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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 computationTue, 29 Nov 2011 12:33:53 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t13225881830fjx7awnk5ma61k.htm/, Retrieved Fri, 26 Apr 2024 01:31:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148629, Retrieved Fri, 26 Apr 2024 01:31:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact75

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] [Gemiddelde consum...] [2011-11-29 17:33:53] [53570eb7f05113140c3a155d32e971f0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
12.27
12.51
12.44
12.47
12.51
12.58
12.5
12.52
12.59
12.51
12.67
12.64
12.54
12.6
12.67
12.62
12.72
12.85
12.85
12.82
12.79
12.94
12.71
12.56

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148629&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148629&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.27250.01258305739211760.0299999999999994
29.320.02581988897471630.0600000000000005
39.3750.04041451884327380.0899999999999999
49.5250.04932882862316240.109999999999999
59.610.03265986323710910.0800000000000001
69.6250.005773502691897160.0100000000000016
79.72250.05251983752196210.119999999999999
89.8350.05000000000000040.120000000000001
99.990.04690415759823390.0899999999999999
1010.10750.03947573094108970.0899999999999999
1110.230.08124038404635960.18
1210.52250.06601767440112810.140000000000001
1310.60.03829708431025350.0800000000000001
1410.70750.05795112883571190.139999999999999
1510.8350.04654746681256350.110000000000001
1610.8950.02380476142847630.0500000000000007
1711.0150.02380476142847570.0499999999999989
1810.970.04690415759823420.0999999999999996
1911.060.1303840481040530.27
2011.390.04966554808583750.119999999999999
2111.690.1246327939722660.26
2211.86250.04193248541803030.0999999999999996
2311.89750.03862210075418840.0800000000000001
2411.9150.06608075867199670.16
2511.9850.1121011448053350.27
2612.23250.1001249219725040.210000000000001
2712.4150.06806859285554040.16
2812.42250.1056330125166060.24
2912.52750.03593976442141310.0800000000000001
3012.60250.06994045086119110.16
3112.60750.05377421934967250.130000000000001
3212.810.06164414002968930.129999999999999
3312.750.1585349593412540.379999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.2725 & 0.0125830573921176 & 0.0299999999999994 \tabularnewline
2 & 9.32 & 0.0258198889747163 & 0.0600000000000005 \tabularnewline
3 & 9.375 & 0.0404145188432738 & 0.0899999999999999 \tabularnewline
4 & 9.525 & 0.0493288286231624 & 0.109999999999999 \tabularnewline
5 & 9.61 & 0.0326598632371091 & 0.0800000000000001 \tabularnewline
6 & 9.625 & 0.00577350269189716 & 0.0100000000000016 \tabularnewline
7 & 9.7225 & 0.0525198375219621 & 0.119999999999999 \tabularnewline
8 & 9.835 & 0.0500000000000004 & 0.120000000000001 \tabularnewline
9 & 9.99 & 0.0469041575982339 & 0.0899999999999999 \tabularnewline
10 & 10.1075 & 0.0394757309410897 & 0.0899999999999999 \tabularnewline
11 & 10.23 & 0.0812403840463596 & 0.18 \tabularnewline
12 & 10.5225 & 0.0660176744011281 & 0.140000000000001 \tabularnewline
13 & 10.6 & 0.0382970843102535 & 0.0800000000000001 \tabularnewline
14 & 10.7075 & 0.0579511288357119 & 0.139999999999999 \tabularnewline
15 & 10.835 & 0.0465474668125635 & 0.110000000000001 \tabularnewline
16 & 10.895 & 0.0238047614284763 & 0.0500000000000007 \tabularnewline
17 & 11.015 & 0.0238047614284757 & 0.0499999999999989 \tabularnewline
18 & 10.97 & 0.0469041575982342 & 0.0999999999999996 \tabularnewline
19 & 11.06 & 0.130384048104053 & 0.27 \tabularnewline
20 & 11.39 & 0.0496655480858375 & 0.119999999999999 \tabularnewline
21 & 11.69 & 0.124632793972266 & 0.26 \tabularnewline
22 & 11.8625 & 0.0419324854180303 & 0.0999999999999996 \tabularnewline
23 & 11.8975 & 0.0386221007541884 & 0.0800000000000001 \tabularnewline
24 & 11.915 & 0.0660807586719967 & 0.16 \tabularnewline
25 & 11.985 & 0.112101144805335 & 0.27 \tabularnewline
26 & 12.2325 & 0.100124921972504 & 0.210000000000001 \tabularnewline
27 & 12.415 & 0.0680685928555404 & 0.16 \tabularnewline
28 & 12.4225 & 0.105633012516606 & 0.24 \tabularnewline
29 & 12.5275 & 0.0359397644214131 & 0.0800000000000001 \tabularnewline
30 & 12.6025 & 0.0699404508611911 & 0.16 \tabularnewline
31 & 12.6075 & 0.0537742193496725 & 0.130000000000001 \tabularnewline
32 & 12.81 & 0.0616441400296893 & 0.129999999999999 \tabularnewline
33 & 12.75 & 0.158534959341254 & 0.379999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148629&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]9.2725[/C][C]0.0125830573921176[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]2[/C][C]9.32[/C][C]0.0258198889747163[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]3[/C][C]9.375[/C][C]0.0404145188432738[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]4[/C][C]9.525[/C][C]0.0493288286231624[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]5[/C][C]9.61[/C][C]0.0326598632371091[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]6[/C][C]9.625[/C][C]0.00577350269189716[/C][C]0.0100000000000016[/C][/ROW]
[ROW][C]7[/C][C]9.7225[/C][C]0.0525198375219621[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]8[/C][C]9.835[/C][C]0.0500000000000004[/C][C]0.120000000000001[/C][/ROW]
[ROW][C]9[/C][C]9.99[/C][C]0.0469041575982339[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]10[/C][C]10.1075[/C][C]0.0394757309410897[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]11[/C][C]10.23[/C][C]0.0812403840463596[/C][C]0.18[/C][/ROW]
[ROW][C]12[/C][C]10.5225[/C][C]0.0660176744011281[/C][C]0.140000000000001[/C][/ROW]
[ROW][C]13[/C][C]10.6[/C][C]0.0382970843102535[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]14[/C][C]10.7075[/C][C]0.0579511288357119[/C][C]0.139999999999999[/C][/ROW]
[ROW][C]15[/C][C]10.835[/C][C]0.0465474668125635[/C][C]0.110000000000001[/C][/ROW]
[ROW][C]16[/C][C]10.895[/C][C]0.0238047614284763[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]17[/C][C]11.015[/C][C]0.0238047614284757[/C][C]0.0499999999999989[/C][/ROW]
[ROW][C]18[/C][C]10.97[/C][C]0.0469041575982342[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]19[/C][C]11.06[/C][C]0.130384048104053[/C][C]0.27[/C][/ROW]
[ROW][C]20[/C][C]11.39[/C][C]0.0496655480858375[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]21[/C][C]11.69[/C][C]0.124632793972266[/C][C]0.26[/C][/ROW]
[ROW][C]22[/C][C]11.8625[/C][C]0.0419324854180303[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]23[/C][C]11.8975[/C][C]0.0386221007541884[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]24[/C][C]11.915[/C][C]0.0660807586719967[/C][C]0.16[/C][/ROW]
[ROW][C]25[/C][C]11.985[/C][C]0.112101144805335[/C][C]0.27[/C][/ROW]
[ROW][C]26[/C][C]12.2325[/C][C]0.100124921972504[/C][C]0.210000000000001[/C][/ROW]
[ROW][C]27[/C][C]12.415[/C][C]0.0680685928555404[/C][C]0.16[/C][/ROW]
[ROW][C]28[/C][C]12.4225[/C][C]0.105633012516606[/C][C]0.24[/C][/ROW]
[ROW][C]29[/C][C]12.5275[/C][C]0.0359397644214131[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]30[/C][C]12.6025[/C][C]0.0699404508611911[/C][C]0.16[/C][/ROW]
[ROW][C]31[/C][C]12.6075[/C][C]0.0537742193496725[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]32[/C][C]12.81[/C][C]0.0616441400296893[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]33[/C][C]12.75[/C][C]0.158534959341254[/C][C]0.379999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148629&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
19.27250.01258305739211760.0299999999999994
29.320.02581988897471630.0600000000000005
39.3750.04041451884327380.0899999999999999
49.5250.04932882862316240.109999999999999
59.610.03265986323710910.0800000000000001
69.6250.005773502691897160.0100000000000016
79.72250.05251983752196210.119999999999999
89.8350.05000000000000040.120000000000001
99.990.04690415759823390.0899999999999999
1010.10750.03947573094108970.0899999999999999
1110.230.08124038404635960.18
1210.52250.06601767440112810.140000000000001
1310.60.03829708431025350.0800000000000001
1410.70750.05795112883571190.139999999999999
1510.8350.04654746681256350.110000000000001
1610.8950.02380476142847630.0500000000000007
1711.0150.02380476142847570.0499999999999989
1810.970.04690415759823420.0999999999999996
1911.060.1303840481040530.27
2011.390.04966554808583750.119999999999999
2111.690.1246327939722660.26
2211.86250.04193248541803030.0999999999999996
2311.89750.03862210075418840.0800000000000001
2411.9150.06608075867199670.16
2511.9850.1121011448053350.27
2612.23250.1001249219725040.210000000000001
2712.4150.06806859285554040.16
2812.42250.1056330125166060.24
2912.52750.03593976442141310.0800000000000001
3012.60250.06994045086119110.16
3112.60750.05377421934967250.130000000000001
3212.810.06164414002968930.129999999999999
3312.750.1585349593412540.379999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.114235854093025
beta0.0157192312658043
S.D.0.00458393718553091
T-STAT3.42919866254314
p-value0.00173143480320143

