::Free Statistics and Forecasting Software::
v1.1.22-r6
 
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:: Univariate Summary Statistics - Free Statistics Software (Calculator) ::
All rights reserved. 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 descriptive, summarizing statistics for any univariate data series. This computation includes the following statistics: central tendency, variability, quantiles, histogram, and kernel density.

Click here to edit the underlying code of this R Module.

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Click here to edit the underlying code of this R Module.




Cite this software as:
Wessa P., (2008), Univariate Summary Statistics (v1.0.4) in Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_summary1.wasp/
The R code is based on :
Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/

Source code of R module
1load(file="createtable")
2x <-sort(x[!is.na(x)])
3num <- 50
4res <- array(NA,dim=c(num,3))
5geomean <- function(x) {
6return(exp(mean(log(x))))
7}
8harmean <- function(x) {
9return(1/mean(1/x))
10}
11quamean <- function(x) {
12return(sqrt(mean(x*x)))
13}
14winmean <- function(x) {
15x <-sort(x[!is.na(x)])
16n<-length(x)
17denom <- 3
18nodenom <- n/denom
19if (nodenom>40) denom <- n/40
20sqrtn = sqrt(n)
21roundnodenom = floor(nodenom)
22win <- array(NA,dim=c(roundnodenom,2))
23for (j in 1:roundnodenom) {
24win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
25win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
26}
27return(win)
28}
29trimean <- function(x) {
30x <-sort(x[!is.na(x)])
31n<-length(x)
32denom <- 3
33nodenom <- n/denom
34if (nodenom>40) denom <- n/40
35sqrtn = sqrt(n)
36roundnodenom = floor(nodenom)
37tri <- array(NA,dim=c(roundnodenom,2))
38for (j in 1:roundnodenom) {
39tri[j,1] <- mean(x,trim=j/n)
40tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
41}
42return(tri)
43}
44midrange <- function(x) {
45return((max(x)+min(x))/2)
46}
47q1 <- function(data,n,p,i,f) {
48np <- n*p;
49i <<- floor(np)
50f <<- np - i
51qvalue <- (1-f)*data[i] + f*data[i+1]
52}
53q2 <- function(data,n,p,i,f) {
54np <- (n+1)*p
55i <<- floor(np)
56f <<- np - i
57qvalue <- (1-f)*data[i] + f*data[i+1]
58}
59q3 <- function(data,n,p,i,f) {
60np <- n*p
61i <<- floor(np)
62f <<- np - i
63if (f==0) {
64qvalue <- data[i]
65} else {
66qvalue <- data[i+1]
67}
68}
69q4 <- function(data,n,p,i,f) {
70np <- n*p
71i <<- floor(np)
72f <<- np - i
73if (f==0) {
74qvalue <- (data[i]+data[i+1])/2
75} else {
76qvalue <- data[i+1]
77}
78}
79q5 <- function(data,n,p,i,f) {
80np <- (n-1)*p
81i <<- floor(np)
82f <<- np - i
83if (f==0) {
84qvalue <- data[i+1]
85} else {
86qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
87}
88}
89q6 <- function(data,n,p,i,f) {
90np <- n*p+0.5
91i <<- floor(np)
92f <<- np - i
93qvalue <- data[i]
94}
95q7 <- function(data,n,p,i,f) {
96np <- (n+1)*p
97i <<- floor(np)
98f <<- np - i
99if (f==0) {
100qvalue <- data[i]
101} else {
102qvalue <- f*data[i] + (1-f)*data[i+1]
103}
104}
105q8 <- function(data,n,p,i,f) {
106np <- (n+1)*p
107i <<- floor(np)
108f <<- np - i
109if (f==0) {
110qvalue <- data[i]
111} else {
112if (f == 0.5) {
113qvalue <- (data[i]+data[i+1])/2
114} else {
115if (f < 0.5) {
116qvalue <- data[i]
117} else {
118qvalue <- data[i+1]
119}
120}
121}
122}
123iqd <- function(x,def) {
124x <-sort(x[!is.na(x)])
125n<-length(x)
126if (def==1) {
127qvalue1 <- q1(x,n,0.25,i,f)
128qvalue3 <- q1(x,n,0.75,i,f)
129}
130if (def==2) {
131qvalue1 <- q2(x,n,0.25,i,f)
