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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, 18 Aug 2009 12:31:46 -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/Aug/18/t12506203566ems5jk3u3h8u6d.htm/, Retrieved Mon, 06 May 2024 21:12:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42865, Retrieved Mon, 06 May 2024 21:12:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [Standard deviatio...] [2009-08-18 18:31:46] [1596366c2ece8f787477cc7d1246d4c7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.46
104.66
103.52
103.71
103.78
103.67
103.66
102.76
102
101.5
101.5
99.22
98.97
98.9
99.78
104.4
106.21
105.46
108.33
111.72
111.88
112.86
113.09
116.9
114.62
118.86
124.71
122.53
127.89
136.16
134.12
130.26
135.35
131.43
129.61
123.96
121.1
125.38
123.1
129.92
136.68
131.17
124.82
122.47
126.15
118.74
116.8
116.64
116.53
117.68
119.46
126.19
124.39
121.9
122.53
122.93
124.66
124.41
120.93
120.18
123.44
126.1
125.82
122.18
117.27
117.86
119.09
123.08
125.42
121.81
121.66
121.27
120.92
122.16
124.17
127.26
134.16
134.09
135.57
136.13
136.23
140.6
136.5
130.59
129.5
135.25
138.06
146.28
145.04
147.96
156.71
160.97
168.17
163.91
153.05
151.76
119.55
119.44
120.25
124.92
126.34
125.88
127.34
127.48
119.41
114.82
115.28
116.37
111.99
113.57
117.69
120.74
122.37
123.57
124.86
122.08
123.56
126.92
134.88
130.64
131.65
130.97
136.77
138.17
146.4
152.07
153.05
142.89
141.11
131.9
118.42
108.27

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=42865&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=42865&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42865&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
1104.33750.8992728544033041.94000000000000
2103.46750.4747894270094881.02000000000000
3101.0551.245833054626502.78
4100.51252.622255708354935.5
5107.932.803771269795986.26
6113.68252.208232702109695.02000000000001
7120.184.4233998990218610.0900000000000
8132.10753.727084427985688.27
9130.08754.7353449363976311.39
10124.8753.790703540681248.82
11128.7856.4192341183872314.21
12119.58254.481163353416179.51
13119.9654.321500511010809.66
14122.93751.057083251215342.48999999999999
15122.5452.320409446627894.47999999999999
16124.3851.893453634675713.91999999999999
17119.3252.615626120071455.81
18122.541.933442525652114.15000000000001
19123.62752.767277543001436.34
20134.98751.022232034977052.03999999999999
21135.984.1121527208993610.01
22137.27256.9822984515606816.78
23152.677.4299528935249715.93
24159.22258.0791722967145516.41
25121.042.611423621960515.48
26126.760.7758006616822851.60000000000001
27116.472.064961662275274.59
28115.99753.971090320470358.75
29123.221.269409311451592.78
301294.8711394970786811.32
31134.393.612792087384307.19999999999999
32148.60254.8058115859862910.1600000000000
33124.92514.494928998331332.84

