SPSS symmetric measures of association

[Kendall's]

Hi friends,

I was looking for measure of associations between variables in my data. The coeffcients I'm using are Pearson chi, Phi, Cramer's V, Kendall's tau-b and Spearman correlation. Most of the time when there's a relation all the above coefficients give similar results with a signifcance level less than the assumed (say p = 0.05). In some instances while Pearson's chi, Phi and Cramer's V indicating a relation give a significance level less than say 0.05 but the values of Kendall's and Speraman r is greater than 0.05, disapproving the relation. I wanted you guys to advice me why and which to take.

[Dominic Lusinchi]

You don't tell us anything about the variables you are using. Are they
nominal or ordinal?

Pearson's chi-squared, Phi, and Cramer's V are applicable to tables with
nominal categories.

Kendall's tau and Spearman's correlation coefficient are applicable to
tables with ordered categories.

Dominic Lusinchi
Statistician
Far West Research
Statistical Consulting
San Francisco, California
415-664-3032
www.farwestresearch.com
-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Kendall's
Sent: Tuesday, November 28, 2006 9:09 AM
To: [hidden email]
Subject: SPSS symmetric measures of association

Hi friends,

I was looking for measure of associations between variables in my data. The
coeffcients I'm using are Pearson chi, Phi, Cramer's V, Kendall's tau-b and
Spearman correlation. Most of the time when there's a relation all the above
coefficients give similar results with a signifcance level less than the
assumed (say p = 0.05). In some instances while Pearson's chi, Phi and
Cramer's V indicating a relation give a significance level less than say
0.05 but the values of Kendall's and Speraman r is greater than 0.05,
disapproving the relation. I wanted you guys to advice me why and which to
take.
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[statisticsdoc]

www.statisticsdoc.com
Stephen Brand

The critical issue here is the measurement level of your variables.  Are they both nominal?  Ordinal?  Is one of them nominal and the other ordinal?   The test statistics themselves lack meaning without knowing the type of measures you are looking at.  Illustratively, if your are you interested in the strength of the association between ordinal variables, look at Phi.  If you are interested in the strength of the association between ordinal variables, look at the Spearman rank order correlation.

HTH,

Stephen Brand

---- Kendall's <[hidden email]> wrote:

> Hi friends,
>
> I was looking for measure of associations between variables in my data. The
> coeffcients I'm using are Pearson chi, Phi, Cramer's V, Kendall's tau-b and
> Spearman correlation. Most of the time when there's a relation all the above
> coefficients give similar results with a signifcance level less than the
> assumed (say p = 0.05). In some instances while Pearson's chi, Phi and
> Cramer's V indicating a relation give a significance level less than say
> 0.05 but the values of Kendall's and Speraman r is greater than 0.05,
> disapproving the relation. I wanted you guys to advice me why and which to
> take.
> --
> View this message in context: http://www.nabble.com/SPSS-symmetric-measures-of-association-tf2719656.html#a7583238
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.

--
For personalized and experienced consulting in statistics and research design, visit www.statisticsdoc.com

[Kendall's]

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

[statisticsdoc]

www.statisticsdoc.com
Stephen Brand

Kendall's,

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.

The correlation coefficient that you want is the rank-biserial coefficient.  The formula for this statistic is given at the following link.  SPSS, and most other packages, do not compute the rank-biserial directly, but you can obtain the elements of the formula by ranking the data on the relevant ordinal variable and then compute the mean rank for cases that answer "yes' and "no".

http://www.andrews.edu/~calkins/math/edrm611/edrm13.htm#RANK

HTH,

Stephen Brand

---- Kendall's <[hidden email]> 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: http://www.nabble.com/SPSS-symmetric-measures-of-association-tf2719656.html#a7585939
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.

--
For personalized and experienced consulting in statistics and research design, visit www.statisticsdoc.com

[statisticsdoc]

www.statisticsdoc.com
Stephen Brand

Kendall's,

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:

http://www.andrews.edu/~calkins/math/edrm611/edrm13.htm#RANK

HTH,

Stephen Brand
---- Kendall's <[hidden email]> 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: http://www.nabble.com/SPSS-symmetric-measures-of-association-tf2719656.html#a7585939
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.

--
For personalized and experienced consulting in statistics and research design, visit www.statisticsdoc.com

[bgreen]

If your sample sizes are not large you could consider an exact test. I
have been looking at linear by linear association tests and there is also
a special case the Cochran Armitage test which may be relevant. Agresti's
books on categorical data analysis discuss these and the other statistical
tests that you mention, as well as the  relationship between them.

Bob

> 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:
> http://www.nabble.com/SPSS-symmetric-measures-of-association-tf2719656.html#a7585939
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>