Calculate p trends

The following table shows the averages of the response variables var1, var2, var3 with respect to the explanatory variable divided in quartiles.

                                Explanatory variable (Quartiles)
Response variables  Q1 < 347    347 ≤ Q2 < 416  416 ≤ Q3 < 480  Q4 ≥ 480
Var 1                 4952           4882            4759         4503
Var 2                 2.26           1.76            1.75         1.59
Var 3                 73.42          73.45           73.22        74.01


It has been suggested to add an extra column showing the p trends...I know what is the p value, but I have never heard "p-trend"...what is that? Any idea how to calculate using Matlab?

Thanks

• Maybe the suggester meant "the p value of the trends". In which case you could calculate a Spearman or Kendall rank correlation between your variables and (1, 2, 3, 4). Wouldn't be too informative with only four data points, though. Can you ask whoever suggested the "p-trend" for clarification? Commented Nov 25, 2015 at 10:59
• Who suggested is a reviewer...I can't ask directly..I think he meant that he would like to see whether there is a trend in the quartiles...I already present whether there are significant differences between the quartiles... Commented Nov 25, 2015 at 11:02
• I'd then go with my suggestion of a correlation test that does not presuppose linearity (like Pearson). Or you could indeed ask the editor, who should pass your request for clarification on to the reviewers. Commented Nov 25, 2015 at 11:23
• Hi, I get the 3 p values equal to 0.0833....is that possible? Commented Dec 2, 2015 at 17:54
• That's correct for Var 1 and Var 2 and Spearman's or Kendall's correlation, since both variables decrease strictly monotonically across the four quartiles and Spearman/Kendall only cares about ranks, not hor far your response drops. It should not happen for Var 3, which is not monotonic. I get $p=0.75$ here. Commented Dec 2, 2015 at 18:33

Maybe the suggester meant "the p value of the trends", in which case you could calculate a or rank correlation between your variables and (1, 2, 3, 4). It won't be too informative with only four data points, though.

I would prefer $$\rho$$ or $$\tau$$ over, say, because they do not presuppose linearity.

For instance, here is how you can test Spearman's correlation between the quartiles (1, 2, 3, 4) and your Var1 in R:

> cor.test(1:4,c(4952,4882,4759,4503),method="spearman")

Spearman's rank correlation rho

data:  1:4 and c(4952, 4882, 4759, 4503)
S = 20, p-value = 0.08333
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho
-1


Since your Var1 and Var2 both decrease monotonically and both $$\rho$$ and $$\tau$$ only care about ranks, you will get $$\rho=\tau=-1$$ for both Var1 and Var2, and always $$p=0.0833$$, since the p value only depends on the correlation estimate and the sample size (which is 4 here). Var3 is not monotonic, and I get $$\rho=0.4$$, $$\tau=0.33$$, with $$p=0.75$$ in both cases.