# Quantile Regression - Interpretation of a significant quantile

I want to perform a quantile regression on two continuous variables; Y (DV) and X (IV). I want to find out if there is an significant association between Y and X.

When doing this in R like:

fit2 <- rq(Y ~ X,tau=c(.05, .25, .5, .75, .95))

If say, the 75% quantile of X is significant with a p-value < 0.05 but rest is not, can I say that X is significant in total? If none of the quantiles are significant, is X not significant in total?

## 1 Answer

As long as you correct for multiplicity (e.g. Bonferroni-Holm), this is one of many possible ways to test for association. Of course it can capture only linear aspects of the association. A non-significant result can thus be due to low power, lack of linear aspects in the true association or due to conservativeness of the correction for multiplicity.

• Thank you for your answer. In this case, would it be enough to multiply a p-value with the number of quantiles tested, in this case 5 (for correction of multiplicity)? – eXpander Oct 23 '13 at 16:22
• Yes. However, if the effects of $x$ on different quantiles are quite similar, the corresponding test decisions will be strongly related and thus your overall test very conservative. – Michael M Oct 23 '13 at 16:55