Thanks to Lise, Dennis and Thom for the responses To clarify, the z-scores were calculated for each level of each within-groups factor. Thus, only the two levels of the between-group factor had different means.
Dennis Roberts may be right in suggesting that I won't get rid of anything. I'm a statistical novice, so I'll explain in a little more detail. I'm measuring sentence durations to follow up studies on the seemingly trivial fact that non-native speakers tend to speak more slowly than native speakers. I'm trying to find the psycholinguistic locus (or loci) of their slowness. The hypothesis I'm testing is that that locus is syntactical processing. The between-groups factor is 'group' (native vs. non-native). The within-group factor is 'syntactic complexity' of the sentences that the subjects repeated (3 levels). In an ANOVA on the raw data, the interaction was significant, and I found that the mean group difference was not significant for the simple sentences, but for the complex sentences. Thus, I might infer that increased syntactic processing load slows non-native talkers down. However, syntactic complexity is confounded with sentence length, because the more complex the syntax of a sentence gets (i.e., the more words there are), the longer it inevitably gets. The group differences are larger for complex sentences (say, 2200 vs. 2500 ms) than simple sentences (say 500 vs. 550 ms). I'm wondering whether the ANOVA went: "Hey look, a delta of 300 is larger than a delta of 50; I'm gonna output a significant interaction". Will the ANOVA recognize that the delta of 50 is based smaller values than the delta of 300? This is why I thought of z-scores. But maybe they won't make a difference? After all, the t- and p-values for simple effects of group are actually very comparable in the raw data ANOVA and in the z-score ANOVA. I just thought that if the results were based on z-scores, I could more justly attribute the different effect of group in simple vs. complex sentences to the different syntactical processing load. At any rate, there is one (other) benefit of using z-scores. It is actually a 4-way ANOVA.I only outlined the problem above pretending it was a 2-way for simplicity. There are 3 within-groups factors and one between (I'll never do 4-way again!). Doing the ANOVA on z-scores tidy up the analysis a lot, because the 3 within-group factors are neutralized. I love that because I'm only interested in the between group factor and the interactions that involve the between group-factor. In the z-score ANOVA I get rid of some uninteresting 3-way interactions compared to the raw data ANOVA. However, I'm wondering whether I'm playing tricks with chance because I neutralized 3 main factors. Or whether the interactions in the raw data analysis were spurious because of the necessarily very different means and SDs of the levels of within-group factor. The results of the z-score ANOVA makes a lot of sense, though. There is a main effect of group and a few interactions. That was a lot of confusing details. Any opinions on what would be appropriate to do? Anders > > If all scores are centered on the grand mean, the ANOVA will be > unaffected. But I think if the data are converted to z's by > groups, then > each group would have equal variance. > > At 09:41 AM 6/2/2004, you wrote: > >Since zs are a linear transformation of the raw data, I > don't see how > >converting data to z will get rid of anything ... > > > >At 07:29 PM 6/1/2004, you wrote: > > > >>Hello, I just joined this list - hope somebody can help me > with this > >>question. > >>I have a 2-way anova with one within- and one > between-groups measure. > >>There is a confound between the 3 levels of the > within-groups measure > >>that I can get rid of by converting to z-scores. However, If I > >>standardized the three levels of the within-groups measure, > the mean for > >>all levels will, of course, be 0 in all 3 cases. This means > that the main > >>effect of this factor is neutralized. That is actually a good thing > >>because I am only interested in the between-groups factor > and in the > >>interaction. My question is whether it is legitimate to do this. > > > . . ================================================================ This list will soon be replaced by the new list EDSTAT-L at Penn State. Please subscribe to the new list using the web interface at http://lists.psu.edu/archives/edstat-l.html. ================================================================
