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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 19 Dec 2016 15:17:17 +0100

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/2016/Dec/19/t148215705940mokfu1yps7ih2.htm/, Retrieved Fri, 17 May 2024 18:46:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301363, Retrieved Fri, 17 May 2024 18:46:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2016-12-19 14:17:17] [e0044ff8caf2d68149dcdb0ba8e86f31] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301363&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301363&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6842.5	1155.23085715944	2620
2	4727.5	563.818824328052	1220
3	6812.5	386.55530005421	840
4	6307.5	539.343737023678	1210
5	5622.5	420.267771783657	970
6	5620	355.621521658443	740
7	5337.5	1123.42853206898	2650
8	5272.5	1028.24688993776	2220
9	5110	194.422220952236	460
10	5217.5	395.842982338536	830
11	4810	317.804971641414	770
12	5430	551.301490414576	1350
13	4362.5	312.663290671184	660
14	4437.5	276.571268693382	610
15	5347.5	206.942020865749	500
16	3887.5	406.560778564124	980
17	6087.5	353.965629216548	760
18	6370	389.444048184931	890
19	6042.5	546.221871892122	1240
20	6997.5	1170.50914847628	2410
21	6437.5	824.717123220643	1800
22	5107.5	855.779371878835	1960
23	4735	400.041664496754	970
24	6962.5	594.046855615503	1420
25	7062.5	1066.31374369835	2460
26	6622.5	1272.43532907047	2760
27	6465	925.364792933036	2120
28	6172.5	641.476162196747	1340
29	4822.5	338.858377497149	770
30	6360	1022.12197576088	2280
31	7250	NA	0
32	NaN	NA	-Inf
33	NaN	NA	-Inf
34	NaN	NA	-Inf
35	NaN	NA	-Inf
36	NaN	NA	-Inf

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6842.5 & 1155.23085715944 & 2620 \tabularnewline
2 & 4727.5 & 563.818824328052 & 1220 \tabularnewline
3 & 6812.5 & 386.55530005421 & 840 \tabularnewline
4 & 6307.5 & 539.343737023678 & 1210 \tabularnewline
5 & 5622.5 & 420.267771783657 & 970 \tabularnewline
6 & 5620 & 355.621521658443 & 740 \tabularnewline
7 & 5337.5 & 1123.42853206898 & 2650 \tabularnewline
8 & 5272.5 & 1028.24688993776 & 2220 \tabularnewline
9 & 5110 & 194.422220952236 & 460 \tabularnewline
10 & 5217.5 & 395.842982338536 & 830 \tabularnewline
11 & 4810 & 317.804971641414 & 770 \tabularnewline
12 & 5430 & 551.301490414576 & 1350 \tabularnewline
13 & 4362.5 & 312.663290671184 & 660 \tabularnewline
14 & 4437.5 & 276.571268693382 & 610 \tabularnewline
15 & 5347.5 & 206.942020865749 & 500 \tabularnewline
16 & 3887.5 & 406.560778564124 & 980 \tabularnewline
17 & 6087.5 & 353.965629216548 & 760 \tabularnewline
18 & 6370 & 389.444048184931 & 890 \tabularnewline
19 & 6042.5 & 546.221871892122 & 1240 \tabularnewline
20 & 6997.5 & 1170.50914847628 & 2410 \tabularnewline
21 & 6437.5 & 824.717123220643 & 1800 \tabularnewline
22 & 5107.5 & 855.779371878835 & 1960 \tabularnewline
23 & 4735 & 400.041664496754 & 970 \tabularnewline
24 & 6962.5 & 594.046855615503 & 1420 \tabularnewline
25 & 7062.5 & 1066.31374369835 & 2460 \tabularnewline
26 & 6622.5 & 1272.43532907047 & 2760 \tabularnewline
27 & 6465 & 925.364792933036 & 2120 \tabularnewline
28 & 6172.5 & 641.476162196747 & 1340 \tabularnewline
29 & 4822.5 & 338.858377497149 & 770 \tabularnewline
30 & 6360 & 1022.12197576088 & 2280 \tabularnewline
31 & 7250 & NA & 0 \tabularnewline
32 & NaN & NA & -Inf \tabularnewline
33 & NaN & NA & -Inf \tabularnewline
34 & NaN & NA & -Inf \tabularnewline
35 & NaN & NA & -Inf \tabularnewline
36 & NaN & NA & -Inf \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301363&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]6842.5[/C][C]1155.23085715944[/C][C]2620[/C][/ROW]
[ROW][C]2[/C][C]4727.5[/C][C]563.818824328052[/C][C]1220[/C][/ROW]
[ROW][C]3[/C][C]6812.5[/C][C]386.55530005421[/C][C]840[/C][/ROW]
[ROW][C]4[/C][C]6307.5[/C][C]539.343737023678[/C][C]1210[/C][/ROW]
[ROW][C]5[/C][C]5622.5[/C][C]420.267771783657[/C][C]970[/C][/ROW]
[ROW][C]6[/C][C]5620[/C][C]355.621521658443[/C][C]740[/C][/ROW]
[ROW][C]7[/C][C]5337.5[/C][C]1123.42853206898[/C][C]2650[/C][/ROW]
[ROW][C]8[/C][C]5272.5[/C][C]1028.24688993776[/C][C]2220[/C][/ROW]
[ROW][C]9[/C][C]5110[/C][C]194.422220952236[/C][C]460[/C][/ROW]
[ROW][C]10[/C][C]5217.5[/C][C]395.842982338536[/C][C]830[/C][/ROW]
[ROW][C]11[/C][C]4810[/C][C]317.804971641414[/C][C]770[/C][/ROW]
[ROW][C]12[/C][C]5430[/C][C]551.301490414576[/C][C]1350[/C][/ROW]
[ROW][C]13[/C][C]4362.5[/C][C]312.663290671184[/C][C]660[/C][/ROW]
[ROW][C]14[/C][C]4437.5[/C][C]276.571268693382[/C][C]610[/C][/ROW]
[ROW][C]15[/C][C]5347.5[/C][C]206.942020865749[/C][C]500[/C][/ROW]
[ROW][C]16[/C][C]3887.5[/C][C]406.560778564124[/C][C]980[/C][/ROW]
[ROW][C]17[/C][C]6087.5[/C][C]353.965629216548[/C][C]760[/C][/ROW]
[ROW][C]18[/C][C]6370[/C][C]389.444048184931[/C][C]890[/C][/ROW]
[ROW][C]19[/C][C]6042.5[/C][C]546.221871892122[/C][C]1240[/C][/ROW]
[ROW][C]20[/C][C]6997.5[/C][C]1170.50914847628[/C][C]2410[/C][/ROW]
[ROW][C]21[/C][C]6437.5[/C][C]824.717123220643[/C][C]1800[/C][/ROW]
[ROW][C]22[/C][C]5107.5[/C][C]855.779371878835[/C][C]1960[/C][/ROW]
[ROW][C]23[/C][C]4735[/C][C]400.041664496754[/C][C]970[/C][/ROW]
[ROW][C]24[/C][C]6962.5[/C][C]594.046855615503[/C][C]1420[/C][/ROW]
[ROW][C]25[/C][C]7062.5[/C][C]1066.31374369835[/C][C]2460[/C][/ROW]
[ROW][C]26[/C][C]6622.5[/C][C]1272.43532907047[/C][C]2760[/C][/ROW]
[ROW][C]27[/C][C]6465[/C][C]925.364792933036[/C][C]2120[/C][/ROW]
[ROW][C]28[/C][C]6172.5[/C][C]641.476162196747[/C][C]1340[/C][/ROW]
[ROW][C]29[/C][C]4822.5[/C][C]338.858377497149[/C][C]770[/C][/ROW]
[ROW][C]30[/C][C]6360[/C][C]1022.12197576088[/C][C]2280[/C][/ROW]
[ROW][C]31[/C][C]7250[/C][C]NA[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]33[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]34[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]35[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]36[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301363&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	6842.5	1155.23085715944	2620
2	4727.5	563.818824328052	1220
3	6812.5	386.55530005421	840
4	6307.5	539.343737023678	1210
5	5622.5	420.267771783657	970
6	5620	355.621521658443	740
7	5337.5	1123.42853206898	2650
8	5272.5	1028.24688993776	2220
9	5110	194.422220952236	460
10	5217.5	395.842982338536	830
11	4810	317.804971641414	770
12	5430	551.301490414576	1350
13	4362.5	312.663290671184	660
14	4437.5	276.571268693382	610
15	5347.5	206.942020865749	500
16	3887.5	406.560778564124	980
17	6087.5	353.965629216548	760
18	6370	389.444048184931	890
19	6042.5	546.221871892122	1240
20	6997.5	1170.50914847628	2410
21	6437.5	824.717123220643	1800
22	5107.5	855.779371878835	1960
23	4735	400.041664496754	970
24	6962.5	594.046855615503	1420
25	7062.5	1066.31374369835	2460
26	6622.5	1272.43532907047	2760
27	6465	925.364792933036	2120
28	6172.5	641.476162196747	1340
29	4822.5	338.858377497149	770
30	6360	1022.12197576088	2280
31	7250	NA	0
32	NaN	NA	-Inf
33	NaN	NA	-Inf
34	NaN	NA	-Inf
35	NaN	NA	-Inf
36	NaN	NA	-Inf

