[EMAIL PROTECTED] wrote: > Paige, > > The person also sent me the message and gave me permission to send it as > follows: ...snip... > > N1 N2 POWER05 POWER01 > > 10 10 56.2 29.4 > 11 9 55.8 29.0 > 13 7 52.3 26.2 > 15 5 45.0 20.8 > 16 4 39.5 17.2 > 17 3 32.7 13.1 > 18 2 24.6 8.8 > 19 1 15.2 4.6" > > Bill here: > > The data above present one half of a roughly bell shaped frequency > distribution. It is abundantly clear that the reduction of cell sizes > reduces the power of the statistics. This fact is also supported by those > graphs from regression analysis that show the standard error increases as > the values of the predictor are more extreme.
I didn't follow this last sentence. What graphs? What standard error? > All of this suggests to me that when ever there is a serious desire to infer > causation from correlational data, it is reasonable to seek out uniformly > sampled putative causes. This would be ideal, and can be done in designed studies, however many studies are not really "designed", the data is collected and you have to live with whatever sample sizes occur. There was a recent discussion in one of these stat newsgroups about inferring causation from correlation data. I note that people fall on both sides of the argument, however, my position is that without subject matter knowledge, you cannot get to causation, you only have correlation. The problem with using corresponding regressions > with normally distributed causes is that there is not enough information in > the extremes to reveal the polarization effect. We see that data degradation > also occurs in the simplest ANOVA designs when the factors are sampled > normally. This confirms the unity of the general linear model. I have no idea what polarization means, nor do I understand the term "factors are sampled normally". I do not understand "unity of the general linear model". > I understand your point that the normality assumption applies to the > dependent variable, at least when F or t are being calculated. The normality assumption applies to the errors in the dependent variable, not the dependent variable itself. > But if y > values in the extremes of x, have a wider dispersion and hence greater error > when the cell sizes are normally distributed, it would seem that uniformity > in the x factor would be the ideal. When we calculate the difference between > y means, across the levels of x, if the underlying variances are not > identical, then different standard errors should be assumed per mean. This > complicates the ANOVA design and the pooling of error variances. Think about > unequal variances in the t-test. > > It may be true that the linear slope calculated on y from x is legitimately > extrapolated across the ranges of y. But the pattern of deviations about > that slope is not uniform and thus the inferences of the points along y are > not based on uniform parameters. I believe this is a well established fact. > Statistics that require more than theoretically extrapolated slopes, are > thus compromised by unequal cell sizes. Your argument seems to rely on assumptions you make that are not universally true. "The pattern of deviations about that slope is not uniform ..." I have many industrial examples where the pattern of deviations is uniform, regardless of the value of X. > My conclusion from all of this is that where SEM users have hypotheses, they > would best spend the extra time and money uniformly sampling their putative > causes, so to better represent the causal model empirically. Well, now you drag in SEM ... you are really stretching to make a point, aren't you? SEM is often done on data that is collected based upon historical studies, where uniform sampling simply isn't possible. What is your point? > Do you agree? I don't agree, I don't disagree, to put it simply, I don't follow what your argument. -- Paige Miller [EMAIL PROTECTED] http://www.kodak.com "It's nothing until I call it!" -- Bill Klem, NL Umpire "When you get the choice to sit it out or dance, I hope you dance" -- Lee Ann Womack . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
