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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

Wed, 14 Dec 2011 03:59:25 -0500

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/Dec/14/t13238532561mreva9c7qvzywg.htm/, Retrieved Wed, 01 May 2024 19:26:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154811, Retrieved Wed, 01 May 2024 19:26:53 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

118

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

-       [Standard Deviation-Mean Plot] [] [2011-12-14 08:59:25] [bbaf0bbad09b34135f8973992e5d67ea] [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	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154811&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154811&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	68.6333333333333	16.8722786806877	48.07
2	96.7458333333333	6.50532573195131	22.63
3	88.2566666666667	5.52737375306398	18.29
4	85.7658333333333	8.80852114131366	31.96
5	107.826666666667	8.13339617462062	22.21
6	133.513333333333	12.4693503026299	41.46
7	246.714166666667	82.1116732326203	232.25
8	375.434166666667	30.957083624191	95.56
9	341.545	27.1902908807872	100.43
10	379.4	61.3909023464315	201.31
11	437.189166666667	12.7714087343803	40.07
12	419.9375	12.871889121083	36.78
13	375.383333333333	28.2648153696214	89.29
14	346.22	16.0534193468953	54.01
15	366.574166666667	17.3613858152004	61.43
16	345.841666666667	17.1436523282384	52.98
17	316.555833333333	12.5896367615543	49.02
18	270.3725	11.7830580418744	40.81
19	277.280833333333	15.3870615413986	58.18
20	254.808333333333	14.3020328074104	50.47
21	322.458333333333	21.0145991821847	73.66
22	308.504166666667	10.793407464604	33.96
23	294.15	9.7780189478981	34.04
24	297.624166666667	7.19128444505548	21.39
25	287.6475	14.4221030650243	39.17
26	258.651666666667	11.9515939091695	39.73
27	274.128333333333	21.5319022650465	66.19
28	299.643333333333	9.4526613215859	27.65
29	316.88	15.6196362429999	48.67
30	326.206666666667	12.944017455133	42.71
31	323.376666666667	14.8172953815547	43.48
32	328.608333333333	6.37703384074921	20.6799999999999
33	399.685	53.4273822372692	145.28
34	491.329166666667	13.2620733730256	38.22
35	539.2875	55.300551554869	158.28
36	625.413333333333	63.5251870353704	190.13
37	724.144166666667	62.0978650574798	162.08
38	983.710833333333	53.706577294564	175.91

