On Mon, 11 Nov 2013 10:31:19 -0800, David Epstein wrote: >On Mon, 11 Nov 2013, Michael Britt went: >>I did a survey which asked respondents how satisfied they are in >>their current (romantic) relationship on a 1=10 point scale (where >>10="very satisfied). While there was some variation, not >>surprisingly, the results are strongly negatively skewed. That makes >>sense - most people are probably satisfied with their relationships >>or they would leave the other person > >So you've got yourself the mirror image of one of these: > < http://psycnet.apa.org/psycinfo/1983-09462-001 > > >|The insidious L-shaped distribution. >|Bradley, James V. >|Bulletin of the Psychonomic Society, Vol 20(2), Aug 1982, 85-88. >| >|L-shaped distributions are probably more prevalent than generally >|realized. They are highly conducive to nonrobustness of >|normality-assuming statistical tests, and strongly resist >|transformation to normality. The thinner the tail of the >|distribution, the more unlikely it is that its L-shapedness will be >|detected by inspecting a sample drawn from it. Yet, as the tail of an >|L-shaped distribution becomes increasingly shallow, its skewness and >|kurtosis depart increasingly from their "normal-distribution" values, >|and the distribution becomes increasingly conducive to drastic >|nonrobustness. Worse, a fairly common type of experimental situation >|in psychological research produces shallow-tailed L-shaped >|distributions.
I have to applaud David's ability to locate obscure journal articles. ;-) I remember this article from graduate school because a Michigan math psychologist referred to it in a class when discussing nonparametric analysis (I should note, however, that his teaching was so atrocious that he was limited to teaching graduate students -- I took a class or two with him and can honestly say I did not understand anything he said, indeed, at times *he* did not seem to know what he was saying but that's another story). Bradley wrote a book on nonparametric analysis titled "Distribution Free Statistics" which my former teacher was fond of which one might consult: http://books.google.com/books?id=NB-rnQEACAAJ&dq=%22James+V.+Bradley%22++nonparametric&hl=en&sa=X&ei=B4-BUsdN7uewBL3UgsAP&ved=0CIMBEOgBMBE >If you do a search on statistical techniques for "zero-inflated >continuous [or semicontinuous] data," you might be able to apply them >to your "ten-inflated data." As others have already mentioned in this thread, one could transform the data and I would suggest taking a look at Tukey's "Ladder of Powers" in his "Exploratory Data Analysis" (the "EDA" book). One summary of this is provided on this website: http://onlinestatbook.com/2/transformations/tukey.html However, I think a couple of questions need to be answered before a meaningful analysis is attempted. Consider: (1) Does one really believe that these numbers come from a normal population distribution? Transforming these makes this assumption. It also makes the assumption that the instrument used suffers from a ceiling effect, that is, just as with a multiple choice test that is too easy, the nature of the questions would not allow a normal distribution to appear in the sample -- assuming that they really do come from a normal distribution. If one has the time and inclination, one can view this as a case of the sample data having a truncated normal distribution, a situation that has been studied by statisticians and economists; see: http://econpapers.repec.org/article/ecmemetrp/v_3a41_3ay_3a1973_3ai_3a6_3ap_3a997-1016.htm This paper by Amemiya is rather old may have been superceded by newer techniques. (2) David's suggestion above seems to suggest that alternative distributions should be considered. There is the zero inflated Poisson distribution but, if memory serves, that is for discrete values. You would have to reverse code the scale and other stuff. But there may be other more appropriate distributions that one might consider. I guess this situation reinforces the need for one to know what population distribution one is collecting one's data from. ;-) -Mike Palij New York University [email protected] --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=30046 or send a blank email to leave-30046-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
