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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

Wed, 03 Aug 2011 10:53:21 -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/Aug/03/t13123832395juwl50m0to2jyb.htm/, Retrieved Tue, 14 May 2024 14:46:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123354, Retrieved Tue, 14 May 2024 14:46:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Sergeyssels Ivan

Estimated Impact

114

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

-       [Standard Deviation-Mean Plot] [Tijdreeks A - Sta...] [2011-08-03 14:53:21] [bc909d11ab9ae813672fa3903785080c] [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=123354&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=123354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123354&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	189404.25	3081.07431209743	7208
2	202102.75	22763.1544002583	47284
3	178013.5	2571.40746155356	5453
4	194846.25	6140.83568552902	14416
5	246230	10432.8243539322	21796
6	252073.25	7669.8406056884	18286
7	272124.75	8182.27781549857	16364
8	319771	13856.5153147054	30947
9	319287.75	5229.35772824924	10912
10	339724.5	6308.34333772875	14582
11	392907.75	12538.907219132	27243
12	387028.75	9935.04317638664	23572
13	400596	6719.57414325243	14588
14	471018.25	11199.8548316485	23539
15	476912.25	15640.5071182704	34651
16	509598.75	20281.8569066872	45534
17	587272.75	11393.4349042186	25321
18	600945.25	13858.4306801552	32696
19	644992	30982.8677928088	67181
20	741689.25	9329.30034443455	20041
21	742169.5	15819.0348104217	36400
22	788944	30767.7823488575	63620
23	895710	7104.73114668435	16337
24	897946.75	16249.2246866325	34651
25	941507	31564.8425203316	69107
26	1060975.5	13594.6481994448	32702
27	1072316.25	14110.7805684165	32702
28	1097718.5	32332.9787729701	69102
29	1225369.5	20706.8788972811	47311
30	1244927	16055.0525173023	32701

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 189404.25 & 3081.07431209743 & 7208 \tabularnewline
2 & 202102.75 & 22763.1544002583 & 47284 \tabularnewline
3 & 178013.5 & 2571.40746155356 & 5453 \tabularnewline
4 & 194846.25 & 6140.83568552902 & 14416 \tabularnewline
5 & 246230 & 10432.8243539322 & 21796 \tabularnewline
6 & 252073.25 & 7669.8406056884 & 18286 \tabularnewline
7 & 272124.75 & 8182.27781549857 & 16364 \tabularnewline
8 & 319771 & 13856.5153147054 & 30947 \tabularnewline
9 & 319287.75 & 5229.35772824924 & 10912 \tabularnewline
10 & 339724.5 & 6308.34333772875 & 14582 \tabularnewline
11 & 392907.75 & 12538.907219132 & 27243 \tabularnewline
12 & 387028.75 & 9935.04317638664 & 23572 \tabularnewline
13 & 400596 & 6719.57414325243 & 14588 \tabularnewline
14 & 471018.25 & 11199.8548316485 & 23539 \tabularnewline
15 & 476912.25 & 15640.5071182704 & 34651 \tabularnewline
16 & 509598.75 & 20281.8569066872 & 45534 \tabularnewline
17 & 587272.75 & 11393.4349042186 & 25321 \tabularnewline
18 & 600945.25 & 13858.4306801552 & 32696 \tabularnewline
19 & 644992 & 30982.8677928088 & 67181 \tabularnewline
20 & 741689.25 & 9329.30034443455 & 20041 \tabularnewline
21 & 742169.5 & 15819.0348104217 & 36400 \tabularnewline
22 & 788944 & 30767.7823488575 & 63620 \tabularnewline
23 & 895710 & 7104.73114668435 & 16337 \tabularnewline
24 & 897946.75 & 16249.2246866325 & 34651 \tabularnewline
25 & 941507 & 31564.8425203316 & 69107 \tabularnewline
26 & 1060975.5 & 13594.6481994448 & 32702 \tabularnewline
27 & 1072316.25 & 14110.7805684165 & 32702 \tabularnewline
28 & 1097718.5 & 32332.9787729701 & 69102 \tabularnewline
29 & 1225369.5 & 20706.8788972811 & 47311 \tabularnewline
30 & 1244927 & 16055.0525173023 & 32701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123354&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]189404.25[/C][C]3081.07431209743[/C][C]7208[/C][/ROW]
[ROW][C]2[/C][C]202102.75[/C][C]22763.1544002583[/C][C]47284[/C][/ROW]
[ROW][C]3[/C][C]178013.5[/C][C]2571.40746155356[/C][C]5453[/C][/ROW]
[ROW][C]4[/C][C]194846.25[/C][C]6140.83568552902[/C][C]14416[/C][/ROW]
[ROW][C]5[/C][C]246230[/C][C]10432.8243539322[/C][C]21796[/C][/ROW]
[ROW][C]6[/C][C]252073.25[/C][C]7669.8406056884[/C][C]18286[/C][/ROW]
[ROW][C]7[/C][C]272124.75[/C][C]8182.27781549857[/C][C]16364[/C][/ROW]
[ROW][C]8[/C][C]319771[/C][C]13856.5153147054[/C][C]30947[/C][/ROW]
[ROW][C]9[/C][C]319287.75[/C][C]5229.35772824924[/C][C]10912[/C][/ROW]
[ROW][C]10[/C][C]339724.5[/C][C]6308.34333772875[/C][C]14582[/C][/ROW]
[ROW][C]11[/C][C]392907.75[/C][C]12538.907219132[/C][C]27243[/C][/ROW]
[ROW][C]12[/C][C]387028.75[/C][C]9935.04317638664[/C][C]23572[/C][/ROW]
[ROW][C]13[/C][C]400596[/C][C]6719.57414325243[/C][C]14588[/C][/ROW]
[ROW][C]14[/C][C]471018.25[/C][C]11199.8548316485[/C][C]23539[/C][/ROW]
[ROW][C]15[/C][C]476912.25[/C][C]15640.5071182704[/C][C]34651[/C][/ROW]
[ROW][C]16[/C][C]509598.75[/C][C]20281.8569066872[/C][C]45534[/C][/ROW]
[ROW][C]17[/C][C]587272.75[/C][C]11393.4349042186[/C][C]25321[/C][/ROW]
[ROW][C]18[/C][C]600945.25[/C][C]13858.4306801552[/C][C]32696[/C][/ROW]
[ROW][C]19[/C][C]644992[/C][C]30982.8677928088[/C][C]67181[/C][/ROW]
[ROW][C]20[/C][C]741689.25[/C][C]9329.30034443455[/C][C]20041[/C][/ROW]
[ROW][C]21[/C][C]742169.5[/C][C]15819.0348104217[/C][C]36400[/C][/ROW]
[ROW][C]22[/C][C]788944[/C][C]30767.7823488575[/C][C]63620[/C][/ROW]
[ROW][C]23[/C][C]895710[/C][C]7104.73114668435[/C][C]16337[/C][/ROW]
[ROW][C]24[/C][C]897946.75[/C][C]16249.2246866325[/C][C]34651[/C][/ROW]
[ROW][C]25[/C][C]941507[/C][C]31564.8425203316[/C][C]69107[/C][/ROW]
[ROW][C]26[/C][C]1060975.5[/C][C]13594.6481994448[/C][C]32702[/C][/ROW]
[ROW][C]27[/C][C]1072316.25[/C][C]14110.7805684165[/C][C]32702[/C][/ROW]
[ROW][C]28[/C][C]1097718.5[/C][C]32332.9787729701[/C][C]69102[/C][/ROW]
[ROW][C]29[/C][C]1225369.5[/C][C]20706.8788972811[/C][C]47311[/C][/ROW]
[ROW][C]30[/C][C]1244927[/C][C]16055.0525173023[/C][C]32701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123354&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	189404.25	3081.07431209743	7208
2	202102.75	22763.1544002583	47284
3	178013.5	2571.40746155356	5453
4	194846.25	6140.83568552902	14416
5	246230	10432.8243539322	21796
6	252073.25	7669.8406056884	18286
7	272124.75	8182.27781549857	16364
8	319771	13856.5153147054	30947
9	319287.75	5229.35772824924	10912
10	339724.5	6308.34333772875	14582
11	392907.75	12538.907219132	27243
12	387028.75	9935.04317638664	23572
13	400596	6719.57414325243	14588
14	471018.25	11199.8548316485	23539
15	476912.25	15640.5071182704	34651
16	509598.75	20281.8569066872	45534
17	587272.75	11393.4349042186	25321
18	600945.25	13858.4306801552	32696
19	644992	30982.8677928088	67181
20	741689.25	9329.30034443455	20041
21	742169.5	15819.0348104217	36400
22	788944	30767.7823488575	63620
23	895710	7104.73114668435	16337
24	897946.75	16249.2246866325	34651
25	941507	31564.8425203316	69107
26	1060975.5	13594.6481994448	32702
27	1072316.25	14110.7805684165	32702
28	1097718.5	32332.9787729701	69102
29	1225369.5	20706.8788972811	47311
30	1244927	16055.0525173023	32701

