```Date: Mon, 20 Sep 2010 05:20:34 -0700 Reply-To: Bruce Weaver Sender: "SPSSX(r) Discussion" From: Bruce Weaver Subject: Re: Normality Issues In-Reply-To: Content-Type: text/plain; charset=us-ascii DorraJ Oet wrote: > > > Hi, > > There are these issues that are bothering me about normality. As we know, > means comparison of means require normailty. > > Suppose if I am going to use an ANOVA testing, and my scale variable is > not normal even after I do a LN or sqrt, what should I do? > > It will be nice also if there is a way for me to know which normalisation > method to use as in sqrt, LN, or something else based on some Statistics. > > Thank you for any advice. > > Dorraj Oet > > What do the distributions look like? Note that you need to plot the two groups separately. And what are your sample sizes? Here are some comments that might give some insight into why I asked those questions. 1. Remember that the normality assumption applies to the errors, which means it is normality within groups, not normality for all of the groups combined. 2. Independence of observations is the far more important assumption. 3. ANOVA and the t-test are quite robust to violations of normality, especially as the sample size increases. All t-tests have the same basic format: t = (statistic - parameter|H0) / SE of the statistic If the statistic in the numerator has a sampling distribution that is approximately normal, the test will be pretty good. For the independent groups t-test, the statistic is the difference between the two sample means. The central limit theorem tells us that: 1. If the populations are normal, the sampling distribution will be normal, regardless of sample size. 2. If the populations are not normal, the sampling distribution will converge on the normal distribution as sample size increases. (E.g., see the sampling distribution demo here: http://onlinestatbook.com/stat_sim/index.html.) So if your population distributions are similar in shape and your sample sizes are large enough, the t-test is probably better than you think. HTH. ----- -- 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/Complex-sampling-plan-problems-tp2845670p2846528.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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