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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 10 Jul 2011 08:50:57 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jul/10/t1310302308jtbl0lbk15dipyx.htm/, Retrieved Sun, 19 May 2024 12:14:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123030, Retrieved Sun, 19 May 2024 12:14:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van den Buys Daphn�

Estimated Impact

204

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [Tijdreeks A-stap 26] [2011-07-10 12:50:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=123030&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=123030&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123030&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1051761.75	17109.1145762524	40026
2	1122276.5	126403.678428807	262568
3	988509	14279.2575203802	30281
4	1081981.25	34100.0738843286	80052
5	1367315	57933.4046240451	121033
6	1399763	42590.5055225536	101542
7	1511108.75	45436.5001980786	90870
8	1775688.25	76945.3628941775	171849
9	1773004.75	29038.5039258223	60594
10	1886490	35030.2717374559	80974
11	2181816.75	69628.6420346062	151281
12	2149170.75	55169.6176373373	130896
13	2224509.5	37313.7360096788	81007
14	2615564.25	62192.7741374886	130712
15	2648293.5	86851.7129844503	192417
16	2829801.75	112625.110729875	252850
17	3261125.5	63267.8132834277	140608
18	3337049	76955.854475147	181561
19	3581640.75	172047.941354292	373056
20	4118600.25	51805.8459273662	111288
21	4121267.25	87843.0241258993	202129
22	4381005.75	170853.570705785	353282
23	4973877.5	39452.7481129853	90720
24	4986298.25	90232.1360579662	192417
25	5228188.5	175279.50378467	383751
26	5891597	75491.0192804416	181594
27	5954572.25	78357.0582712028	181594
28	6095631	179544.875788757	383723
29	6804476.75	114985.230913583	262718
30	6913079.5	89153.8282913303	181589

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1051761.75 & 17109.1145762524 & 40026 \tabularnewline
2 & 1122276.5 & 126403.678428807 & 262568 \tabularnewline
3 & 988509 & 14279.2575203802 & 30281 \tabularnewline
4 & 1081981.25 & 34100.0738843286 & 80052 \tabularnewline
5 & 1367315 & 57933.4046240451 & 121033 \tabularnewline
6 & 1399763 & 42590.5055225536 & 101542 \tabularnewline
7 & 1511108.75 & 45436.5001980786 & 90870 \tabularnewline
8 & 1775688.25 & 76945.3628941775 & 171849 \tabularnewline
9 & 1773004.75 & 29038.5039258223 & 60594 \tabularnewline
10 & 1886490 & 35030.2717374559 & 80974 \tabularnewline
11 & 2181816.75 & 69628.6420346062 & 151281 \tabularnewline
12 & 2149170.75 & 55169.6176373373 & 130896 \tabularnewline
13 & 2224509.5 & 37313.7360096788 & 81007 \tabularnewline
14 & 2615564.25 & 62192.7741374886 & 130712 \tabularnewline
15 & 2648293.5 & 86851.7129844503 & 192417 \tabularnewline
16 & 2829801.75 & 112625.110729875 & 252850 \tabularnewline
17 & 3261125.5 & 63267.8132834277 & 140608 \tabularnewline
18 & 3337049 & 76955.854475147 & 181561 \tabularnewline
19 & 3581640.75 & 172047.941354292 & 373056 \tabularnewline
20 & 4118600.25 & 51805.8459273662 & 111288 \tabularnewline
21 & 4121267.25 & 87843.0241258993 & 202129 \tabularnewline
22 & 4381005.75 & 170853.570705785 & 353282 \tabularnewline
23 & 4973877.5 & 39452.7481129853 & 90720 \tabularnewline
24 & 4986298.25 & 90232.1360579662 & 192417 \tabularnewline
25 & 5228188.5 & 175279.50378467 & 383751 \tabularnewline
26 & 5891597 & 75491.0192804416 & 181594 \tabularnewline
27 & 5954572.25 & 78357.0582712028 & 181594 \tabularnewline
28 & 6095631 & 179544.875788757 & 383723 \tabularnewline
29 & 6804476.75 & 114985.230913583 & 262718 \tabularnewline
30 & 6913079.5 & 89153.8282913303 & 181589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123030&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]1051761.75[/C][C]17109.1145762524[/C][C]40026[/C][/ROW]
[ROW][C]2[/C][C]1122276.5[/C][C]126403.678428807[/C][C]262568[/C][/ROW]
[ROW][C]3[/C][C]988509[/C][C]14279.2575203802[/C][C]30281[/C][/ROW]
[ROW][C]4[/C][C]1081981.25[/C][C]34100.0738843286[/C][C]80052[/C][/ROW]
[ROW][C]5[/C][C]1367315[/C][C]57933.4046240451[/C][C]121033[/C][/ROW]
[ROW][C]6[/C][C]1399763[/C][C]42590.5055225536[/C][C]101542[/C][/ROW]
[ROW][C]7[/C][C]1511108.75[/C][C]45436.5001980786[/C][C]90870[/C][/ROW]
[ROW][C]8[/C][C]1775688.25[/C][C]76945.3628941775[/C][C]171849[/C][/ROW]
[ROW][C]9[/C][C]1773004.75[/C][C]29038.5039258223[/C][C]60594[/C][/ROW]
[ROW][C]10[/C][C]1886490[/C][C]35030.2717374559[/C][C]80974[/C][/ROW]
[ROW][C]11[/C][C]2181816.75[/C][C]69628.6420346062[/C][C]151281[/C][/ROW]
[ROW][C]12[/C][C]2149170.75[/C][C]55169.6176373373[/C][C]130896[/C][/ROW]
[ROW][C]13[/C][C]2224509.5[/C][C]37313.7360096788[/C][C]81007[/C][/ROW]
[ROW][C]14[/C][C]2615564.25[/C][C]62192.7741374886[/C][C]130712[/C][/ROW]
[ROW][C]15[/C][C]2648293.5[/C][C]86851.7129844503[/C][C]192417[/C][/ROW]
[ROW][C]16[/C][C]2829801.75[/C][C]112625.110729875[/C][C]252850[/C][/ROW]
[ROW][C]17[/C][C]3261125.5[/C][C]63267.8132834277[/C][C]140608[/C][/ROW]
[ROW][C]18[/C][C]3337049[/C][C]76955.854475147[/C][C]181561[/C][/ROW]
[ROW][C]19[/C][C]3581640.75[/C][C]172047.941354292[/C][C]373056[/C][/ROW]
[ROW][C]20[/C][C]4118600.25[/C][C]51805.8459273662[/C][C]111288[/C][/ROW]
[ROW][C]21[/C][C]4121267.25[/C][C]87843.0241258993[/C][C]202129[/C][/ROW]
[ROW][C]22[/C][C]4381005.75[/C][C]170853.570705785[/C][C]353282[/C][/ROW]
[ROW][C]23[/C][C]4973877.5[/C][C]39452.7481129853[/C][C]90720[/C][/ROW]
[ROW][C]24[/C][C]4986298.25[/C][C]90232.1360579662[/C][C]192417[/C][/ROW]
[ROW][C]25[/C][C]5228188.5[/C][C]175279.50378467[/C][C]383751[/C][/ROW]
[ROW][C]26[/C][C]5891597[/C][C]75491.0192804416[/C][C]181594[/C][/ROW]
[ROW][C]27[/C][C]5954572.25[/C][C]78357.0582712028[/C][C]181594[/C][/ROW]
[ROW][C]28[/C][C]6095631[/C][C]179544.875788757[/C][C]383723[/C][/ROW]
[ROW][C]29[/C][C]6804476.75[/C][C]114985.230913583[/C][C]262718[/C][/ROW]
[ROW][C]30[/C][C]6913079.5[/C][C]89153.8282913303[/C][C]181589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123030&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123030&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
Section	Mean	Standard Deviation	Range
1	1051761.75	17109.1145762524	40026
2	1122276.5	126403.678428807	262568
3	988509	14279.2575203802	30281
4	1081981.25	34100.0738843286	80052
5	1367315	57933.4046240451	121033
6	1399763	42590.5055225536	101542
7	1511108.75	45436.5001980786	90870
8	1775688.25	76945.3628941775	171849
9	1773004.75	29038.5039258223	60594
10	1886490	35030.2717374559	80974
11	2181816.75	69628.6420346062	151281
12	2149170.75	55169.6176373373	130896
13	2224509.5	37313.7360096788	81007
14	2615564.25	62192.7741374886	130712
15	2648293.5	86851.7129844503	192417
16	2829801.75	112625.110729875	252850
17	3261125.5	63267.8132834277	140608
18	3337049	76955.854475147	181561
19	3581640.75	172047.941354292	373056
20	4118600.25	51805.8459273662	111288
21	4121267.25	87843.0241258993	202129
22	4381005.75	170853.570705785	353282
23	4973877.5	39452.7481129853	90720
24	4986298.25	90232.1360579662	192417
25	5228188.5	175279.50378467	383751
26	5891597	75491.0192804416	181594
27	5954572.25	78357.0582712028	181594
28	6095631	179544.875788757	383723
29	6804476.75	114985.230913583	262718
30	6913079.5	89153.8282913303	181589

