I have conducted Spearman's Rho tests with two ordinal variables (one with 4 possible answers and the other with 6). I have obtained a statistically significant correlation between the two. My question is, how can I graphically (or some other way) determine which answer of each correlate together - as a scatterplot would not work with my data (since it is not scale).
Let's create some toy data in R:
> set.seed(1) > nn <- 60 > xx <- floor(4*runif(nn))+1 > yy <- pmin(6,pmax(1,xx+rnorm(nn,0,3))) > > Q1 <- ordered(letters[xx],levels=letters[1:4]) > Q2 <- ordered(LETTERS[yy],levels=LETTERS[1:6])
Here is a Spearman's rho correlation test:
> cor.test(as.numeric(Q1),as.numeric(Q2),method="spearman") Spearman's rank correlation rho data: as.numeric(Q1) and as.numeric(Q2) S = 24468, p-value = 0.01264 alternative hypothesis: true rho is not equal to 0 sample estimates: rho 0.3201582 Warnmeldung: In cor.test.default(as.numeric(Q1), as.numeric(Q2), method = "spearman") : Kann exakten p-Wert bei Bindungen nicht berechnen
Now, one way of understanding this would be a simple incidence table:
> table(Q1,Q2) Q2 Q1 A B C D E F a 10 1 1 0 1 0 b 6 2 1 1 2 5 c 4 3 3 4 1 1 d 3 2 2 1 4 2
Alternatively, you can certainly plot your data. Simply transform them to the underlying integers and add a little jittering:
> delta <- 0.2 > plot(as.numeric(Q1)+runif(nn,-delta,delta),as.numeric(Q2)+runif(nn,-delta,delta),pch=19,xlab="Q1",ylab="Q2",xaxt="n",yaxt="n") > axis(1,1:4,levels(Q1)) > axis(2,1:6,levels(Q2),las=2)
Alternatively, create a sunflowerplot:
sunflowerplot(Q1,Q2,xaxt="n",yaxt="n") axis(1,1:4,levels(Q1)) axis(2,1:6,levels(Q2),las=2)
(To be honest, I'm not too keen on the default sunflowerplot, but you can customize the colors and the widths of the segments rather well, see
Sometimes people overlook the convenient way in which a Chi-square procedure can answer questions like this. Specifically, each of your 24 cells' Chi-square residuals -- or better yet, standardized residuals -- will tell to what extent the count of observations in that cell is disproportionate, given the entire bivariate distribution. In SPSS:
cross Q1 by Q2 / stat chi /cells count sresid.
Standardized residuals beyond +/- 2 are typically the ones that signal notably disproportionate counts (although this is only a rule of thumb). You'll probably be most interested in values >2 since you want to know which pairs of answers tend to co-occur.