132qvalue3 <- q2(x,n,0.75,i,f)
133}
134if (def==3) {
135qvalue1 <- q3(x,n,0.25,i,f)
136qvalue3 <- q3(x,n,0.75,i,f)
137}
138if (def==4) {
139qvalue1 <- q4(x,n,0.25,i,f)
140qvalue3 <- q4(x,n,0.75,i,f)
141}
142if (def==5) {
143qvalue1 <- q5(x,n,0.25,i,f)
144qvalue3 <- q5(x,n,0.75,i,f)
145}
146if (def==6) {
147qvalue1 <- q6(x,n,0.25,i,f)
148qvalue3 <- q6(x,n,0.75,i,f)
149}
150if (def==7) {
151qvalue1 <- q7(x,n,0.25,i,f)
152qvalue3 <- q7(x,n,0.75,i,f)
153}
154if (def==8) {
155qvalue1 <- q8(x,n,0.25,i,f)
156qvalue3 <- q8(x,n,0.75,i,f)
157}
158iqdiff <- qvalue3 - qvalue1
159return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
160}
161midmean <- function(x,def) {
162x <-sort(x[!is.na(x)])
163n<-length(x)
164if (def==1) {
165qvalue1 <- q1(x,n,0.25,i,f)
166qvalue3 <- q1(x,n,0.75,i,f)
167}
168if (def==2) {
169qvalue1 <- q2(x,n,0.25,i,f)
170qvalue3 <- q2(x,n,0.75,i,f)
171}
172if (def==3) {
173qvalue1 <- q3(x,n,0.25,i,f)
174qvalue3 <- q3(x,n,0.75,i,f)
175}
176if (def==4) {
177qvalue1 <- q4(x,n,0.25,i,f)
178qvalue3 <- q4(x,n,0.75,i,f)
179}
180if (def==5) {
181qvalue1 <- q5(x,n,0.25,i,f)
182qvalue3 <- q5(x,n,0.75,i,f)
183}
184if (def==6) {
185qvalue1 <- q6(x,n,0.25,i,f)
186qvalue3 <- q6(x,n,0.75,i,f)
187}
188if (def==7) {
189qvalue1 <- q7(x,n,0.25,i,f)
190qvalue3 <- q7(x,n,0.75,i,f)
191}
192if (def==8) {
193qvalue1 <- q8(x,n,0.25,i,f)
194qvalue3 <- q8(x,n,0.75,i,f)
195}
196midm <- 0
197myn <- 0
198roundno4 <- round(n/4)
199round3no4 <- round(3*n/4)
200for (i in 1:n) {
201if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
202midm = midm + x[i]
203myn = myn + 1
204}
205}
206midm = midm / myn
207return(midm)
208}
209range <- max(x) - min(x)
210lx <- length(x)
211biasf <- (lx-1)/lx
212varx <- var(x)
213bvarx <- varx*biasf
214sdx <- sqrt(varx)
215mx <- mean(x)
216bsdx <- sqrt(bvarx)
217x2 <- x*x
218mse0 <- sum(x2)/lx
219xmm <- x-mx
220xmm2 <- xmm*xmm
221msem <- sum(xmm2)/lx
222axmm <- abs(x - mx)
223medx <- median(x)
224axmmed <- abs(x - medx)
225xmmed <- x - medx
226xmmed2 <- xmmed*xmmed
227msemed <- sum(xmmed2)/lx
228qarr <- array(NA,dim=c(8,3))
229for (j in 1:8) {
230qarr[j,] <- iqd(x,j)
231}
232sdpo <- 0
233adpo <- 0
234for (i in 1:(lx-1)) {
235for (j in (i+1):lx) {
236ldi <- x[i]-x[j]
237aldi <- abs(ldi)
238sdpo = sdpo + ldi * ldi
239adpo = adpo + aldi
240}
241}
242denom <- (lx*(lx-1)/2)
243sdpo = sdpo / denom
244adpo = adpo / denom
245gmd <- 0
246for (i in 1:lx) {
247for (j in 1:lx) {
248ldi <- abs(x[i]-x[j])
249gmd = gmd + ldi
250}
251}
252gmd <- gmd / (lx*(lx-1))
253sumx <- sum(x)
254pk <- x / sumx
255ck <- cumsum(pk)
256dk <- array(NA,dim=lx)
257for (i in 1:lx) {
258if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
259}
260bigd <- sum(dk) * 2 / (lx-1)
261iod <- 1 - sum(pk*pk)
262res[1,] <- c("Absolute range","http://www.xycoon.com/absolute.htm", range)
263res[2,] <- c("Relative range (unbiased)","http://www.xycoon.com/relative.htm", range/sd(x))
264res[3,] <- c("Relative range (biased)","http://www.xycoon.com/relative.htm", range/sqrt(varx*biasf))
265res[4,] <- c("Variance (unbiased)","http://www.xycoon.com/unbiased.htm", varx)
266res[5,] <- c("Variance (biased)","http://www.xycoon.com/biased.htm", bvarx)
267res[6,] <- c("Standard Deviation (unbiased)","http://www.xycoon.com/unbiased1.htm", sdx)
268res[7,] <- c("Standard Deviation (biased)","http://www.xycoon.com/biased1.htm", bsdx)
269res[8,] <- c("Coefficient of Variation (unbiased)","http://www.xycoon.com/variation.htm", sdx/mx)
270res[9,] <- c("Coefficient of Variation (biased)","http://www.xycoon.com/variation.htm", bsdx/mx)
