Re: comparing 2 slopes
Ellen Hertz wrote: Mike, Yes, you are correct. A purist might say that you didn't actually prove that the slopes are the same, only that you failed to demonstrate a significant difference between them (because non-significant parameters can become significant with more data). However, your interpretation is correct and, also, including an interaction term to examine its statistical significance is the best approach. Careful! I think you have to take the purist's view - with most data sets I could get a non-significant interaction even if the slopes are different, just by removing some of the data. If the data it plentiful, then the interpretation may be reasonable (even if still not strivtly correct). The interpretation you're advocating is logically dodgy - your conclusion could depend as much on the number of data points you have as on the difference between the slopes. If you want to argue that two slopes are the same, then it's better to look at the confidence limits, and see if they only cover a range that is practically insignificant, then you can say that any difference is too small to worry about. Bob -- Bob O'Hara Metapopulation Research Group Division of Population Biology Department of Ecology and Systematics PO Box 17 (Arkadiankatu 7) FIN-00014 University of Helsinki Finland tel: +358 9 191 28782 fax: +358 9 191 28701 email: [EMAIL PROTECTED] To induce catatonia, visit: http://www.helsinki.fi/science/metapop/ It is being said of a certain poet, that though he tortures the English language, he has still never yet succeeded in forcing it to reveal his meaning - Beachcomber = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Late Absentee Ballot Acceptance Rates in Florida
(J. Williams) wrote: Snip Since the envelopes containing the absentee ballots were separated from the ballots themselves, no information about the voter was available: The Times asked Gary King, a Harvard expert on voting patterns and statistical models, what would have happened had the flawed ballots been discarded. He concluded that there was no way to declare a winner with mathematical certainty under those circumstances. His best estimate, he said, was that Mr. Bush's margin would have been reduced to 245 votes. Dr. King estimated that there was only a slight chance that discarding the questionable ballots would have made Mr. Gore the winner. I thought that Gary King's conclusion to be the most interesting part of the lengthy Times analysis. However, I will freely admit that I don't understand King's A Solution to the ecological inference problem. I bought his book, read it twice, am convinced with King that the ecological inference problem is important and that previous methods are inadequate, but his description of the algorithm left me utterly confused. The synopsis of King's statistical analysis for the Times doesn't help much: http://www.nytimes.com/2001/07/15/politics/15METH.html?searchpv=nyt I'd like to include King's method in my stats class. I think there are many instances of the ecological inference problem in ecology, but I have to understand his book solution first. Today In his analysis for The Times, Dr. King first examined the actual vote and the count of flawed ballots, and he computed the maximum and minimum numbers of absentee votes that Mr. Gore and Mr. Bush could possibly have received in each county. He then used the methodology described in his book, A Solution to the Ecological Inference Problem, to estimate the unknown voting behavior of the 680 voters whose votes were found to be flawed, and subtracted them from the vote totals. The analysis took into account actual overseas absentee vote totals for each county that were certified on Nov. 26 by Secretary of State Katherine Harris. Dr. King also weighed other factors, like the race and party of overseas voters and their military status, and other election results in each county. The analysis then averaged these 62 separate but similar models, weighting each according to its statistical importance, to produce a single best estimate of the results. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Interpreting effect size.
I have done a paired t-test on a measure of self-esteem before and after a six-week group intervention. There is a significant difference (in the right direction!) between the means using a paired t-test, p=.009. The effect size is .29 if I divide by the standard deviation of the pre-test mean, and .33 if I divide by the pooled standard deviation. Question 1: Which is the correct standard deviation to use? Question 2: Can an effect size of .29 (or .33) be considered clinically significant? Melady Preece, Ph.D. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Interpreting effect size.
