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Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 22 Dec 2011 16:46:24 -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/Dec/22/t1324590400ha3rxvndns9ydq5.htm/, Retrieved Fri, 03 May 2024 06:32:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160018, Retrieved Fri, 03 May 2024 06:32:49 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2011-12-22 21:46:24] [c7041fab4904771a5085f5eb0f28763f] [Current]
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Dataseries X:
4581945
3874038
4086290
4364364
3793586
4533914
4823043
3981535
4746356
5284534
4264830
3924674
3734753
3762290
3609739
3877594
3636415
3578195
3604342
3459513
3366571
3371277
3724848
3350830
3305159
3390736
3349758
3253655
3734250
3455433
2966726
2993716
3009320
3169713
3170061
3368934
3292638
3337344
3208306
3359130
3223078
3437159
3400156
3657576
3765613
3481921
3604800
3981340
3734078
4018173
3887417
3919880
4014466
4197758
3896531
3964742
4201847
4050512
3997402
4314479
4925744
5130631
4444855
3967319
3931250
4235952
4169219
3779064
3558810
3699466
3650693
3525633
3470276
3859094
3661155
3356365
3344440
3338684
3404294
3289319
3469252
3571850
3639914
3091730
3078149
3188115
3246082
3486992
3378187
3282306
3288345
3325749
3352262
3531954
3722622
3809365
3750617
3615286
3696556
4123959
4136163
3933392
4035576
4551202
4032195
3970893
4489016
5426127
4578224
4126390
4892100
4128697
4408721
4199465
4074767
4161758
3891319
4470302
4283111
3845962
3911471
3798478
3644313
3784029
3647134
3994662
3607836
3566008
3511412
3258665
3486573
3369443
3465544
3905224
3733881
3220642
3225812
3354461
3352261
3450652




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160018&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160018&T=0

As an alternative you can also use a 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'Gwilym Jenkins' @ jenkins.wessa.net







Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14226659.25310502.729254108707907
24283019.5477846.3788516841029457
34555098.5591705.5664937311359860
43746094109963.425316481267855
53569616.2577167.0726988958176902
63453381.5181188.743768296374018
7332482758928.8691276752137081
83287531.25372823.483172555767524
93179507147231.510044555359614
103299354.566711.4513783054150824
113429492.25178464.220724818434498
123708418.5215866.677250103499419
133889887117812.595854603284095
144018374.25128990.955745936301227
154141060144459.648573572317077
164617137.25519890.6580980111163312
174028871.25211749.45773622456888
183608650.580396.9476887442173833
193586722.5220870.094729157502729
203344184.2547094.5710273488114975
213443186.5244579.289918423548184
223249834.5172764.742403265408843
233318646.7544099.620137252995881
243604050.75203967.806746351457103
253796604.5225212.432768856508673
264164083.25271030.768911791617810
274479557.75672050.6085900451455234
284431352.75373480.019257947765710
294211177.75141669.484527367333954
304122673.5303688.395300731624340
313784572.75109498.272383251267158
323703910196644.70054729428654
333406523.25116399.626838964252747
343581322.75300932.640174259684582
353345796.592209.5791137414224840

