RE: Mean and Standard Deviation
Title: RE: Mean and Standard Deviation Well, what about the standard normal distribution: N(0,1)? Dale N. Glaser, Ph.D. Pacific Science & Engineering Group 6310 Greenwich Drive; Suite 200 San Diego, CA 92122 Phone: (858) 535-1661 Fax: (858) 535-1665 http://www.pacific-science.com -Original Message- From: Simon, Steve, PhD [mailto:[EMAIL PROTECTED]] Sent: Friday, October 12, 2001 3:27 PM To: 'Edward Dreyer'; [EMAIL PROTECTED] Subject: RE: Mean and Standard Deviation Edward Dreyer writes: >A colleague of mine - not a subscriber to this helpful >list - asked me if it is possible for the standard deviation >to be larger than the mean. If so, under what conditions? > >At first blush I do not think so - but then I believe >I have seen some research results in which standard >deviation was larger than the mean. Well, if the mean is negative, then it is indeed very possible for the standard deviation to be larger. I suspect that you were considering the special case where the variable is non-negative. Then it is still possible for the standard deviation to be larger than the mean. In this special case, it serves as evidence of a highly right skewed distribution. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. http://www.childrens-mercy.org/stats
Re: Mean and Standard Deviation
In article <[EMAIL PROTECTED]>, Edward Dreyer <[EMAIL PROTECTED]> wrote: > A colleague of mine - not a subscriber to this helpful list - asked me if > it is possible for the standard deviation > to be larger than the mean. If so, under what conditions? > Easily. Any highly skewed distribution will produce this. For example enter 1,1,1,1,1 into a stats program and look at the descriptive statistics. Ken = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Mean and Standard Deviation
At 04:32 PM 10/12/01 -0500, you wrote: >A colleague of mine - not a subscriber to this helpful list - asked me if >it is possible for the standard deviation >to be larger than the mean. If so, under what conditions? what about z scores??? mean = 0 and sd = 1 >At first blush I do not think so - but then I believe I have seen >some research results in which standard deviation was larger than the mean. > >Any help will be greatly appreciated.. >cheersECD > >___ > >Edward C. Dreyer >Political Science >The University of Tulsa > > > > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= > == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
RE: Mean and Standard Deviation
Title: RE: Mean and Standard Deviation Edward Dreyer writes: >A colleague of mine - not a subscriber to this helpful >list - asked me if it is possible for the standard deviation >to be larger than the mean. If so, under what conditions? > >At first blush I do not think so - but then I believe >I have seen some research results in which standard >deviation was larger than the mean. Well, if the mean is negative, then it is indeed very possible for the standard deviation to be larger. I suspect that you were considering the special case where the variable is non-negative. Then it is still possible for the standard deviation to be larger than the mean. In this special case, it serves as evidence of a highly right skewed distribution. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. http://www.childrens-mercy.org/stats
Bimodal distribution
Is there any mathematical analysis to find how much the two peaks stand out from the other data? Is there any formulas to find the variance/deviation/etc that's similar to the unimodal distribution case? Thanks a lot. Cheers, Desmond = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Final Exam story
I had promised a colleague a story that illustrates probability and now I forgot how to solve it formally. The story is about six students who go off on a trip and get drunk the weekend before their statistics final. They return a few days late and beg for a second chance to take the final exam. They tell a story about how they were caught in a storm and their car blew a tire and ended up in a ditch and they needed brief hospitalization etc. The instructor seems very easy going about the whole thing and tells them to report the next day for an exam with only one question. If they all get it right they all pass. They were seated at corners of the room and could not communicate. The one question was, "Which tire?" I remember that the liklihood of all four pickng the same tire was quite small, but I forgot how to calculate it explicitly (except for listing all the possible outcomes). I would particularly appreciate a general solution (N students, M tires). Thanks. Stephen Dubin VMD http://www.hometown.aol.com/dubinse [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Mean and Standard Deviation
A colleague of mine - not a subscriber to this helpful list - asked me if it is possible for the standard deviation to be larger than the mean. If so, under what conditions? At first blush I do not think so - but then I believe I have seen some research results in which standard deviation was larger than the mean. Any help will be greatly appreciated.. cheersECD ___ Edward C. Dreyer Political Science The University of Tulsa = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Are parametric assumptions importat ?