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.3375 & 0.899272854403304 & 1.94000000000000 \tabularnewline
2 & 103.4675 & 0.474789427009488 & 1.02000000000000 \tabularnewline
3 & 101.055 & 1.24583305462650 & 2.78 \tabularnewline
4 & 100.5125 & 2.62225570835493 & 5.5 \tabularnewline
5 & 107.93 & 2.80377126979598 & 6.26 \tabularnewline
6 & 113.6825 & 2.20823270210969 & 5.02000000000001 \tabularnewline
7 & 120.18 & 4.42339989902186 & 10.0900000000000 \tabularnewline
8 & 132.1075 & 3.72708442798568 & 8.27 \tabularnewline
9 & 130.0875 & 4.73534493639763 & 11.39 \tabularnewline
10 & 124.875 & 3.79070354068124 & 8.82 \tabularnewline
11 & 128.785 & 6.41923411838723 & 14.21 \tabularnewline
12 & 119.5825 & 4.48116335341617 & 9.51 \tabularnewline
13 & 119.965 & 4.32150051101080 & 9.66 \tabularnewline
14 & 122.9375 & 1.05708325121534 & 2.48999999999999 \tabularnewline
15 & 122.545 & 2.32040944662789 & 4.47999999999999 \tabularnewline
16 & 124.385 & 1.89345363467571 & 3.91999999999999 \tabularnewline
17 & 119.325 & 2.61562612007145 & 5.81 \tabularnewline
18 & 122.54 & 1.93344252565211 & 4.15000000000001 \tabularnewline
19 & 123.6275 & 2.76727754300143 & 6.34 \tabularnewline
20 & 134.9875 & 1.02223203497705 & 2.03999999999999 \tabularnewline
21 & 135.98 & 4.11215272089936 & 10.01 \tabularnewline
22 & 137.2725 & 6.98229845156068 & 16.78 \tabularnewline
23 & 152.67 & 7.42995289352497 & 15.93 \tabularnewline
24 & 159.2225 & 8.07917229671455 & 16.41 \tabularnewline
25 & 121.04 & 2.61142362196051 & 5.48 \tabularnewline
26 & 126.76 & 0.775800661682285 & 1.60000000000001 \tabularnewline
27 & 116.47 & 2.06496166227527 & 4.59 \tabularnewline
28 & 115.9975 & 3.97109032047035 & 8.75 \tabularnewline
29 & 123.22 & 1.26940931145159 & 2.78 \tabularnewline
30 & 129 & 4.87113949707868 & 11.32 \tabularnewline
31 & 134.39 & 3.61279208738430 & 7.19999999999999 \tabularnewline
32 & 148.6025 & 4.80581158598629 & 10.1600000000000 \tabularnewline
33 & 124.925 & 14.4949289983313 & 32.84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42865&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]104.3375[/C][C]0.899272854403304[/C][C]1.94000000000000[/C][/ROW]
[ROW][C]2[/C][C]103.4675[/C][C]0.474789427009488[/C][C]1.02000000000000[/C][/ROW]
[ROW][C]3[/C][C]101.055[/C][C]1.24583305462650[/C][C]2.78[/C][/ROW]
[ROW][C]4[/C][C]100.5125[/C][C]2.62225570835493[/C][C]5.5[/C][/ROW]
[ROW][C]5[/C][C]107.93[/C][C]2.80377126979598[/C][C]6.26[/C][/ROW]
[ROW][C]6[/C][C]113.6825[/C][C]2.20823270210969[/C][C]5.02000000000001[/C][/ROW]
[ROW][C]7[/C][C]120.18[/C][C]4.42339989902186[/C][C]10.0900000000000[/C][/ROW]
[ROW][C]8[/C][C]132.1075[/C][C]3.72708442798568[/C][C]8.27[/C][/ROW]
[ROW][C]9[/C][C]130.0875[/C][C]4.73534493639763[/C][C]11.39[/C][/ROW]
[ROW][C]10[/C][C]124.875[/C][C]3.79070354068124[/C][C]8.82[/C][/ROW]
[ROW][C]11[/C][C]128.785[/C][C]6.41923411838723[/C][C]14.21[/C][/ROW]
[ROW][C]12[/C][C]119.5825[/C][C]4.48116335341617[/C][C]9.51[/C][/ROW]
[ROW][C]13[/C][C]119.965[/C][C]4.32150051101080[/C][C]9.66[/C][/ROW]
[ROW][C]14[/C][C]122.9375[/C][C]1.05708325121534[/C][C]2.48999999999999[/C][/ROW]
[ROW][C]15[/C][C]122.545[/C][C]2.32040944662789[/C][C]4.47999999999999[/C][/ROW]
[ROW][C]16[/C][C]124.385[/C][C]1.89345363467571[/C][C]3.91999999999999[/C][/ROW]
[ROW][C]17[/C][C]119.325[/C][C]2.61562612007145[/C][C]5.81[/C][/ROW]
[ROW][C]18[/C][C]122.54[/C][C]1.93344252565211[/C][C]4.15000000000001[/C][/ROW]
[ROW][C]19[/C][C]123.6275[/C][C]2.76727754300143[/C][C]6.34[/C][/ROW]
[ROW][C]20[/C][C]134.9875[/C][C]1.02223203497705[/C][C]2.03999999999999[/C][/ROW]
[ROW][C]21[/C][C]135.98[/C][C]4.11215272089936[/C][C]10.01[/C][/ROW]
[ROW][C]22[/C][C]137.2725[/C][C]6.98229845156068[/C][C]16.78[/C][/ROW]
[ROW][C]23[/C][C]152.67[/C][C]7.42995289352497[/C][C]15.93[/C][/ROW]
[ROW][C]24[/C][C]159.2225[/C][C]8.07917229671455[/C][C]16.41[/C][/ROW]
[ROW][C]25[/C][C]121.04[/C][C]2.61142362196051[/C][C]5.48[/C][/ROW]
[ROW][C]26[/C][C]126.76[/C][C]0.775800661682285[/C][C]1.60000000000001[/C][/ROW]
[ROW][C]27[/C][C]116.47[/C][C]2.06496166227527[/C][C]4.59[/C][/ROW]
[ROW][C]28[/C][C]115.9975[/C][C]3.97109032047035[/C][C]8.75[/C][/ROW]
[ROW][C]29[/C][C]123.22[/C][C]1.26940931145159[/C][C]2.78[/C][/ROW]
[ROW][C]30[/C][C]129[/C][C]4.87113949707868[/C][C]11.32[/C][/ROW]
[ROW][C]31[/C][C]134.39[/C][C]3.61279208738430[/C][C]7.19999999999999[/C][/ROW]
[ROW][C]32[/C][C]148.6025[/C][C]4.80581158598629[/C][C]10.1600000000000[/C][/ROW]
[ROW][C]33[/C][C]124.925[/C][C]14.4949289983313[/C][C]32.84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42865&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42865&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
1104.33750.8992728544033041.94000000000000
2103.46750.4747894270094881.02000000000000
3101.0551.245833054626502.78
4100.51252.622255708354935.5
5107.932.803771269795986.26
6113.68252.208232702109695.02000000000001
7120.184.4233998990218610.0900000000000
8132.10753.727084427985688.27
9130.08754.7353449363976311.39
10124.8753.790703540681248.82
11128.7856.4192341183872314.21
12119.58254.481163353416179.51
13119.9654.321500511010809.66
14122.93751.057083251215342.48999999999999
15122.5452.320409446627894.47999999999999
16124.3851.893453634675713.91999999999999
17119.3252.615626120071455.81
18122.541.933442525652114.15000000000001
19123.62752.767277543001436.34
20134.98751.022232034977052.03999999999999
21135.984.1121527208993610.01
22137.27256.9822984515606816.78
23152.677.4299528935249715.93
24159.22258.0791722967145516.41
25121.042.611423621960515.48
26126.760.7758006616822851.60000000000001
27116.472.064961662275274.59
28115.99753.971090320470358.75
29123.221.269409311451592.78
301294.8711394970786811.32
31134.393.612792087384307.19999999999999
32148.60254.8058115859862910.1600000000000
33124.92514.494928998331332.84