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6313.39786473287
beta	0.0133953757786465
S.D.	0.00403429423803501
T-STAT	3.32037649915465
p-value	0.00250633392289015

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6313.39786473287 \tabularnewline
beta & 0.0133953757786465 \tabularnewline
S.D. & 0.00403429423803501 \tabularnewline
T-STAT & 3.32037649915465 \tabularnewline
p-value & 0.00250633392289015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123354&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6313.39786473287[/C][/ROW]
[ROW][C]beta[/C][C]0.0133953757786465[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00403429423803501[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.32037649915465[/C][/ROW]
[ROW][C]p-value[/C][C]0.00250633392289015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123354&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123354&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	6313.39786473287
beta	0.0133953757786465
S.D.	0.00403429423803501
T-STAT	3.32037649915465
p-value	0.00250633392289015

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.660051915286549
beta	0.664857690568654
S.D.	0.152663171681276
T-STAT	4.35506273875089
p-value	0.000161142694610988
Lambda	0.335142309431346

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.660051915286549 \tabularnewline
beta & 0.664857690568654 \tabularnewline
S.D. & 0.152663171681276 \tabularnewline
T-STAT & 4.35506273875089 \tabularnewline
p-value & 0.000161142694610988 \tabularnewline
Lambda & 0.335142309431346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123354&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.660051915286549[/C][/ROW]
[ROW][C]beta[/C][C]0.664857690568654[/C][/ROW]
[ROW][C]S.D.[/C][C]0.152663171681276[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.35506273875089[/C][/ROW]
[ROW][C]p-value[/C][C]0.000161142694610988[/C][/ROW]
[ROW][C]Lambda[/C][C]0.335142309431346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123354&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123354&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	0.660051915286549
beta	0.664857690568654
S.D.	0.152663171681276
T-STAT	4.35506273875089
p-value	0.000161142694610988
Lambda	0.335142309431346

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