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4226659.25 & 310502.729254108 & 707907 \tabularnewline
2 & 4283019.5 & 477846.378851684 & 1029457 \tabularnewline
3 & 4555098.5 & 591705.566493731 & 1359860 \tabularnewline
4 & 3746094 & 109963.425316481 & 267855 \tabularnewline
5 & 3569616.25 & 77167.0726988958 & 176902 \tabularnewline
6 & 3453381.5 & 181188.743768296 & 374018 \tabularnewline
7 & 3324827 & 58928.8691276752 & 137081 \tabularnewline
8 & 3287531.25 & 372823.483172555 & 767524 \tabularnewline
9 & 3179507 & 147231.510044555 & 359614 \tabularnewline
10 & 3299354.5 & 66711.4513783054 & 150824 \tabularnewline
11 & 3429492.25 & 178464.220724818 & 434498 \tabularnewline
12 & 3708418.5 & 215866.677250103 & 499419 \tabularnewline
13 & 3889887 & 117812.595854603 & 284095 \tabularnewline
14 & 4018374.25 & 128990.955745936 & 301227 \tabularnewline
15 & 4141060 & 144459.648573572 & 317077 \tabularnewline
16 & 4617137.25 & 519890.658098011 & 1163312 \tabularnewline
17 & 4028871.25 & 211749.45773622 & 456888 \tabularnewline
18 & 3608650.5 & 80396.9476887442 & 173833 \tabularnewline
19 & 3586722.5 & 220870.094729157 & 502729 \tabularnewline
20 & 3344184.25 & 47094.5710273488 & 114975 \tabularnewline
21 & 3443186.5 & 244579.289918423 & 548184 \tabularnewline
22 & 3249834.5 & 172764.742403265 & 408843 \tabularnewline
23 & 3318646.75 & 44099.6201372529 & 95881 \tabularnewline
24 & 3604050.75 & 203967.806746351 & 457103 \tabularnewline
25 & 3796604.5 & 225212.432768856 & 508673 \tabularnewline
26 & 4164083.25 & 271030.768911791 & 617810 \tabularnewline
27 & 4479557.75 & 672050.608590045 & 1455234 \tabularnewline
28 & 4431352.75 & 373480.019257947 & 765710 \tabularnewline
29 & 4211177.75 & 141669.484527367 & 333954 \tabularnewline
30 & 4122673.5 & 303688.395300731 & 624340 \tabularnewline
31 & 3784572.75 & 109498.272383251 & 267158 \tabularnewline
32 & 3703910 & 196644.70054729 & 428654 \tabularnewline
33 & 3406523.25 & 116399.626838964 & 252747 \tabularnewline
34 & 3581322.75 & 300932.640174259 & 684582 \tabularnewline
35 & 3345796.5 & 92209.5791137414 & 224840 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160018&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]4226659.25[/C][C]310502.729254108[/C][C]707907[/C][/ROW]
[ROW][C]2[/C][C]4283019.5[/C][C]477846.378851684[/C][C]1029457[/C][/ROW]
[ROW][C]3[/C][C]4555098.5[/C][C]591705.566493731[/C][C]1359860[/C][/ROW]
[ROW][C]4[/C][C]3746094[/C][C]109963.425316481[/C][C]267855[/C][/ROW]
[ROW][C]5[/C][C]3569616.25[/C][C]77167.0726988958[/C][C]176902[/C][/ROW]
[ROW][C]6[/C][C]3453381.5[/C][C]181188.743768296[/C][C]374018[/C][/ROW]
[ROW][C]7[/C][C]3324827[/C][C]58928.8691276752[/C][C]137081[/C][/ROW]
[ROW][C]8[/C][C]3287531.25[/C][C]372823.483172555[/C][C]767524[/C][/ROW]
[ROW][C]9[/C][C]3179507[/C][C]147231.510044555[/C][C]359614[/C][/ROW]
[ROW][C]10[/C][C]3299354.5[/C][C]66711.4513783054[/C][C]150824[/C][/ROW]
[ROW][C]11[/C][C]3429492.25[/C][C]178464.220724818[/C][C]434498[/C][/ROW]
[ROW][C]12[/C][C]3708418.5[/C][C]215866.677250103[/C][C]499419[/C][/ROW]
[ROW][C]13[/C][C]3889887[/C][C]117812.595854603[/C][C]284095[/C][/ROW]
[ROW][C]14[/C][C]4018374.25[/C][C]128990.955745936[/C][C]301227[/C][/ROW]
[ROW][C]15[/C][C]4141060[/C][C]144459.648573572[/C][C]317077[/C][/ROW]
[ROW][C]16[/C][C]4617137.25[/C][C]519890.658098011[/C][C]1163312[/C][/ROW]
[ROW][C]17[/C][C]4028871.25[/C][C]211749.45773622[/C][C]456888[/C][/ROW]
[ROW][C]18[/C][C]3608650.5[/C][C]80396.9476887442[/C][C]173833[/C][/ROW]
[ROW][C]19[/C][C]3586722.5[/C][C]220870.094729157[/C][C]502729[/C][/ROW]
[ROW][C]20[/C][C]3344184.25[/C][C]47094.5710273488[/C][C]114975[/C][/ROW]
[ROW][C]21[/C][C]3443186.5[/C][C]244579.289918423[/C][C]548184[/C][/ROW]
[ROW][C]22[/C][C]3249834.5[/C][C]172764.742403265[/C][C]408843[/C][/ROW]
[ROW][C]23[/C][C]3318646.75[/C][C]44099.6201372529[/C][C]95881[/C][/ROW]
[ROW][C]24[/C][C]3604050.75[/C][C]203967.806746351[/C][C]457103[/C][/ROW]
[ROW][C]25[/C][C]3796604.5[/C][C]225212.432768856[/C][C]508673[/C][/ROW]
[ROW][C]26[/C][C]4164083.25[/C][C]271030.768911791[/C][C]617810[/C][/ROW]
[ROW][C]27[/C][C]4479557.75[/C][C]672050.608590045[/C][C]1455234[/C][/ROW]
[ROW][C]28[/C][C]4431352.75[/C][C]373480.019257947[/C][C]765710[/C][/ROW]
[ROW][C]29[/C][C]4211177.75[/C][C]141669.484527367[/C][C]333954[/C][/ROW]
[ROW][C]30[/C][C]4122673.5[/C][C]303688.395300731[/C][C]624340[/C][/ROW]
[ROW][C]31[/C][C]3784572.75[/C][C]109498.272383251[/C][C]267158[/C][/ROW]
[ROW][C]32[/C][C]3703910[/C][C]196644.70054729[/C][C]428654[/C][/ROW]
[ROW][C]33[/C][C]3406523.25[/C][C]116399.626838964[/C][C]252747[/C][/ROW]
[ROW][C]34[/C][C]3581322.75[/C][C]300932.640174259[/C][C]684582[/C][/ROW]
[ROW][C]35[/C][C]3345796.5[/C][C]92209.5791137414[/C][C]224840[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160018&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14226659.25310502.729254108707907
24283019.5477846.3788516841029457
34555098.5591705.5664937311359860
43746094109963.425316481267855
53569616.2577167.0726988958176902
63453381.5181188.743768296374018
7332482758928.8691276752137081
83287531.25372823.483172555767524
93179507147231.510044555359614
103299354.566711.4513783054150824
113429492.25178464.220724818434498
123708418.5215866.677250103499419
133889887117812.595854603284095
144018374.25128990.955745936301227
154141060144459.648573572317077
164617137.25519890.6580980111163312
174028871.25211749.45773622456888
183608650.580396.9476887442173833
193586722.5220870.094729157502729
203344184.2547094.5710273488114975
213443186.5244579.289918423548184
223249834.5172764.742403265408843
233318646.7544099.620137252995881
243604050.75203967.806746351457103
253796604.5225212.432768856508673
264164083.25271030.768911791617810
274479557.75672050.6085900451455234
284431352.75373480.019257947765710
294211177.75141669.484527367333954
304122673.5303688.395300731624340
313784572.75109498.272383251267158
323703910196644.70054729428654
333406523.25116399.626838964252747
343581322.75300932.640174259684582
353345796.592209.5791137414224840







Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-748527.236272174
beta0.257132355334123
S.D.0.0461933218677873
T-STAT5.5664400163746
p-value3.4644645506862e-06

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -748527.236272174 \tabularnewline
beta & 0.257132355334123 \tabularnewline
S.D. & 0.0461933218677873 \tabularnewline
T-STAT & 5.5664400163746 \tabularnewline
p-value & 3.4644645506862e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160018&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-748527.236272174[/C][/ROW]
[ROW][C]beta[/C][C]0.257132355334123[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0461933218677873[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.5664400163746[/C][/ROW]
[ROW][C]p-value[/C][C]3.4644645506862e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160018&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160018&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-748527.236272174
beta0.257132355334123
S.D.0.0461933218677873
T-STAT5.5664400163746
p-value3.4644645506862e-06







Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-50.3296242333222
beta4.12297752586553
S.D.0.846939227301715
T-STAT4.8680913493652
p-value2.71952777968691e-05
Lambda-3.12297752586553

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -50.3296242333222 \tabularnewline
beta & 4.12297752586553 \tabularnewline
S.D. & 0.846939227301715 \tabularnewline
T-STAT & 4.8680913493652 \tabularnewline
p-value & 2.71952777968691e-05 \tabularnewline
Lambda & -3.12297752586553 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160018&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-50.3296242333222[/C][/ROW]
[ROW][C]beta[/C][C]4.12297752586553[/C][/ROW]
[ROW][C]S.D.[/C][C]0.846939227301715[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.8680913493652[/C][/ROW]
[ROW][C]p-value[/C][C]2.71952777968691e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.12297752586553[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160018&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160018&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-50.3296242333222
beta4.12297752586553
S.D.0.846939227301715
T-STAT4.8680913493652
p-value2.71952777968691e-05
Lambda-3.12297752586553



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')