It wouldn't make much sense, because a categorical variable doesn't have order. Presumably what you want to do is compare the means of the different groups, or something like that. If you give more details about your design and the hypothesis you want to test, people here might be able to give more specific recommendations.

Actually Pearson's r downgrades to point biserial correlation coefficient when one variable is dichotomous and the other is continuous. For the interpretation please have a look at the third link I attached. It has also literature references.

Here are other references http://projecteuclid.org/euclid.aoms/1177730103

Correlation Between a Discrete and a Continuous Variable. Point-Biserial Correlation

Robert F. Tate

The Annals of Mathematical Statistics

Vol. 25, No. 3 (Sep., 1954), pp. 603-607

http://core.ecu.edu/psyc/wuenschk/docs30/Biserial.pdf

https://www.andrews.edu/~calkins/math/edrm611/edrm13.htm

http://jalt.org/test/bro_12.htm

Thank you all for your responses and help.

I will check the provided link.

In fact my problem is as Mr Mehmet mentionned,I want to measure association between a discrete variable (dichotomous in particular) and a continous variable using continous scoring measure like pearson correlation , distance correlation and hoeffding measure of dependence.

Because my problem is not limited to linear association ,I was asking if there is a method that can help use continous score association to evaluate association between a discrete variable and a continous variable not limited to linear assocition.

Particularly,I want to do association studies for feature selection in the context of regression/classification

Thank you already ,I will look at the suggestions given.

Here is a more general alternative to correlation

http://stats.stackexchange.com/questions/81659/mutual-information-versus-correlation

Thank you Mr Mehmet,

I am aware of Mutual Information and Maximal Information Coefficient(MIC) score

but actually my problem is one how can use these continuous measures to check association between a Quantitative and Categorical Variable.

Is it valid to make the categorical variable discrete (0 or 1)?

Your contributions are already helpful and welcome