```Date: Tue, 8 Mar 2011 04:30:23 -0800 Reply-To: Bruce Weaver Sender: "SPSSX(r) Discussion" From: Bruce Weaver Subject: Re: T-test or nonparametric test? Confused. In-Reply-To: <9524a1b9f0d18b9604d83457d507afc5.squirrel@webmail.uci.edu> Content-Type: text/plain; charset=UTF-8 Several points here. 1. All t-tests have the form t = (statistic - parameter|H0) / SE(statistic). The test will be pretty good if the sampling distribution of the statistic in the numerator is approximately normal. As the sample size increases, the sampling distribution of the statistic converges on a normal distribution (almost regardless of population shape). 2. I said "approximately" in point 1, because as George Box said, normal distributions (and straight lines) do not exist in nature. 3. The t-test would be an exact test only if the two populations were perfectly normal, and the two population variances exactly equal. Since neither of those conditions will ever hold, the t-test on real data is an approximate test. Therefore, the real question becomes whether the approximation is good enough to be "useful". (I refer to another George Box quote here: "All models are wrong. Some are useful.") 4. Normality (which never holds) applies to the POPULATIONS from which you sampled. 5. If you are going to assess normality via plots, you can't do it by looking at one plot--you need two plots, one for each group. (Suppose the two populations were perfectly normal, but with different means. In this case, you would most likely see a bimodal distribution if you made one plot.) 6. The t-test is quite robust to non-normality of populations. If your library has it, take a look at Figure 12.2 in Statistical Methods in Education and Psychology , 3rd Edition (by Glass & Hopkins). It shows that the t-test performs quite well under the following circumstances: R/R – both populations rectangular; n1 = n2 = 5 S/S – both populations skewed; n1 = n2 = 15 N/S – one population normal, one skewed; n1 = n2 = 15 R/S – one population rectangular, one skewed; n1 = n2 = 15 L/L – both populations leptokurtic (i.e., tails thicker than the normal distribution); n1 = 5, n2 = 15 ES/ES – both populations extremely skewed in same direction; n1 = 5, n2 = 15 M/M – both populations multimodal; n1 = 5, n2 = 15 SP/SP – both populations spiked; n1 = 5, n2 = 15 T/T – both populations triangular; n1 = 5, n2 = 15 And for dichotomous populations with: P = .5, Q = .5, n = 11 P = .6, Q = .4, n = 11 P = .75, Q = .25, n = 11 HTH. Bridgette Portman wrote: > > Hi everyone, > > This is a rather elementary statistics question and I feel kind of stupid > asking it. But I've managed to thoroughly confuse myself. I hope someone > can help me out. > > I've collected survey data from 260 respondents. As I'm analyzing > demographic information, I have noticed that the distribution of ages in > my sample is not normal. In fact, it is bimodal, with peaks around 20 and > 60, and a trough around 40. This was due to my sampling method, not to any > intrinsic pattern in the population I was sampling from. I want to be able > to compare ages between various groups, such as men and women, in my > sample. But can I use a t-test, given the abnormal distribution? Should I > use a nonparametric test like Mann-Whitney U instead? > > The reason I'm confused is that the bimodality is in my sample alone, do > to my sampling technique. The ages in the population as a whole, I'm sure, > has an underlying normal distribution. I am studying political activists, > and in order to get at them, I sampled from a) college student political > clubs, and b) actual political parties. The college kids tended to be > around 20, while the party people were 50+. I know one alternative would > be to just recode age into something like "below 40" and "above 40" but > I'd rather avoid doing that if I can. > > Can anyone offer advice? > > Thanks, > Bridgette > > ===================== > To manage your subscription to SPSSX-L, send a message to > LISTSERV@LISTSERV.UGA.EDU (not to SPSSX-L), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSX-L > For a list of commands to manage subscriptions, send the command > INFO REFCARD > ----- -- Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." NOTE: My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Anova-SS1-vSS3-using-v-17-0-tp3412630p3413863.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to LISTSERV@LISTSERV.UGA.EDU (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ```

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