At 01:44 PM 10/12/01 -0400, Lise DeShea wrote: >I tell my students that the ANOVA is not robust to violation of the equal >variances assumption, but that it's a stupid statistic anyway. All it can >say is either, "These means are equal," or "There's a difference somewhere >among these means, but I can't tell you where it is." i don't see that this is anymore stupid that many other null hypothesis tests we do ... if you want to think " stupid" ... then think that it is stupid to think that the null can REALLY be exactly true ... so, the notion of doing a TEST to see if you retain or reject ... is rather stupid TOO since, we know that the null is NOT exactly true ... before we even do the test _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
RE: Are parametric assumptions importat ?
Lise advised "I tell my students that the ANOVA is not robust to violation of the equal variances assumption, but that it's a stupid statistic anyway. All it can say is either, "These means are equal," or "There's a difference somewhere among these means, but I can't tell you where it is." I tell them to move along to a good MCP and don't worry about the ANOVA. Most MCP's don't require a significant F anyway. And if you have unequal n's, use Games-Howell's MCP to find where the differences are." Excellent advice, copied to my students (so they don't hear it only from me). Now if we could only get our colleagues to listen! ;-) + Karl L. Wuensch, Department of Psychology, East Carolina University, Greenville NC 27858-4353 Voice: 252-328-4102 Fax: 252-328-6283 [EMAIL PROTECTED] http://core.ecu.edu/psyc/wuenschk/klw.htm
Re: Are parametric assumptions importat ?
Re robustness of the between-subjects ANOVA, I obtained permission from Dr. Rand Wilcox to copy three pages from his book, "New Statistical Procedures for the Social Sciences," and place them on a webpage for my students. He cites research showing that with four groups of 50 observations each and population standard deviations of 4, 1, 1, and 1, the empirical Type I error rate was .088, which is beyond Bradley's liberal limits on sampling variability [.025 to .075]. You can read this excerpt at www.uky.edu/~ldesh2/stats.htm -- look for the link to "Handout on ANOVA, Sept. 19-20, 2001." Error rates are much worse when sample sizes are unequal and the smaller groups are paired with the larger sigma -- up to an empirical alpha of .309 when six groups, ranging in size from 6 to 25, have sigmas of 4, 1, 1, 1, 1, 1. The independent-samples t-test has an inoculation against unequal variances -- make sure you have equal n's of at least 15 per group, and it doesn't matter much what your variances are (Ramsey, 1980, I think). But the ANOVA doesn't have an inoculation. I tell my students that the ANOVA is not robust to violation of the equal variances assumption, but that it's a stupid statistic anyway. All it can say is either, "These means are equal," or "There's a difference somewhere among these means, but I can't tell you where it is." I tell them to move along to a good MCP and don't worry about the ANOVA. Most MCP's don't require a significant F anyway. And if you have unequal n's, use Games-Howell's MCP to find where the differences are. Cheers. Lise ~~~ Lise DeShea, Ph.D. Assistant Professor Educational and Counseling Psychology Department University of Kentucky 245 Dickey Hall Lexington KY 40506 Email: [EMAIL PROTECTED] Phone: (859) 257-9884 Website for students: www.uky.edu/~ldesh2/stats.htm
Re: Are parametric assumptions importat ?
At 12:59 PM 10/12/01 -0300, you wrote: >While consulting people from depts of statistics about this, a few of them >were arguing that these assumption testing are just a "legend" and that >there is no problem in not respecting them ! note: you should NOT respect any stat expert who says that there is no problem ... and not to worry about the so called "classic" assumptions all they are doing is making their consultation with you EASIER for them! every test you might want to do has 1 or more assumptions about either how samples were taken and/or parameters (and other things) about the population in some cases, violations of one or more of these make little difference in the "validity" of the tests (simulation studies can verify this) ... but, in other cases, violations of one or more can lead to serious consequences (ie, yielding a much larger type I error rate for example that you thought you were working with) ... there is no easy way to make some blanket statement as to what assumptions are important and which are not because ... this depends on a specific test (or family of similar tests) usually, for a particular test ... "good" texts will enumerate the assumptions that are made AND, will give you some mini capsule of the impact of violations TO those assumptions _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Are parametric assumptions importat ?
