I'm trying to see if there is a correlation between the height of grass and the height under branches available for grass to grow. I have 227 paired observations:
GrassHeight HeightUnderDebris 0 0 0 0 0 0 8 16 0 0 0 0 0 0 2 2 6 6 0 0 0 0 1 1 0 0 0 0 0 0 8 15 0 0 7 7 15 15
My data is not normally distributed and it fails at the assumption of bivariate normality:
result<-hzTest(data,cov = TRUE,qqplot = FALSE) result<-mardiaTest(data,cov = TRUE,qqplot = FALSE) result<-roystonTest(data,qqplot = FALSE)
Therefore, I need to use a Spearman's rho or Kendall's tau. Firstly, Spearman's rho results in a warning message:
cor.test(GrassHeight, HeightUnderDebris, method="spearman") Spearman's rank correlation rho data: GrassHeight and HeightUnderDebris S = 123090, p-value < 2.2e-16 alternative hypothesis: true rho is not equal to 0 sample estimates: rho 0.9368622 Warning message: In cor.test.default(GrassHeight, HeightUnderDebris, method = "spearman") : Cannot compute exact p-value with ties
So I then decided to use Kendall's tau as it can deal with ties:
cor.test(GrassHeight, HeightUnderDebris, method="kendall") Kendall's rank correlation tau data: GrassHeight and HeightUnderDebris z = 17.202, p-value < 2.2e-16 alternative hypothesis: true tau is not equal to 0 sample estimates: tau 0.858494
Firstly, should I be concerned that my data has many zeros? They are important as they reflect that if there is no space under branches, then there is no space for grass growth hence why the grass height is 0.
Secondly, how would you interpret Kendall's results? Is it right that the two variables are uncorrelated at 0.05 significance level if their correlation coefficient is zero? In this case, tau is 0.858. That is not zero and will be rounded up to 1. Can I say that the two variables are correlated based on this?
Should I rather look at
rpudplus and the function
rpucor, which now uses Kendall’s tau-b to compute the correlation coefficient?
What post-hoc test can I do to find out the nature of the correlation, i.e: as the height between the ground and branch increases, grass height increases?