271res[10,] <- c("Mean Squared Error (MSE versus 0)","http://www.xycoon.com/mse.htm", mse0)
272res[11,] <- c("Mean Squared Error (MSE versus Mean)","http://www.xycoon.com/mse.htm", msem)
273res[12,] <- c("Mean Absolute Deviation from Mean (MAD Mean)", "http://www.xycoon.com/mean2.htm", sum(axmm)/lx)
274res[13,] <- c("Mean Absolute Deviation from Median (MAD Median)", "http://www.xycoon.com/median1.htm", sum(axmmed)/lx)
275res[14,] <- c("Median Absolute Deviation from Mean", "http://www.xycoon.com/mean3.htm", median(axmm))
276res[15,] <- c("Median Absolute Deviation from Median", "http://www.xycoon.com/median2.htm", median(axmmed))
277res[16,] <- c("Mean Squared Deviation from Mean", "http://www.xycoon.com/mean1.htm", msem)
278res[17,] <- c("Mean Squared Deviation from Median", "http://www.xycoon.com/median.htm", msemed)
279mylink1 <- hyperlink("http://www.xycoon.com/difference.htm","Interquartile Difference","")
280mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ")
281res[18,] <- c("", mylink2, qarr[1,1])
282mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ")
283res[19,] <- c("", mylink2, qarr[2,1])
284mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ")
285res[20,] <- c("", mylink2, qarr[3,1])
286mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ")
287res[21,] <- c("", mylink2, qarr[4,1])
288mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ")
289res[22,] <- c("", mylink2, qarr[5,1])
290mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ")
291res[23,] <- c("", mylink2, qarr[6,1])
292mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ")
293res[24,] <- c("", mylink2, qarr[7,1])
294mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ")
295res[25,] <- c("", mylink2, qarr[8,1])
296mylink1 <- hyperlink("http://www.xycoon.com/deviation.htm","Semi Interquartile Difference","")
297mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ")
298res[26,] <- c("", mylink2, qarr[1,2])
299mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ")
300res[27,] <- c("", mylink2, qarr[2,2])
301mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ")
302res[28,] <- c("", mylink2, qarr[3,2])
303mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ")
304res[29,] <- c("", mylink2, qarr[4,2])
305mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ")
306res[30,] <- c("", mylink2, qarr[5,2])
307mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ")
308res[31,] <- c("", mylink2, qarr[6,2])
309mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ")
310res[32,] <- c("", mylink2, qarr[7,2])
311mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ")
312res[33,] <- c("", mylink2, qarr[8,2])
313mylink1 <- hyperlink("http://www.xycoon.com/variation1.htm","Coefficient of Quartile Variation","")
314mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_1.htm","(Weighted Average at Xnp)",""),sep=" ")
315res[34,] <- c("", mylink2, qarr[1,3])
316mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_2.htm","(Weighted Average at X(n+1)p)",""),sep=" ")
317res[35,] <- c("", mylink2, qarr[2,3])
318mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_3.htm","(Empirical Distribution Function)",""),sep=" ")
319res[36,] <- c("", mylink2, qarr[3,3])
320mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_4.htm","(Empirical Distribution Function - Averaging)",""),sep=" ")
321res[37,] <- c("", mylink2, qarr[4,3])
322mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_5.htm","(Empirical Distribution Function - Interpolation)",""),sep=" ")
