991
69.33750.02499999999999950.0599999999999987
79.27250.01258305739211760.0299999999999994
89.320.02581988897471630.0600000000000005
99.3750.04041451884327380.0899999999999999
109.5250.04932882862316240.109999999999999
119.610.03265986323710910.08
129.6250.005773502691897160.0100000000000016
139.72250.05251983752196210.119999999999999
149.8350.05000000000000040.120000000000001
159.990.04690415759823390.0899999999999999
1610.10750.03947573094108970.0899999999999999
1710.230.08124038404635960.180000000000000
1810.52250.06601767440112810.140000000000001
1910.60.03829708431025350.08
2010.70750.05795112883571190.139999999999999
2110.8350.04654746681256350.110000000000001
2210.8950.02380476142847630.0500000000000007
2311.0150.02380476142847570.0499999999999989
2410.970.04690415759823420.0999999999999996
2511.060.1303840481040530.270000000000000
2611.390.04966554808583750.119999999999999
2711.690.1246327939722660.26
2811.86250.04193248541803030.0999999999999996
2911.89750.03862210075418840.08
3011.9150.06608075867199670.16
3111.9850.1121011448053350.270000000000000
3212.23250.1001249219725040.210000000000001
3312.4150.06806859285554040.16

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.285 & 0.0208166599946616 & 0.0500000000000007 \tabularnewline
2 & 9.2675 & 0.0125830573921176 & 0.0299999999999994 \tabularnewline
3 & 9.315 & 0.0129099444873578 & 0.0299999999999994 \tabularnewline
4 & 9.33 & 0.0282842712474621 & 0.0600000000000005 \tabularnewline
5 & 9.355 & 0.0191485421551264 & 0.0399999999999991 \tabularnewline
6 & 9.3375 & 0.0249999999999995 & 0.0599999999999987 \tabularnewline
7 & 9.2725 & 0.0125830573921176 & 0.0299999999999994 \tabularnewline
8 & 9.32 & 0.0258198889747163 & 0.0600000000000005 \tabularnewline
9 & 9.375 & 0.0404145188432738 & 0.0899999999999999 \tabularnewline
10 & 9.525 & 0.0493288286231624 & 0.109999999999999 \tabularnewline
11 & 9.61 & 0.0326598632371091 & 0.08 \tabularnewline
12 & 9.625 & 0.00577350269189716 & 0.0100000000000016 \tabularnewline
13 & 9.7225 & 0.0525198375219621 & 0.119999999999999 \tabularnewline
14 & 9.835 & 0.0500000000000004 & 0.120000000000001 \tabularnewline
15 & 9.99 & 0.0469041575982339 & 0.0899999999999999 \tabularnewline
16 & 10.1075 & 0.0394757309410897 & 0.0899999999999999 \tabularnewline
17 & 10.23 & 0.0812403840463596 & 0.180000000000000 \tabularnewline
18 & 10.5225 & 0.0660176744011281 & 0.140000000000001 \tabularnewline
19 & 10.6 & 0.0382970843102535 & 0.08 \tabularnewline
20 & 10.7075 & 0.0579511288357119 & 0.139999999999999 \tabularnewline
21 & 10.835 & 0.0465474668125635 & 0.110000000000001 \tabularnewline
22 & 10.895 & 0.0238047614284763 & 0.0500000000000007 \tabularnewline
23 & 11.015 & 0.0238047614284757 & 0.0499999999999989 \tabularnewline
24 & 10.97 & 0.0469041575982342 & 0.0999999999999996 \tabularnewline
25 & 11.06 & 0.130384048104053 & 0.270000000000000 \tabularnewline
26 & 11.39 & 0.0496655480858375 & 0.119999999999999 \tabularnewline
27 & 11.69 & 0.124632793972266 & 0.26 \tabularnewline
28 & 11.8625 & 0.0419324854180303 & 0.0999999999999996 \tabularnewline
29 & 11.8975 & 0.0386221007541884 & 0.08 \tabularnewline
30 & 11.915 & 0.0660807586719967 & 0.16 \tabularnewline
31 & 11.985 & 0.112101144805335 & 0.270000000000000 \tabularnewline
32 & 12.2325 & 0.100124921972504 & 0.210000000000001 \tabularnewline
33 & 12.415 & 0.0680685928555404 & 0.16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42334&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]9.285[/C][C]0.0208166599946616[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]2[/C][C]9.2675[/C][C]0.0125830573921176[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]3[/C][C]9.315[/C][C]0.0129099444873578[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]4[/C][C]9.33[/C][C]0.0282842712474621[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]5[/C][C]9.355[/C][C]0.0191485421551264[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]6[/C][C]9.3375[/C][C]0.0249999999999995[/C][C]0.0599999999999987[/C][/ROW]
[ROW][C]7[/C][C]9.2725[/C][C]0.0125830573921176[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]8[/C][C]9.32[/C][C]0.0258198889747163[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]9[/C][C]9.375[/C][C]0.0404145188432738[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]10[/C][C]9.525[/C][C]0.0493288286231624[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]11[/C][C]9.61[/C][C]0.0326598632371091[/C][C]0.08[/C][/ROW]
[ROW][C]12[/C][C]9.625[/C][C]0.00577350269189716[/C][C]0.0100000000000016[/C][/ROW]
[ROW][C]13[/C][C]9.7225[/C][C]0.0525198375219621[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]14[/C][C]9.835[/C][C]0.0500000000000004[/C][C]0.120000000000001[/C][/ROW]
[ROW][C]15[/C][C]9.99[/C][C]0.0469041575982339[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]16[/C][C]10.1075[/C][C]0.0394757309410897[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]17[/C][C]10.23[/C][C]0.0812403840463596[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]18[/C][C]10.5225[/C][C]0.0660176744011281[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]19[/C][C]10.6[/C][C]0.0382970843102535[/C][C]0.08[/C][/ROW]
[ROW][C]20[/C][C]10.7075[/C][C]0.0579511288357119[/C][C]0.139999999999999[/C][/ROW]
[ROW][C]21[/C][C]10.835[/C][C]0.0465474668125635[/C][C]0.110000000000001[/C][/ROW]
[ROW][C]22[/C][C]10.895[/C][C]0.0238047614284763[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]23[/C][C]11.015[/C][C]0.0238047614284757[/C][C]0.0499999999999989[/C][/ROW]
[ROW][C]24[/C][C]10.97[/C][C]0.0469041575982342[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]25[/C][C]11.06[/C][C]0.130384048104053[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]26[/C][C]11.39[/C][C]0.0496655480858375[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]27[/C][C]11.69[/C][C]0.124632793972266[/C][C]0.26[/C][/ROW]
[ROW][C]28[/C][C]11.8625[/C][C]0.0419324854180303[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]29[/C][C]11.8975[/C][C]0.0386221007541884[/C][C]0.08[/C][/ROW]
[ROW][C]30[/C][C]11.915[/C][C]0.0660807586719967[/C][C]0.16[/C][/ROW]
[ROW][C]31[/C][C]11.985[/C][C]0.112101144805335[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]32[/C][C]12.2325[/C][C]0.100124921972504[/C][C]0.210000000000001[/C][/ROW]
[ROW][C]33[/C][C]12.415[/C][C]0.0680685928555404[/C][C]0.16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42334&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
19.2850.02081665999466160.0500000000000007
29.26750.01258305739211760.0299999999999994
39.3150.01290994448735780.0299999999999994
49.330.02828427124746210.0600000000000005
59.3550.01914854215512640.0399999999999991
69.33750.02499999999999950.0599999999999987
79.27250.01258305739211760.0299999999999994
89.320.02581988897471630.0600000000000005
99.3750.04041451884327380.0899999999999999
109.5250.04932882862316240.109999999999999
119.610.03265986323710910.08
129.6250.005773502691897160.0100000000000016
139.72250.05251983752196210.119999999999999
149.8350.05000000000000040.120000000000001
159.990.04690415759823390.0899999999999999
1610.10750.03947573094108970.0899999999999999
1710.230.08124038404635960.180000000000000
1810.52250.06601767440112810.140000000000001
1910.60.03829708431025350.08
2010.70750.05795112883571190.139999999999999
2110.8350.04654746681256350.110000000000001
2210.8950.02380476142847630.0500000000000007
2311.0150.02380476142847570.0499999999999989
2410.970.04690415759823420.0999999999999996
2511.060.1303840481040530.270000000000000
2611.390.04966554808583750.119999999999999
2711.690.1246327939722660.26
2811.86250.04193248541803030.0999999999999996
2911.89750.03862210075418840.08
3011.9150.06608075867199670.16
3111.9850.1121011448053350.270000000000000
3212.23250.1001249219725040.210000000000001
3312.4150.06806859285554040.16






