You might find it enlightening to perform Tukey's "median polish" to this two-way table, and display the residuals in the quasi-3-dimensional plot there demonstrated. (See Tukey, "Exploratory Data Analysis", Addison-Wesley, 1977; or it may be in Mosteller & Tukey, "Regression and Data Analysis"; neither of which is conveniently at hand for me to check.)
For K-W to find a significant effect, as Thom and Rich have pointed out, the median educational level needs to differ across marital status. For the chi-square analysis to be significant, all you need is that the proportions of cases falling into the several educational levels differ across marital status; and as Thom's "simple example" showed, this can happen, and even happen quite strongly, without inducing any differences at all in the _median_ educational levels for each marital status. I'd guess that something like that example, if perhaps a little more complex, is going on in your data. In fact, it sounds as though the data might be quite interesting in these regards. I don't have access to the book you mention; would you be kind enough to post, or send to me privately, the two-way table of frequencies? On Thu, 20 May 2004, G.S.Clarke wrote: > I have asked some students to use SPSS to analyse some data from > Pallant�s book �the SPSS survival manual� and I am working through the > questions myself. I�ve asked the students to examine whether there is > any relationship between educational status (ranging from not much > education � running through to higher degree level) which can be > considered an ordinal variable, and marital status (married, single, > divorced, widowed etc.) � which really seems to be a categorical > variable. > > In doing the examples though, some thoughts/problems occur to me, which > probably have a simple answer, though right now � I can�t see it! > > I initially decided to group educational status, using marital status as > the factor and apply a Kruskal-Wallis test. This test gives a �non > significant� result. Next I decided to apply a Chi-Square analysis > treating both variables as categorical and this time both the pearson�s > and likelihood ratio variants of the test say that there is a highly > significant result. > > OK � two questions. > > First � is there any good reason why kruskal-wallis (which I would > have taken as being the more powerful technique) doesn�t show > significance when the chi-squared tests do (in other words, am I > correct in my assumptions as to which is the more powerful technique). > > Secondly chi-squared provides a �symmetrical� analysis � it says (at > least I think that it does) that having information about one of the > variables provides information about the other variable � and vice > versa. However is Kruskal-Wallis �symmetrical� in this sense. Does > not KW say (had it been significant) that the marital status of the > subjects (the factor) informs us somewhat on their educational status > (the dependent variable). Now logically if this is true then the > educational status should inform us somewhat on the marital status, > however is this also the case �statistically� i.e. will any > significance level generated by the KW using education (dependent) v > marital status (independent) also apply to phrasing the question the > �other way around�? > > I hope that what I�ve written makes some kind of sense. I appreciate > that this might be a �simple� or even �stupid� question (I have these > 'blips' every now and again) but I�d like to get it clear in my own > head before approaching the students with what I think is the �right > answer�. > > Best Regards and Many Thanks > > Graham ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