323res[38,] <- c("", mylink2, qarr[5,3])
324mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_6.htm","(Closest Observation)",""),sep=" ")
325res[39,] <- c("", mylink2, qarr[6,3])
326mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_7.htm","(True Basic - Statistics Graphics Toolkit)",""),sep=" ")
327res[40,] <- c("", mylink2, qarr[7,3])
328mylink2 <- paste(mylink1,hyperlink("http://www.xycoon.com/method_8.htm","(MS Excel (old versions))",""),sep=" ")
329res[41,] <- c("", mylink2, qarr[8,3])
330res[42,] <- c("Number of all Pairs of Observations", "http://www.xycoon.com/pair_numbers.htm", lx*(lx-1)/2)
331res[43,] <- c("Squared Differences between all Pairs of Observations", "http://www.xycoon.com/squared_differences.htm", sdpo)
332res[44,] <- c("Mean Absolute Differences between all Pairs of Observations", "http://www.xycoon.com/mean_abs_differences.htm", adpo)
333res[45,] <- c("Gini Mean Difference", "http://www.xycoon.com/gini_mean_difference.htm", gmd)
334res[46,] <- c("Leik Measure of Dispersion", "http://www.xycoon.com/leiks_d.htm", bigd)
335res[47,] <- c("Index of Diversity", "http://www.xycoon.com/diversity.htm", iod)
336res[48,] <- c("Index of Qualitative Variation", "http://www.xycoon.com/qualitative_variation.htm", iod*lx/(lx-1))
337res[49,] <- c("Coefficient of Dispersion", "http://www.xycoon.com/dispersion.htm", sum(axmm)/lx/medx)
338res[50,] <- c("Observations", "", lx)
339res
340(arm <- mean(x))
341sqrtn <- sqrt(length(x))
342(armse <- sd(x) / sqrtn)
343(armose <- arm / armse)
344(geo <- geomean(x))
345(har <- harmean(x))
346(qua <- quamean(x))
347(win <- winmean(x))
348(tri <- trimean(x))
349(midr <- midrange(x))
350midm <- array(NA,dim=8)
351for (j in 1:8) midm[j] <- midmean(x,j)
352midm
353bitmap(file="test1.png")
354lb <- win[,1] - 2*win[,2]
355ub <- win[,1] + 2*win[,2]
356if ((ylimmin == "") | (ylimmax == "")) plot(win[,1],type="b",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Winsorized Mean(j/n)", ylim=c(min(lb),max(ub))) else plot(win[,1],type="l",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Winsorized Mean(j/n)", ylim=c(ylimmin,ylimmax))
357lines(ub,lty=3)
358lines(lb,lty=3)
359grid()
360dev.off()
361bitmap(file="test2.png")
362lb <- tri[,1] - 2*tri[,2]
363ub <- tri[,1] + 2*tri[,2]
364if ((ylimmin == "") | (ylimmax == "")) plot(tri[,1],type="b",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Trimmed Mean(j/n)", ylim=c(min(lb),max(ub))) else plot(tri[,1],type="l",main="Robustness of Central Tendency", xlab="j", pch=19, ylab="Trimmed Mean(j/n)", ylim=c(ylimmin,ylimmax))
365lines(ub,lty=3)
366lines(lb,lty=3)
367grid()
368dev.off()
369a<-table.start()
370a<-table.row.start(a)
371a<-table.element(a,"Central Tendency - Ungrouped Data",4,TRUE)
372a<-table.row.end(a)
373a<-table.row.start(a)
374a<-table.element(a,"Measure",header=TRUE)
375a<-table.element(a,"Value",header=TRUE)
376a<-table.element(a,"S.E.",header=TRUE)
377a<-table.element(a,"Value/S.E.",header=TRUE)
378a<-table.row.end(a)
379a<-table.row.start(a)
380a<-table.element(a,hyperlink("http://www.xycoon.com/arithmetic_mean.htm", "Arithmetic Mean", "click to view the definition of the Arithmetic Mean"),header=TRUE)
381a<-table.element(a,arm)
382a<-table.element(a,hyperlink("http://www.xycoon.com/arithmetic_mean_standard_error.htm", armse, "click to view the definition of the Standard Error of the Arithmetic Mean"))
383a<-table.element(a,armose)
384a<-table.row.end(a)
385a<-table.row.start(a)
