I am testing the association between gender and morality (measured in 0=not moral at all, 1, 2, 3, 4, 5=extremely moral), and i was thinking of using Spearman's rho because of non normality, but after looking it up online i see that there is no agreement on this, some say yes some say it is not appropriate.
My other variables that again i have to test the association with morality are religion, age, ethnicity, and parenting style.
Hi Calli. Assuming your gender variable has 2 levels, your situation matches almost exactly the example Dave Howell uses in his notes on "Chi-square with Ordinal Data" (see the link below). The only difference is that his ordinal variable has 5 levels, whereas yours has 7. And I see that you listed SPSS as one of the topics, so you'll be able to easily use the approach Howell shows. HTH.
p.s. - If you are uncomfortable with using a statistic based on Pearson's r, notice that Howell cites Agresti (1996) in support of this approach. And Agresti is pretty universally recognized as a leading expert on analysis of categorical data.
https://www.uvm.edu/~dhowell/StatPages/More_Stuff/OrdinalChisq/OrdinalChiSq.html
Even sites that are specialized in statistical selection and i subscribed do not have a clear answer regarding which test is appropriate for associations of ordinal and nominal variables.
Maybe the point-biserial correlation might help (it is intended for dichotomous variables which your could use sex for; the nominal nature is disregarded in that context).
Greetings, David
https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient
David my data violate the assumption of normality, so i cannot use point-biserial.
So sex is not balanced or your moral score is not normal? In the latter case you could (log) transform it...
Hi Calli. Assuming your gender variable has 2 levels, your situation matches almost exactly the example Dave Howell uses in his notes on "Chi-square with Ordinal Data" (see the link below). The only difference is that his ordinal variable has 5 levels, whereas yours has 7. And I see that you listed SPSS as one of the topics, so you'll be able to easily use the approach Howell shows. HTH.
p.s. - If you are uncomfortable with using a statistic based on Pearson's r, notice that Howell cites Agresti (1996) in support of this approach. And Agresti is pretty universally recognized as a leading expert on analysis of categorical data.
https://www.uvm.edu/~dhowell/StatPages/More_Stuff/OrdinalChisq/OrdinalChiSq.html
Dear Calli
Please, read the file in the following link ( page 4 ), I hope to be helpful for you.
http://www.math.yorku.ca/Who/Faculty/Ng/adms3352/association.PDF
Good Luck
Hello Calli,
You could use the coefficient of concordance, which makes no distributional shape assumptions, and (like phi, or Cramer's V) may be derived from the chi-square statistic from a two-way contingency table (in your case a 2 x 7 table):
C = square root[ chi-square / (N + chi-square) ]
Spearman rho could also work, but do understand that rho is simply the Pearson correlation of two sets of rank scores (and you'd obviously have lots of tied rank values, given the limited number of categories for each variable).
Good luck with your work.
I'm with Bruce Weaver's suggestion, but I'm a little worried about what SPSS does when there is more than one nominal category.
When one variable is ordinal and one variable is nominal, the test is called Cochran–Armitage test. ("extended" if more than two nominal categories).
When both variables are ordinal, this is called the linear-by-linear test. (Agresti's term).
These are obviously two different tests.
Except that when there are two nominal categories, they are equivalent.
From the SPSS ouput shown, it looks like SPSS assumes that both variables are ordinal, and goes with the linear-by-linear test. If this is true, that will not be the correct test when there are more than 2 nominal categories.
Below are some examples using R for these two tests. Note that there is different coding for the Cochran-Armitage (one ordinal, one nominal) and linear-by-linear (both ordinal) cases.
http://rcompanion.org/handbook/H_09.html
Is there an explicit Cochran–Armitage test option in SPSS?
Salvatore, re the Cohran-Armitage test in SPSS, see the Technote linked below.
Cheers, Bruce
http://www-01.ibm.com/support/docview.wss?uid=swg21480127
As one final note, in this case I would probably use Kruskal-Wallis, treating each ordinal measurements as a DV, and the nominal groups as the IVs individually. Simple, familiar to readers, only minorly controversial, and good options for post-hoc.
Hi Salvatore. I am not a fan of using rank-based tests (e.g., Wilcoxon-Mann-Whitney, Kruskal-Wallis) when one has a relatively small number of ordered categories. In that case, there must be a large number of ties. Yes, I know there are methods to correct for ties. But I think that rank-based tests work best when the proportion of ties is relatively low.
Cheers,
Bruce
Agreed, Bruce. Usually I make a stronger statement of "controversial" for using traditional nonparametric tests for Likert data, for a few reasons.*
In general, _I_ think using nonparametric tests is not a bad option for Likert data, tho I would advise other methods as preferable.
I think one problem is that people get afraid of things like ordinal regression, appropriate permutation tests in R, Cochran-Armitage test. It doesn't help that some software seem to make some of these things difficult.
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* I really do end up writing the same things on this site over and over again. It's obvious that we don't do a good job teaching people how to handle Likert data.
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