Voltolini wrote: > > Hi, I am Biologist preparing a class on experiments in ecology including > a short and simple text about how to use and to choose the most commom > statistical tests (chi-square, t tests, ANOVA, correlation and regression). > > I am planning to include the idea that testing the assumptions for > parametric tests (normality and homocedasticity) is very important > to decide between a parametric (e.g., ANOVA) or the non parametric > test (e. g. Kruskal-Wallis). I am using the Shapiro-Wilk and the Levene > test for the assumption testing but.. It's not that simple. Some points: (1) normality is rarely important, provided the sample sizes are largish. The larger the less important. (2) The Shapiro-Wilk test is far too sensitive with large samples and not sensitive enough for small samples. This is not the fault of Shapiro and Wilk, it's a flaw in the idea of testing for normality. The question that such a test answers is "is there enough evidence to conclude that population is even slightly non-normal?" whereas what we *ought* to be asking is "do we have reason to believe that the population is approximately normal?" Levene's test has the same problem, as fairly severe heteroscedasticity can be worked around with a conservative assumption of degrees of freedom - which is essentially costless if the samples are large. In each case, the criterion of "detectability at p=0.05" simply does not coincide withthe criterion "far enough off assumption to matter" except sometimes by chance. (3) Approximate symmetry is usually important to the *relevance* of mean-based testing, no matter how big the sample size is. Unless the sum of the data (or of population elements) is of primary importance, or unless the distribution is symmetirc (so that almost all measures of location coincide) you should not assume that the mean is a good measure of location. The median need not be either! (4) Most nonparametric tests make assumptions too. The rank-sum test assumes symmetry; the Wilcoxon-Mann-Whitney and Kruskal-Wallis tersts are usually taken to assume a pure shift alternative (which is actually rather unlikely for an asymmetric distribution.) In fact symmetry will do instead; Potthoff has shown that the WMW is a test for the median if distributions are symmetric. If there exists a transformation that renders the populations equally-distributed or symmetric (eg, lognormal family) they will work, too. In the absence of some such assumption strange things can happen. I have shown (preprint available on request) that the WMW test is intransitive for "most" Behrens-Fisher families (that is, it can consistently indicate X>Y>Z>X with p -> 1 as n -> infinity), although the intransitivity is not pronounced for most realistic distributions and sample sizes. Note - a Behrens-Fisher family is one differing both by location and by spread but not by shape. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Are parametric assumptions importat ?
Hi, I am Biologist preparing a class on experiments in ecology including a short and simple text about how to use and to choose the most commom statistical tests (chi-square, t tests, ANOVA, correlation and regression). I am planning to include the idea that testing the assumptions for parametric tests (normality and homocedasticity) is very important to decide between a parametric (e.g., ANOVA) or the non parametric test (e. g. Kruskal-Wallis). I am using the Shapiro-Wilk and the Levene test for the assumption testing but.. While consulting people from depts of statistics about this, a few of them were arguing that these assumption testing are just a "legend" and that there is no problem in not respecting them ! It seems to me that normal distribution is not very important for some tests like t tests and ANOVA but anyway. What is correct ??? What I will teach to my students ??? To test or not to test the assumptions of parametric tests: thats the question. Thanks for any help Voltolini _ Prof. J. C. Voltolini Grupo de Estudos em Ecologia de Mamiferos - ECOMAM Universidade de Taubate - Depto. Biologia Praca Marcellino Monteiro 63, Bom Conselho, Taubate, SP - BRASIL. 12030-010 TEL: 0XX12-2254165 (lab.), 2254277 (depto.) FAX: 0XX12-2322947 E-Mail: [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