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8.82350974098627
beta0.100432024629409
S.D.0.0320431731850999
T-STAT3.13427212870759
p-value0.00375188673342546

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -8.82350974098627 \tabularnewline
beta & 0.100432024629409 \tabularnewline
S.D. & 0.0320431731850999 \tabularnewline
T-STAT & 3.13427212870759 \tabularnewline
p-value & 0.00375188673342546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42865&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.82350974098627[/C][/ROW]
[ROW][C]beta[/C][C]0.100432024629409[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0320431731850999[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.13427212870759[/C][/ROW]
[ROW][C]p-value[/C][C]0.00375188673342546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42865&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42865&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-8.82350974098627
beta0.100432024629409
S.D.0.0320431731850999
T-STAT3.13427212870759
p-value0.00375188673342546






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-17.2181016476983
beta3.79117849631169
S.D.1.05583864156739
T-STAT3.59067981323709
p-value0.00112273889003271
Lambda-2.79117849631169

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -17.2181016476983 \tabularnewline
beta & 3.79117849631169 \tabularnewline
S.D. & 1.05583864156739 \tabularnewline
T-STAT & 3.59067981323709 \tabularnewline
p-value & 0.00112273889003271 \tabularnewline
Lambda & -2.79117849631169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42865&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-17.2181016476983[/C][/ROW]
[ROW][C]beta[/C][C]3.79117849631169[/C][/ROW]
[ROW][C]S.D.[/C][C]1.05583864156739[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.59067981323709[/C][/ROW]
[ROW][C]p-value[/C][C]0.00112273889003271[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.79117849631169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42865&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42865&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-17.2181016476983
beta3.79117849631169
S.D.1.05583864156739
T-STAT3.59067981323709
p-value0.00112273889003271
Lambda-2.79117849631169


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; par2 = 12 ;
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')