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.114235854093025 \tabularnewline
beta & 0.0157192312658043 \tabularnewline
S.D. & 0.00458393718553091 \tabularnewline
T-STAT & 3.42919866254314 \tabularnewline
p-value & 0.00173143480320143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148629&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.114235854093025[/C][/ROW]
[ROW][C]beta[/C][C]0.0157192312658043[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00458393718553091[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.42919866254314[/C][/ROW]
[ROW][C]p-value[/C][C]0.00173143480320143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148629&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-0.114235854093025
beta0.0157192312658043
S.D.0.00458393718553091
T-STAT3.42919866254314
p-value0.00173143480320143






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.241049556174
beta3.43653124340748
S.D.0.934782779043933
T-STAT3.67628856719233
p-value0.000890187605689942
Lambda-2.43653124340748

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.241049556174 \tabularnewline
beta & 3.43653124340748 \tabularnewline
S.D. & 0.934782779043933 \tabularnewline
T-STAT & 3.67628856719233 \tabularnewline
p-value & 0.000890187605689942 \tabularnewline
Lambda & -2.43653124340748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148629&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.241049556174[/C][/ROW]
[ROW][C]beta[/C][C]3.43653124340748[/C][/ROW]
[ROW][C]S.D.[/C][C]0.934782779043933[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.67628856719233[/C][/ROW]
[ROW][C]p-value[/C][C]0.000890187605689942[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.43653124340748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148629&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148629&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-11.241049556174
beta3.43653124340748
S.D.0.934782779043933
T-STAT3.67628856719233
p-value0.000890187605689942
Lambda-2.43653124340748


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')