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 68.6333333333333 & 16.8722786806877 & 48.07 \tabularnewline
2 & 96.7458333333333 & 6.50532573195131 & 22.63 \tabularnewline
3 & 88.2566666666667 & 5.52737375306398 & 18.29 \tabularnewline
4 & 85.7658333333333 & 8.80852114131366 & 31.96 \tabularnewline
5 & 107.826666666667 & 8.13339617462062 & 22.21 \tabularnewline
6 & 133.513333333333 & 12.4693503026299 & 41.46 \tabularnewline
7 & 246.714166666667 & 82.1116732326203 & 232.25 \tabularnewline
8 & 375.434166666667 & 30.957083624191 & 95.56 \tabularnewline
9 & 341.545 & 27.1902908807872 & 100.43 \tabularnewline
10 & 379.4 & 61.3909023464315 & 201.31 \tabularnewline
11 & 437.189166666667 & 12.7714087343803 & 40.07 \tabularnewline
12 & 419.9375 & 12.871889121083 & 36.78 \tabularnewline
13 & 375.383333333333 & 28.2648153696214 & 89.29 \tabularnewline
14 & 346.22 & 16.0534193468953 & 54.01 \tabularnewline
15 & 366.574166666667 & 17.3613858152004 & 61.43 \tabularnewline
16 & 345.841666666667 & 17.1436523282384 & 52.98 \tabularnewline
17 & 316.555833333333 & 12.5896367615543 & 49.02 \tabularnewline
18 & 270.3725 & 11.7830580418744 & 40.81 \tabularnewline
19 & 277.280833333333 & 15.3870615413986 & 58.18 \tabularnewline
20 & 254.808333333333 & 14.3020328074104 & 50.47 \tabularnewline
21 & 322.458333333333 & 21.0145991821847 & 73.66 \tabularnewline
22 & 308.504166666667 & 10.793407464604 & 33.96 \tabularnewline
23 & 294.15 & 9.7780189478981 & 34.04 \tabularnewline
24 & 297.624166666667 & 7.19128444505548 & 21.39 \tabularnewline
25 & 287.6475 & 14.4221030650243 & 39.17 \tabularnewline
26 & 258.651666666667 & 11.9515939091695 & 39.73 \tabularnewline
27 & 274.128333333333 & 21.5319022650465 & 66.19 \tabularnewline
28 & 299.643333333333 & 9.4526613215859 & 27.65 \tabularnewline
29 & 316.88 & 15.6196362429999 & 48.67 \tabularnewline
30 & 326.206666666667 & 12.944017455133 & 42.71 \tabularnewline
31 & 323.376666666667 & 14.8172953815547 & 43.48 \tabularnewline
32 & 328.608333333333 & 6.37703384074921 & 20.6799999999999 \tabularnewline
33 & 399.685 & 53.4273822372692 & 145.28 \tabularnewline
34 & 491.329166666667 & 13.2620733730256 & 38.22 \tabularnewline
35 & 539.2875 & 55.300551554869 & 158.28 \tabularnewline
36 & 625.413333333333 & 63.5251870353704 & 190.13 \tabularnewline
37 & 724.144166666667 & 62.0978650574798 & 162.08 \tabularnewline
38 & 983.710833333333 & 53.706577294564 & 175.91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154811&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]68.6333333333333[/C][C]16.8722786806877[/C][C]48.07[/C][/ROW]
[ROW][C]2[/C][C]96.7458333333333[/C][C]6.50532573195131[/C][C]22.63[/C][/ROW]
[ROW][C]3[/C][C]88.2566666666667[/C][C]5.52737375306398[/C][C]18.29[/C][/ROW]
[ROW][C]4[/C][C]85.7658333333333[/C][C]8.80852114131366[/C][C]31.96[/C][/ROW]
[ROW][C]5[/C][C]107.826666666667[/C][C]8.13339617462062[/C][C]22.21[/C][/ROW]
[ROW][C]6[/C][C]133.513333333333[/C][C]12.4693503026299[/C][C]41.46[/C][/ROW]
[ROW][C]7[/C][C]246.714166666667[/C][C]82.1116732326203[/C][C]232.25[/C][/ROW]
[ROW][C]8[/C][C]375.434166666667[/C][C]30.957083624191[/C][C]95.56[/C][/ROW]
[ROW][C]9[/C][C]341.545[/C][C]27.1902908807872[/C][C]100.43[/C][/ROW]
[ROW][C]10[/C][C]379.4[/C][C]61.3909023464315[/C][C]201.31[/C][/ROW]
[ROW][C]11[/C][C]437.189166666667[/C][C]12.7714087343803[/C][C]40.07[/C][/ROW]
[ROW][C]12[/C][C]419.9375[/C][C]12.871889121083[/C][C]36.78[/C][/ROW]
[ROW][C]13[/C][C]375.383333333333[/C][C]28.2648153696214[/C][C]89.29[/C][/ROW]
[ROW][C]14[/C][C]346.22[/C][C]16.0534193468953[/C][C]54.01[/C][/ROW]
[ROW][C]15[/C][C]366.574166666667[/C][C]17.3613858152004[/C][C]61.43[/C][/ROW]
[ROW][C]16[/C][C]345.841666666667[/C][C]17.1436523282384[/C][C]52.98[/C][/ROW]
[ROW][C]17[/C][C]316.555833333333[/C][C]12.5896367615543[/C][C]49.02[/C][/ROW]
[ROW][C]18[/C][C]270.3725[/C][C]11.7830580418744[/C][C]40.81[/C][/ROW]
[ROW][C]19[/C][C]277.280833333333[/C][C]15.3870615413986[/C][C]58.18[/C][/ROW]
[ROW][C]20[/C][C]254.808333333333[/C][C]14.3020328074104[/C][C]50.47[/C][/ROW]
[ROW][C]21[/C][C]322.458333333333[/C][C]21.0145991821847[/C][C]73.66[/C][/ROW]
[ROW][C]22[/C][C]308.504166666667[/C][C]10.793407464604[/C][C]33.96[/C][/ROW]
[ROW][C]23[/C][C]294.15[/C][C]9.7780189478981[/C][C]34.04[/C][/ROW]
[ROW][C]24[/C][C]297.624166666667[/C][C]7.19128444505548[/C][C]21.39[/C][/ROW]
[ROW][C]25[/C][C]287.6475[/C][C]14.4221030650243[/C][C]39.17[/C][/ROW]
[ROW][C]26[/C][C]258.651666666667[/C][C]11.9515939091695[/C][C]39.73[/C][/ROW]
[ROW][C]27[/C][C]274.128333333333[/C][C]21.5319022650465[/C][C]66.19[/C][/ROW]
[ROW][C]28[/C][C]299.643333333333[/C][C]9.4526613215859[/C][C]27.65[/C][/ROW]
[ROW][C]29[/C][C]316.88[/C][C]15.6196362429999[/C][C]48.67[/C][/ROW]
[ROW][C]30[/C][C]326.206666666667[/C][C]12.944017455133[/C][C]42.71[/C][/ROW]
[ROW][C]31[/C][C]323.376666666667[/C][C]14.8172953815547[/C][C]43.48[/C][/ROW]
[ROW][C]32[/C][C]328.608333333333[/C][C]6.37703384074921[/C][C]20.6799999999999[/C][/ROW]
[ROW][C]33[/C][C]399.685[/C][C]53.4273822372692[/C][C]145.28[/C][/ROW]
[ROW][C]34[/C][C]491.329166666667[/C][C]13.2620733730256[/C][C]38.22[/C][/ROW]
[ROW][C]35[/C][C]539.2875[/C][C]55.300551554869[/C][C]158.28[/C][/ROW]
[ROW][C]36[/C][C]625.413333333333[/C][C]63.5251870353704[/C][C]190.13[/C][/ROW]
[ROW][C]37[/C][C]724.144166666667[/C][C]62.0978650574798[/C][C]162.08[/C][/ROW]
[ROW][C]38[/C][C]983.710833333333[/C][C]53.706577294564[/C][C]175.91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154811&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	68.6333333333333	16.8722786806877	48.07
2	96.7458333333333	6.50532573195131	22.63
3	88.2566666666667	5.52737375306398	18.29
4	85.7658333333333	8.80852114131366	31.96
5	107.826666666667	8.13339617462062	22.21
6	133.513333333333	12.4693503026299	41.46
7	246.714166666667	82.1116732326203	232.25
8	375.434166666667	30.957083624191	95.56
9	341.545	27.1902908807872	100.43
10	379.4	61.3909023464315	201.31
11	437.189166666667	12.7714087343803	40.07
12	419.9375	12.871889121083	36.78
13	375.383333333333	28.2648153696214	89.29
14	346.22	16.0534193468953	54.01
15	366.574166666667	17.3613858152004	61.43
16	345.841666666667	17.1436523282384	52.98
17	316.555833333333	12.5896367615543	49.02
18	270.3725	11.7830580418744	40.81
19	277.280833333333	15.3870615413986	58.18
20	254.808333333333	14.3020328074104	50.47
21	322.458333333333	21.0145991821847	73.66
22	308.504166666667	10.793407464604	33.96
23	294.15	9.7780189478981	34.04
24	297.624166666667	7.19128444505548	21.39
25	287.6475	14.4221030650243	39.17
26	258.651666666667	11.9515939091695	39.73
27	274.128333333333	21.5319022650465	66.19
28	299.643333333333	9.4526613215859	27.65
29	316.88	15.6196362429999	48.67
30	326.206666666667	12.944017455133	42.71
31	323.376666666667	14.8172953815547	43.48
32	328.608333333333	6.37703384074921	20.6799999999999
33	399.685	53.4273822372692	145.28
34	491.329166666667	13.2620733730256	38.22
35	539.2875	55.300551554869	158.28
36	625.413333333333	63.5251870353704	190.13
37	724.144166666667	62.0978650574798	162.08
38	983.710833333333	53.706577294564	175.91

