::Free Statistics and Forecasting Software::

:: Standard Deviation Plot - Free Statistics Software (Calculator) ::

The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Standard Deviation Plot for the (time) series. First the series is segmented into a number of blocks (preferably years). Then the standard deviation, range, and interquartile range is computed for the set of all i-th observations of each block (eg, all values of the same month). The resulting variability statistics for each periodic subseries are plotted. In addition the following notched box plots are generated: the periodic subseries, the sequential blocks, and the overall statistics.

Enter (or paste) your data delimited by hard returns.

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Data:
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# periods
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Cite this software as:

Wessa P., (2006), Standard Deviation Plot (v1.0.0) in Free Statistics Software (v1.1.20), Office for Research Development and Education, URL http://www.wessa.net/rwasp_sdplot.wasp/

The R code is based on :

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03.

Source code of R module
1	par1 <- as.numeric(par1)
2	(n <- length(x))
3	(np <- floor(n / par1))
4	arr <- array(NA,dim=c(par1,np+1))
5	ari <- array(0,dim=par1)
6	j <- 0
7	for (i in 1:n)
8	{
9	j = j + 1
10	ari[j] = ari[j] + 1
11	arr[j,ari[j]] <- x[i]
12	if (j == par1) j = 0
13	}
14	ari
15	arr
16	arr.sd <- array(NA,dim=par1)
17	arr.range <- array(NA,dim=par1)
18	arr.iqr <- array(NA,dim=par1)
19	for (j in 1:par1)
20	{
21	arr.sd[j] <- sqrt(var(arr[j,],na.rm=TRUE))
22	arr.range[j] <- max(arr[j,],na.rm=TRUE) - min(arr[j,],na.rm=TRUE)
23	arr.iqr[j] <- quantile(arr[j,],0.75,na.rm=TRUE) - quantile(arr[j,],0.25,na.rm=TRUE)
24	}
25	overall.sd <- sqrt(var(x))
26	overall.range <- max(x) - min(x)
27	overall.iqr <- quantile(x,0.75) - quantile(x,0.25)
28	bitmap(file="plot1.png")
29	plot(arr.sd,type="b",ylab="S.D.",main="Standard Deviation Plot",xlab="Periodic Index")
30	mtext(paste("# blocks = ",np))
31	abline(overall.sd,0)
32	dev.off()
33	bitmap(file="plot2.png")
34	plot(arr.range,type="b",ylab="range",main="Range Plot",xlab="Periodic Index")
35	mtext(paste("# blocks = ",np))
36	abline(overall.range,0)
37	dev.off()
38	bitmap(file="plot3.png")
39	plot(arr.iqr,type="b",ylab="IQR",main="Interquartile Range Plot",xlab="Periodic Index")
40	mtext(paste("# blocks = ",np))
41	abline(overall.iqr,0)
42	dev.off()
43	bitmap(file="plot4.png")
44	z <- data.frame(t(arr))
45	names(z) <- c(1:par1)
46	(boxplot(z,notch=TRUE,col="grey",xlab="Periodic Index",ylab="Value",main="Notched Box Plots - Periodic Subseries"))
47	dev.off()
48	bitmap(file="plot5.png")
49	z <- data.frame(arr)
50	names(z) <- c(1:np)
51	(boxplot(z,notch=TRUE,col="grey",xlab="Block Index",ylab="Value",main="Notched Box Plots - Sequential Blocks"))
52	dev.off()
53	bitmap(file="plot6.png")
54	z <- data.frame(cbind(arr.sd,arr.range,arr.iqr))
55	names(z) <- list("S.D.","Range","IQR")
56	(boxplot(z,notch=TRUE,col="grey",ylab="Overall Variability",main="Notched Box Plots"))
57	dev.off()

To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.20, URL http://www.wessa.net/

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Software Version : 1.1.20
Algorithms & Software : Prof. dr. P. Wessa
Facilities : Resa R&D - Office for Research, Development, and Education
Server : www.wessa.net

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