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Date:         Tue, 28 Nov 2006 19:18:23 -0500
Reply-To:     Statisticsdoc <>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Statisticsdoc <>
Subject:      Re: SPSS symmetric measures of association
Comments: To: Kendall's <fasilag@YAHOO.COM>
Content-Type: text/plain; charset=utf-8 Stephen Brand


This information is very helpful.

Phi applies to the relationship between binary variables. This is not the case in the example you give of a relationship between a yes/no and a trichotmous variable.

Cramer's V is a measure of association between nominal variables with no ordering.

Kendall's tau-b gets to the question of whether cases are concordant or discordant on two variables, which does not seem to apply to your example.

Chi-square would be an appropriate test of the hypothesis that the variables are independent, but does not give you a measure of association. Since chi-square is significant, the variables appear to be related, but you might also want an index of the strength of association.

The correlation coefficient that you want is the rank-biserial coefficient. SPSS, and most other packages, does not directly compute this coefficient, but you can compute the elements that are required by the formula. Rank order the data on the relevant ordinal variables, and assign ranks to the cases. Compute the average rank for the cases that answer "yes" and for those that answer "no" on the relevant binary variable. Then plug the mean ranks into the formula given here:


Stephen Brand ---- Kendall's <fasilag@YAHOO.COM> wrote: > Hi Dominic, > > Thanks for your attention. > > My data are both nominal and ordinal. I'm doing research on public > perception of flooding. To give an example on the responses: one variable is > "yes" and "no" and the second is "no", Minor risk", and "major risk", the > second seems ordinal. The results i've is, the significance level for > Chi-square, Phi, and Cramer's V is 0.000; however Kendall's tau-b and > Speraman correlation have resulted with a negative value at a significance > level between 0.491 and 0.51. It's strange! Does this information help? > Please come back if you need more info. > > Take care, > Kendall's > -- > View this message in context: > Sent from the SPSSX Discussion mailing list archive at

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