R help - Oct 2008 - correlation between a discrete variable and a continuous variable

What test would you use to determine if a correlation exists between a
discrete variable and a continuous variable?

For example, I have a rating for stream water quality (excellent,
good, fair, poor) and a corresponding nitrogen concentration. I want
to see if there is a correlation between the water quality rating and
the concentration of nitrogen in the stream.

Help?

Since water quality is ordered, you could use cor.test with method of kendall or
spearman.  This will basically give a test of whether the rank based correlation
is significantly different from 0.  Often more interesting information can come
from the data if you do some more work.  Start by graphing your data to see what
is there and if anything stands out.  Then decide what you really want to learn
from the data to decide what other tests to do.  If you want to predict nitrogen
given water quality, then you can use lm or aov (or other related methods), if
you want to predict quality given nitrogen, then possibilities include
proportional odds logistic regression (polr in MASS, lrm in Design) or recursive
partitioning (rpart and other packages).

Hope this helps,

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of kdebusk
> Sent: Thursday, October 16, 2008 6:54 AM
> To: r-help at r-project.org
> Subject: [R] correlation between a discrete variable and a continuous
> variable
>
> What test would you use to determine if a correlation exists between a
> discrete variable and a continuous variable?
>
> For example, I have a rating for stream water quality (excellent,
> good, fair, poor) and a corresponding nitrogen concentration. I want
> to see if there is a correlation between the water quality rating and
> the concentration of nitrogen in the stream.
>
> Help?
>
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