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Re: Z-test for density

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Thu, 31 Jul 2008 02:11:34 -0700

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 ```Hi, I'm referring to the last email on z-test. I'm trying to do the same, by comparing the density estimates of several birds (multiple species) at two different levels of disturbance. I used CDS with post-stratification based on disturbance level and density was estimated for each species. In the distance book (Buckland et al 2001) at page 353, there is the z test calculation. The example was from fin whale survey and the z test tested the differences of mean size of two different pods (cluster size). Would that be a problem if I use the same calculation to compare the density estimates at two disturbance levels? Thanks. Best, Nurul  Nurul Winarni Email1. [log in to unmask] Email2. [log in to unmask] http://noonathome.wordpress.com/ http://wildlifewisdom.wordpress.com ----- Original Message ---- From: Jeff Laake <[log in to unmask]> To: [log in to unmask] Sent: Monday, June 23, 2008 11:06:58 PM Subject: Re: [DIST-SAMP] Z-test for density Sergio You are confusing two different types of tests. The one you describe is testing whether a sample mean is different from a population mean or whether it is different from a hypothesized value (eg. 0). The other is testing whether two sample means differ from each other and this is the more common. The first is a one sample test and the second is a 2-sample test. There are many different types of 2 sample tests. They can be paired or non-paired samples and non-paired tests can assume a common variance or different variances. The test we have been discussing is non-paired with different variances. Also, note that the formula you gave for the one sample test was incorrect because the denominator should have been the standard error of the mean and what you wrote was the sample variance/ sqrt (n). It should have been sqrt(sample variance/n) which is the standard error of the mean. On this point, the standard errors for density (from DISTANCE) are equivalent to the standard error of the mean and they are not standard deviations, so you do NOT divide the std error by the sqrt of n. This often confuses folks. For parameters (eg density) we use standard errors and not standard deviations. A standard deviation describes the spread in the data and a standard error is the uncertainty about a parameter (eg mean). The confusion comes from the fact that the standard error for a sample mean is the standard deviation divided by the sqrt of n. That does not apply to all parameters and there is typically no relationship between the standard deviation (of the data) and the standard error of a parameter, except for a mean. With regards to the contents of Snedecor and Cochran, my reference to it was a wry joke at myself because it is so old. Any basic stats text should give the formula for the hypothesis test we described. Len Thomas replied to me individually that my book (used) can be bought for \$4.80 at http://www.abebooks.com/. Note that I'm not recommending either this site or book. On a related subject, for what you want to do you are probably less interested in hypothesis testing than you are in estimating differences in densities between various guild. In the ecology and other fields there is a move away from hypothesis testing towards model selection. David Anderson or others may want to add more here. Unfortunately, the current DISTANCE software does not provide a lot of options (at present) to represent the abundance data by models. We have models for detection probability but the estimates of density are based on sampling concepts and are not model based for most of the analysis techniques in DISTANCE. I believe in one of the past list server messages Steve Buckland mentioned a paper that he and others have put together on analysis of experimental distance sampling data, so he may have more to contribute here. regards --jeff SERGIO . wrote: > Dear All, > > The equation: D^_1 - D^_2 Z = ----------------------------------- sqrt[{se(D^_1)}**2 + {se(D^_2)}**2] > > that Claire Meid referes to in his email, it is not the classical z-test equation to compare a sample mean with the population mean. How can i cited this formula to compare density between guilds and/or habitats and how can i consider this a validated equation (aproximation of z-test?) for my bird census analysis? > > The original formula at statistics books and statistics tests is this one: > > x - Uo > Z = ------------------ > var / sqrt [N] > > where x is a sample mean, Uo the population mean, var is the variance of the population and N is the sample size. > > In the density case the N could be always the same so its not consider and i can use densities from 2 samples to be compared, but the acceptance range could be always the same for z-test with this modifications? - 1,96 Thanks to all, > > Best Regards, > > Sergio Nolazco Plasier > Bach. Biology > Lima-Peru > > > > _________________________________________________________________ > Express yourself instantly with MSN Messenger! Download today it's FREE! > http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/ > -- > distance-sampling list home page: > http://www.jiscmail.ac.uk/lists/distance-sampling.html > To unsubscribe, go to the home page and click "Join or leave the list", > or email [log in to unmask] with the following message body: > leave distance-sampling > Before posting to the list, read the list guidelines at > http://www.jiscmail.ac.uk/files/distance-sampling/ > distance-sampling.welcome > Any questions, email the list owner at > [log in to unmask] > -- > -- distance-sampling list home page:   http://www.jiscmail.ac.uk/lists/distance-sampling.html To unsubscribe, go to the home page and click "Join or leave the list",   or email [log in to unmask] with the following message body:   leave distance-sampling Before posting to the list, read the list guidelines at   http://www.jiscmail.ac.uk/files/distance-sampling/     distance-sampling.welcome Any questions, email the list owner at   [log in to unmask] -- -- distance-sampling list home page:   http://www.jiscmail.ac.uk/lists/distance-sampling.html To unsubscribe, go to the home page and click "Join or leave the list",   or email [log in to unmask] with the following message body:   leave distance-sampling Before posting to the list, read the list guidelines at   http://www.jiscmail.ac.uk/files/distance-sampling/     distance-sampling.welcome Any questions, email the list owner at   [log in to unmask] --       ```