On Sun, 15 Jul 2001, Melady Preece wrote: I have done a paired t-test on a measure of self-esteem before and after a six-week group intervention. There is a significant difference (in the right direction!) between the means using a paired t-test, p=.009. The effect size is .29 if I divide by the standard deviation of the pre-test mean, and .33 if I divide by the pooled standard deviation. This implies that the effect size would be larger than .33 if you were to divide by the s.d. of the post-test mean: which is evidently smaller (although probably not significantly so?) than the s.d. of the pre-test mean. But if you have paired pre/post values, you are essentially calculating the difference score (post minus pre), and constructing a t ratio using the s.d. of those differences. This would ordinarily be expected to be noticeably smaller than the s.d. of either pre-test or post-test means. Do you have a reason for not using _that_ s.d.? Question 1: Which is the correct standard deviation to use? Well, you have a choice of four: the s.d. of the pre-test mean, the s.d. of the post-test mean, the s.d. of the difference, and the pooled s.d. (resulting from pooling together the variances pre and post). The pooled s.d. would be (at least possibly) appropriate if you were performing a t-test for independent groups, but I cannot see how it could be thought suitable for paired differences (unless, perhaps, you and I mean different things by pooled s.d.). Of the other three, and in the absence of other considerations which may apply to your situation that you haven't told us about, I'd be inclined to report all three; unless circumstances (among the other considerations) led me to prefer one of them in particular. Using the pre-test s.d. may make it possible for your readers to estimate what differences they might expect to find, based on pre-test information, before getting to the post-test stage; this might be of value to some readers. Similar interpretations can be made of effect sizes calculated from the other s.d.s. I would also want to report the raw difference in means, if the raw scores are (as I assume to be the case) values that are more or less understood (e.g., number of right answers out of the number of items), since it provides something like a common-sensical measure... I'd also be interested (as a potential reader) in some summary information about the difference scores, like what proportion were negative... Question 2: Can an effect size of .29 (or .33) be considered clinically significant? Not enough information for me to tell. (And I just discovered my watch had stopped -- forgot to wind it this morning -- and am in danger of being late for today's next agendum. Good luck!) -- DFB. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
nonlinear regression comparison
Guess what folks, after reviewing my assay data closely, it occured to me that it is relatively nonlinear. So I've been reviewing some notes from a short course on applied nonlinear regression taught by George Milliken. While these may not be available to most of you, he cites a related ref. in Milliken and DeBruin (1978)A procedure to test hypotheses for nonlinear models, Comm.Stat.Theor. Meth.,A(71):65-79. Al = Date: Fri, 13 Jul 2001 11:26:00 -0700 (PDT) From: Alfred Barron [EMAIL PROTECTED] Subject: parallel-line assay I have to compare treatment dose-response assay data. This can be done using regression as in Finney's book (among other references). However, I understand that non-parametric tests for the parallelism of 2 regression lines was coded in SAS in the late 70s. While I have some old proc matrix code described in SAS SUGI 4 (1979) to do it, does anyone have something more current that is online somewhere or that they could share ? My study involves bacterial strains measured under different treatment conditions. thanks, Al Barron Metuchen, NJ __ Do You Yahoo!? Get personalized email addresses from Yahoo! Mail http://personal.mail.yahoo.com/ = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
EdStat: Probabilistic inference in resampling?
John Tukey differentiates data analysis and statistics. The former may or may not employ probability while the latter is based upon probability. Resampling techniques use empirical probability. In the Fisherian sense, probability is based upon infinite hypothetical distributions. But for Rechenbach and von Mises, probability is empirically based on limited cases that generate relative frequency. It seems to me that resampling is qualified as a probabilistic model in Rechenbach and von Mises' view, but not in the Fisherian tradition. My question is: Should resampling be counted as a probabilistic model? What is the nature of inference resulted from bootstrapping? Is it a probabilistic inference? As I recall, Philip Good said that permutuation tests are still subject to the Behrens-Fisher problem (unknown population variance). If resampling is based on empirical probability within the reference set, then why do we care about the population variance? Any help will be greatly appreciated. Chong-ho (Alex) Yu, Ph.D., MCSE, CNE Academic Research Professional/Manager Educational Data Communication, Assessment, Research and Evaluation Farmer 418 Arizona State University Tempe AZ 85287-0611 Email: [EMAIL PROTECTED] URL:http://seamonkey.ed.asu.edu/~alex/ = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