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.152690036468237
beta0.0192431613755005
S.D.0.00424045293733318
T-STAT4.53799668570371
p-value8.03615032573362e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.152690036468237 \tabularnewline
beta & 0.0192431613755005 \tabularnewline
S.D. & 0.00424045293733318 \tabularnewline
T-STAT & 4.53799668570371 \tabularnewline
p-value & 8.03615032573362e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42334&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.152690036468237[/C][/ROW]
[ROW][C]beta[/C][C]0.0192431613755005[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00424045293733318[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.53799668570371[/C][/ROW]
[ROW][C]p-value[/C][C]8.03615032573362e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42334&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-0.152690036468237
beta0.0192431613755005
S.D.0.00424045293733318
T-STAT4.53799668570371
p-value8.03615032573362e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-14.1718671559464
beta4.66574772795916
S.D.0.990046857994273
T-STAT4.7126534368398
p-value4.88631117271924e-05
Lambda-3.66574772795916

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -14.1718671559464 \tabularnewline
beta & 4.66574772795916 \tabularnewline
S.D. & 0.990046857994273 \tabularnewline
T-STAT & 4.7126534368398 \tabularnewline
p-value & 4.88631117271924e-05 \tabularnewline
Lambda & -3.66574772795916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42334&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.1718671559464[/C][/ROW]
[ROW][C]beta[/C][C]4.66574772795916[/C][/ROW]
[ROW][C]S.D.[/C][C]0.990046857994273[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.7126534368398[/C][/ROW]
[ROW][C]p-value[/C][C]4.88631117271924e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.66574772795916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42334&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-14.1718671559464
beta4.66574772795916
S.D.0.990046857994273
T-STAT4.7126534368398
p-value4.88631117271924e-05
Lambda-3.66574772795916


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')