386a<-table.element(a,hyperlink("http://www.xycoon.com/geometric_mean.htm", "Geometric Mean", "click to view the definition of the Geometric Mean"),header=TRUE)
387a<-table.element(a,geo)
388a<-table.element(a,"")
389a<-table.element(a,"")
390a<-table.row.end(a)
391a<-table.row.start(a)
392a<-table.element(a,hyperlink("http://www.xycoon.com/harmonic_mean.htm", "Harmonic Mean", "click to view the definition of the Harmonic Mean"),header=TRUE)
393a<-table.element(a,har)
394a<-table.element(a,"")
395a<-table.element(a,"")
396a<-table.row.end(a)
397a<-table.row.start(a)
398a<-table.element(a,hyperlink("http://www.xycoon.com/quadratic_mean.htm", "Quadratic Mean", "click to view the definition of the Quadratic Mean"),header=TRUE)
399a<-table.element(a,qua)
400a<-table.element(a,"")
401a<-table.element(a,"")
402a<-table.row.end(a)
403for (j in 1:length(win[,1])) {
404a<-table.row.start(a)
405mylabel <- paste("Winsorized Mean (",j)
406mylabel <- paste(mylabel,"/")
407mylabel <- paste(mylabel,length(win[,1]))
408mylabel <- paste(mylabel,")")
409a<-table.element(a,hyperlink("http://www.xycoon.com/winsorized_mean.htm", mylabel, "click to view the definition of the Winsorized Mean"),header=TRUE)
410a<-table.element(a,win[j,1])
411a<-table.element(a,win[j,2])
412a<-table.element(a,win[j,1]/win[j,2])
413a<-table.row.end(a)
414}
415for (j in 1:length(tri[,1])) {
416a<-table.row.start(a)
417mylabel <- paste("Trimmed Mean (",j)
418mylabel <- paste(mylabel,"/")
419mylabel <- paste(mylabel,length(tri[,1]))
420mylabel <- paste(mylabel,")")
421a<-table.element(a,hyperlink("http://www.xycoon.com/arithmetic_mean.htm", mylabel, "click to view the definition of the Trimmed Mean"),header=TRUE)
422a<-table.element(a,tri[j,1])
423a<-table.element(a,tri[j,2])
424a<-table.element(a,tri[j,1]/tri[j,2])
425a<-table.row.end(a)
426}
427a<-table.row.start(a)
428a<-table.element(a,hyperlink("http://www.xycoon.com/median_1.htm", "Median", "click to view the definition of the Median"),header=TRUE)
429a<-table.element(a,median(x))
430a<-table.element(a,"")
431a<-table.element(a,"")
432a<-table.row.end(a)
433a<-table.row.start(a)
434a<-table.element(a,hyperlink("http://www.xycoon.com/midrange.htm", "Midrange", "click to view the definition of the Midrange"),header=TRUE)
435a<-table.element(a,midr)
436a<-table.element(a,"")
437a<-table.element(a,"")
438a<-table.row.end(a)
439a<-table.row.start(a)
440mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
441mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_1.htm","Weighted Average at Xnp",""),sep=" - ")
442a<-table.element(a,mylabel,header=TRUE)
443a<-table.element(a,midm[1])
444a<-table.element(a,"")
445a<-table.element(a,"")
446a<-table.row.end(a)
447a<-table.row.start(a)
448mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
449mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_2.htm","Weighted Average at X(n+1)p",""),sep=" - ")
450a<-table.element(a,mylabel,header=TRUE)
451a<-table.element(a,midm[2])
452a<-table.element(a,"")
453a<-table.element(a,"")
454a<-table.row.end(a)
455a<-table.row.start(a)
456mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
457mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_3.htm","Empirical Distribution Function",""),sep=" - ")
458a<-table.element(a,mylabel,header=TRUE)
459a<-table.element(a,midm[3])
460a<-table.element(a,"")
461a<-table.element(a,"")
462a<-table.row.end(a)
463a<-table.row.start(a)
464mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
465mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_4.htm","Empirical Distribution Function - Averaging",""),sep=" - ")
466a<-table.element(a,mylabel,header=TRUE)
467a<-table.element(a,midm[4])
468a<-table.element(a,"")
469a<-table.element(a,"")
470a<-table.row.end(a)
471a<-table.row.start(a)
472mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
473mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_5.htm","Empirical Distribution Function - Interpolation",""),sep=" - ")
474a<-table.element(a,mylabel,header=TRUE)
475a<-table.element(a,midm[5])
476a<-table.element(a,"")
477a<-table.element(a,"")
478a<-table.row.end(a)
479a<-table.row.start(a)
480mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
481mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_6.htm","Closest Observation",""),sep=" - ")
482a<-table.element(a,mylabel,header=TRUE)
483a<-table.element(a,midm[6])
484a<-table.element(a,"")
485a<-table.element(a,"")
486a<-table.row.end(a)
487a<-table.row.start(a)
488mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
489mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_7.htm","True Basic - Statistics Graphics Toolkit",""),sep=" - ")
490a<-table.element(a,mylabel,header=TRUE)
491a<-table.element(a,midm[7])
492a<-table.element(a,"")
493a<-table.element(a,"")
494a<-table.row.end(a)
495a<-table.row.start(a)
496mymid <- hyperlink("http://www.xycoon.com/midmean.htm", "Midmean", "click to view the definition of the Midmean")
497mylabel <- paste(mymid,hyperlink("http://www.xycoon.com/method_8.htm","MS Excel (old versions)",""),sep=" - ")
498a<-table.element(a,mylabel,header=TRUE)
499a<-table.element(a,midm[8])
500a<-table.element(a,"")
501a<-table.element(a,"")
502a<-table.row.end(a)
503a<-table.row.start(a)
504a<-table.element(a,"Number of observations",header=TRUE)
505a<-table.element(a,length(x))
506a<-table.element(a,"")
507a<-table.element(a,"")
508a<-table.row.end(a)
509a<-table.end(a)
510table.save(a,file="mytable.tab")
511a<-table.start()
512a<-table.row.start(a)
513a<-table.element(a,"Variability - Ungrouped Data",2,TRUE)
514a<-table.row.end(a)
515for (i in 1:num) {
516a<-table.row.start(a)
517if (res[i,1] != "") {
518a<-table.element(a,hyperlink(res[i,2],res[i,1],""),header=TRUE)
519} else {
520a<-table.element(a,res[i,2],header=TRUE)
521}
522a<-table.element(a,res[i,3])
523a<-table.row.end(a)
524}
525a<-table.end(a)
526table.save(a,file="mytable1.tab")
527lx <- length(x)
528qval <- array(NA,dim=c(99,8))
529mystep <- 25
530mystart <- 25
531if (lx>10){
532mystep=10
533mystart=10
534}
535if (lx>20){
536mystep=5
537mystart=5
538}
539if (lx>50){
540mystep=2
541mystart=2
542}
543if (lx>=100){
544mystep=1
545mystart=1
546}
547for (perc in seq(mystart,99,mystep)) {
548qval[perc,1] <- q1(x,lx,perc/100,i,f)
549qval[perc,2] <- q2(x,lx,perc/100,i,f)
550qval[perc,3] <- q3(x,lx,perc/100,i,f)
551qval[perc,4] <- q4(x,lx,perc/100,i,f)
552qval[perc,5] <- q5(x,lx,perc/100,i,f)
553qval[perc,6] <- q6(x,lx,perc/100,i,f)
554qval[perc,7] <- q7(x,lx,perc/100,i,f)
555qval[perc,8] <- q8(x,lx,perc/100,i,f)
556}
557bitmap(file="test3.png")
558myqqnorm <- qqnorm(x,col=2)
559qqline(x)
560grid()
561dev.off()
562a<-table.start()
563a<-table.row.start(a)
564a<-table.element(a,"Percentiles - Ungrouped Data",9,TRUE)
565a<-table.row.end(a)
566a<-table.row.start(a)
567a<-table.element(a,"p",1,TRUE)
568a<-table.element(a,hyperlink("http://www.xycoon.com/method_1.htm", "Weighted Average at Xnp",""),1,TRUE)
569a<-table.element(a,hyperlink("http://www.xycoon.com/method_2.htm","Weighted Average at X(n+1)p",""),1,TRUE)