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.32960118487711
beta	0.0647941818129443
S.D.	0.0154884485621547
T-STAT	4.18338748086532
p-value	0.000175926711690903

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.32960118487711 \tabularnewline
beta & 0.0647941818129443 \tabularnewline
S.D. & 0.0154884485621547 \tabularnewline
T-STAT & 4.18338748086532 \tabularnewline
p-value & 0.000175926711690903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154811&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.32960118487711[/C][/ROW]
[ROW][C]beta[/C][C]0.0647941818129443[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0154884485621547[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.18338748086532[/C][/ROW]
[ROW][C]p-value[/C][C]0.000175926711690903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154811&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	1.32960118487711
beta	0.0647941818129443
S.D.	0.0154884485621547
T-STAT	4.18338748086532
p-value	0.000175926711690903

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.21692780404547
beta	0.718197050047751
S.D.	0.169939594314022
T-STAT	4.22619021156798
p-value	0.000155000327253659
Lambda	0.281802949952249

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.21692780404547 \tabularnewline
beta & 0.718197050047751 \tabularnewline
S.D. & 0.169939594314022 \tabularnewline
T-STAT & 4.22619021156798 \tabularnewline
p-value & 0.000155000327253659 \tabularnewline
Lambda & 0.281802949952249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154811&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.21692780404547[/C][/ROW]
[ROW][C]beta[/C][C]0.718197050047751[/C][/ROW]
[ROW][C]S.D.[/C][C]0.169939594314022[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.22619021156798[/C][/ROW]
[ROW][C]p-value[/C][C]0.000155000327253659[/C][/ROW]
[ROW][C]Lambda[/C][C]0.281802949952249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154811&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154811&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	-1.21692780404547
beta	0.718197050047751
S.D.	0.169939594314022
T-STAT	4.22619021156798
p-value	0.000155000327253659
Lambda	0.281802949952249

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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