On Tue, 16 Oct 2007, azzza wrote: > > Thats what is frustrating me....I've done a lot of reading, but there doesnt > seem to be much info on sign changes..............I dont udnerstand why the > poportion of sign changes is much less than 50%, despite the proportion of > heads being equal to that of tails. >
I think some earlier posters have misunderstood what you are trying to do: they thought you were interested in runs of heads of tails, but it seems to me that you are interested in whether the sample proportion is above or below 1/2. Code to compute the number of sign changes looks like x<-rbinom(1000,1,0.5) proportion <- cumsum(x)/(1:1000) above <- proportion > 1/2 nchanges<-length(rle(above)$values) You might also want to plot the cumulative sum plot(1:1000, cumsum(x)) abline(h=0) Looking at the plot you should be able to see why the number of changes is relatively small: to get a sign change you need the curve to go in the right direction (50:50) but you also need to be close enough to zero. -thomas > Marc Schwartz wrote: >> >> You might want to do some more research on "Bernoulli Trials" and "Fair >> Coins", which would provide some enlightenment on why you would not >> "expect" 500 sign changes in 1,000 tosses and why you should, if the >> coin is "fair", expect to *approach* a 50/50 distribution of heads and >> tails in a large number of tosses, but not actually observe it. >> >> HTH, >> >> Marc Schwartz >> >> >> On Tue, 2007-10-16 at 09:05 -0700, azzza wrote: >>> >>> You are right, I was a bit too vague. I am trying to simulate 1000 coin >>> Tosses. Then to write a code for the number of heads/Tails.....naturally, >>> we >>> would expect the proportion of heads to be 50% so the number of heads >>> would >>> be around 500. Secondly, I'm trying to look at the number of sign changes >>> in >>> 1000 tosses. The example in the book shows that the number of sign >>> changes >>> is WAY less than 50%. so I was trying to look for a code that shows the >>> number of sign changes, which someone pointed out would be to use >>> rle(x).....my concern however is that when the rle(x) is used, the >>> proportion of sign changes is about 50% (around 500), which would be >>> logical >>> to expect, however, real life experiments have shown that the number of >>> sign >>> changes is actually much less than 50%. The other thing I was trying to >>> do >>> is to plot a line graph of number of sign changes versus the number of >>> tosses. Yes, the number of tosses should begin at zero, and at zero coin >>> toss, the sign change is zero. The range of the number of sign changes in >>> the Y-axis should include negative values of Y. So, for toss number zero, >>> the sign change is 0, for the first toss, the sign change may be +3 for >>> instance, for the 50th toss, the sign change may be -5 for instance. The >>> plot shown in the book shows that for most of the tosses, the sign >>> changes >>> were negative, and this would explain how the overall number of sign >>> changes >>> is very low. >>> >>> so basically, i was looking for a code to show the number of sign >>> changes, >>> and a plot of sign changes versus toss number (from toss #0 to toss >>> number >>> 1000). The Y axis (number of sign changes, should include negative values >>> of >>> Y) >>> >>> thanks >>> >>> >>> >>> Daniel Nordlund wrote: >>>> >>>>> -----Original Message----- >>>>> From: [EMAIL PROTECTED] >>> [mailto:[EMAIL PROTECTED] >>>>> On Behalf >>>>> Of azzza >>>>> Sent: Monday, October 15, 2007 6:06 PM >>>>> To: r-help@r-project.org >>>>> Subject: Re: [R] Need some help >>>>> >>>>> >>>>> >>>>> Thanks Jholtman. >>>>> However, the plot didnt come out the way I envisone dit to be. On the >>> Y >>>>> axis, i should have sign changes in 1000 tosses, the range being from >>>>> negative to postitive, and a straight horizontal line across y=0. The >>>>> X-axis should have the toss number, range 0-1000 >>>>> >>>> >>>> You would probably get more prompt and useful help if you would provide >>> a >>>> small, self- contained example of what you wanted (maybe small enough >>> that >>>> you could work it by hand). Also, if you provided some code using the >>>> help that you have already received, that would show that you are >>> trying >>>> to solve the problem yourself and others could help with the specific R >>>> program issues that you are having. For example, it is not clear to me >>> if >>>> you want to count the first run of tosses as 0 or 1 sign change. I >>> will >>>> assume it is zero. So with that assumption, does this get you what you >>>> want? >>>> >>>> n <- 1000 >>>> x <- sample(c(0,1), n, TRUE) >>>> y <- rle(x) >>>> >>>> z <- rep(1:length(y$lengths),y$lengths) >>>> plot(1:n,z-1) >>>> >>>> Hope this is helpful, >>>> >>>> Dan >>>> >>>> Daniel Nordlund >>>> Bothell, WA USA >>>> >>>> ______________________________________________ >>>> R-help@r-project.org mailing list >>>> https://stat.ethz.ch/mailman/listinfo/r-help >>>> PLEASE do read the posting guide >>>> http://www.R-project.org/posting-guide.html >>>> and provide commented, minimal, self-contained, reproducible code. >>>> >>>> >>> >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> >> > > -- > View this message in context: > http://www.nabble.com/Need-some-help-tf4624513.html#a13238567 > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > Thomas Lumley Assoc. Professor, Biostatistics [EMAIL PROTECTED] University of Washington, Seattle ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.