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	35058.3497989893
beta	0.013395369271764
S.D.	0.00403429098481514
T-STAT	3.32037756378592
p-value	0.00250632709011299

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 35058.3497989893 \tabularnewline
beta & 0.013395369271764 \tabularnewline
S.D. & 0.00403429098481514 \tabularnewline
T-STAT & 3.32037756378592 \tabularnewline
p-value & 0.00250632709011299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123030&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]35058.3497989893[/C][/ROW]
[ROW][C]beta[/C][C]0.013395369271764[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00403429098481514[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.32037756378592[/C][/ROW]
[ROW][C]p-value[/C][C]0.00250632709011299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123030&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123030&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	35058.3497989893
beta	0.013395369271764
S.D.	0.00403429098481514
T-STAT	3.32037756378592
p-value	0.00250632709011299

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.23461279736574
beta	0.664856834577417
S.D.	0.152662857175153
T-STAT	4.35506610369944
p-value	0.00016114122266209
Lambda	0.335143165422583

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.23461279736574 \tabularnewline
beta & 0.664856834577417 \tabularnewline
S.D. & 0.152662857175153 \tabularnewline
T-STAT & 4.35506610369944 \tabularnewline
p-value & 0.00016114122266209 \tabularnewline
Lambda & 0.335143165422583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123030&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.23461279736574[/C][/ROW]
[ROW][C]beta[/C][C]0.664856834577417[/C][/ROW]
[ROW][C]S.D.[/C][C]0.152662857175153[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.35506610369944[/C][/ROW]
[ROW][C]p-value[/C][C]0.00016114122266209[/C][/ROW]
[ROW][C]Lambda[/C][C]0.335143165422583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123030&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123030&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	1.23461279736574
beta	0.664856834577417
S.D.	0.152662857175153
T-STAT	4.35506610369944
p-value	0.00016114122266209
Lambda	0.335143165422583

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code