570a<-table.element(a,hyperlink("http://www.xycoon.com/method_3.htm","Empirical Distribution Function",""),1,TRUE)
571a<-table.element(a,hyperlink("http://www.xycoon.com/method_4.htm","Empirical Distribution Function - Averaging",""),1,TRUE)
572a<-table.element(a,hyperlink("http://www.xycoon.com/method_5.htm","Empirical Distribution Function - Interpolation",""),1,TRUE)
573a<-table.element(a,hyperlink("http://www.xycoon.com/method_6.htm","Closest Observation",""),1,TRUE)
574a<-table.element(a,hyperlink("http://www.xycoon.com/method_7.htm","True Basic - Statistics Graphics Toolkit",""),1,TRUE)
575a<-table.element(a,hyperlink("http://www.xycoon.com/method_8.htm","MS Excel (old versions)",""),1,TRUE)
576a<-table.row.end(a)
577for (perc in seq(mystart,99,mystep)) {
578a<-table.row.start(a)
579a<-table.element(a,round(perc/100,2),1,TRUE)
580for (j in 1:8) {
581a<-table.element(a,round(qval[perc,j],6))
582}
583a<-table.row.end(a)
584}
585a<-table.end(a)
586table.save(a,file="mytable2.tab")
587bitmap(file="histogram1.png")
588myhist<-hist(x)
589dev.off()
590myhist
591n <- length(x)
592a<-table.start()
593a<-table.row.start(a)
594a<-table.element(a,hyperlink("http://www.xycoon.com/histogram.htm","Frequency Table (Histogram)",""),6,TRUE)
595a<-table.row.end(a)
596a<-table.row.start(a)
597a<-table.element(a,"Bins",header=TRUE)
598a<-table.element(a,"Midpoint",header=TRUE)
599a<-table.element(a,"Abs. Frequency",header=TRUE)
600a<-table.element(a,"Rel. Frequency",header=TRUE)
601a<-table.element(a,"Cumul. Rel. Freq.",header=TRUE)
602a<-table.element(a,"Density",header=TRUE)
603a<-table.row.end(a)
604crf <- 0
605mybracket <- "["
606mynumrows <- (length(myhist$breaks)-1)
607for (i in 1:mynumrows) {
608a<-table.row.start(a)
609if (i == 1)
610dum <- paste("[",myhist$breaks[i],sep="")
611else
612dum <- paste(mybracket,myhist$breaks[i],sep="")
613dum <- paste(dum,myhist$breaks[i+1],sep=",")
614if (i==mynumrows)
615dum <- paste(dum,"]",sep="")
616else
617dum <- paste(dum,mybracket,sep="")
618a<-table.element(a,dum,header=TRUE)
619a<-table.element(a,myhist$mids[i])
620a<-table.element(a,myhist$counts[i])
621rf <- myhist$counts[i]/n
622crf <- crf + rf
623a<-table.element(a,round(rf,6))
624a<-table.element(a,round(crf,6))
625a<-table.element(a,round(myhist$density[i],6))
626a<-table.row.end(a)
627}
628a<-table.end(a)
629table.save(a,file="mytable5.tab")
630bitmap(file="density1.png")
631mydensity1<-density(x,kernel="gaussian",na.rm=TRUE)
632plot(mydensity1,main="Gaussian Kernel")
633grid()
634dev.off()
635mydensity1
636a<-table.start()
637a<-table.row.start(a)
638a<-table.element(a,"Properties of Density Trace",2,TRUE)
639a<-table.row.end(a)
640a<-table.row.start(a)
641a<-table.element(a,"Bandwidth",header=TRUE)
642a<-table.element(a,mydensity1$bw)
643a<-table.row.end(a)
644a<-table.row.start(a)
645a<-table.element(a,"#Observations",header=TRUE)
646a<-table.element(a,mydensity1$n)
647a<-table.row.end(a)
648a<-table.end(a)
649table.save(a,file="mytable4.tab")
Delete history
Server DateModuleCommand
Sat, 17 May 2008 14:34:39 -0600Start of session-

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Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/

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Software Version : 1.1.22-r6
Algorithms & Software : Prof. dr. P. Wessa
Facilities : Resa R&D - Office for Research, Development, and Education
Server : www.wessa.net

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