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-535.514585649812
beta	0.202470133157057
S.D.	0.0589450509979873
T-STAT	3.43489622502779
p-value	0.00186647484024209

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -535.514585649812 \tabularnewline
beta & 0.202470133157057 \tabularnewline
S.D. & 0.0589450509979873 \tabularnewline
T-STAT & 3.43489622502779 \tabularnewline
p-value & 0.00186647484024209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301363&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-535.514585649812[/C][/ROW]
[ROW][C]beta[/C][C]0.202470133157057[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0589450509979873[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.43489622502779[/C][/ROW]
[ROW][C]p-value[/C][C]0.00186647484024209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301363&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301363&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	-535.514585649812
beta	0.202470133157057
S.D.	0.0589450509979873
T-STAT	3.43489622502779
p-value	0.00186647484024209

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-9.51380444725912
beta	1.82973072654666
S.D.	0.53796359553438
T-STAT	3.40121662829083
p-value	0.00203612757523197
Lambda	-0.829730726546656

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.51380444725912 \tabularnewline
beta & 1.82973072654666 \tabularnewline
S.D. & 0.53796359553438 \tabularnewline
T-STAT & 3.40121662829083 \tabularnewline
p-value & 0.00203612757523197 \tabularnewline
Lambda & -0.829730726546656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301363&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.51380444725912[/C][/ROW]
[ROW][C]beta[/C][C]1.82973072654666[/C][/ROW]
[ROW][C]S.D.[/C][C]0.53796359553438[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.40121662829083[/C][/ROW]
[ROW][C]p-value[/C][C]0.00203612757523197[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.829730726546656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301363&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301363&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	-9.51380444725912
beta	1.82973072654666
S.D.	0.53796359553438
T-STAT	3.40121662829083
p-value	0.00203612757523197
Lambda	-0.829730726546656

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code