Difference between two variables In my data set I have two variables: month (March or April) and wind direction (N, NE, E, SE, S, SW, W, NW). I have to know if there is a difference in wind direction between these months. What kind of test statistic should I use? (I work in R.)
Here's some more information: 
The data is from a study that examines the extent to which background noise in a certain neighborhood depends on the time and certain weather conditions.
The question is: Determine the dominant wind direction in the month 
March and April? Is there a difference in wind direction between these months? 
For the first question, I thought I just needed to look at table(month, wind direction).
The data consist of 2357 measurements of eight variables (month, day, hour, weekday, background noise, wind direction, windspeed and wind angles) that were registered every hour of 50 days in March and April 2010 in the backyard of a particular house. 
http://r.789695.n4.nabble.com/attachment/4700349/0/achtergrondlawaai.txt
 A: Wind direction in essence isn't qualitative. The use of abbreviations and the division of the compass into 8 classes are just conventions used by you or by whoever collected the data. Wind direction underneath that is a quantitative variable, specifically a directional variable and more specifically yet circular data. That gives you some keywords with which to search. Terminology aside, the key defining characteristic that should drive data analysis is the circularity of the scale so that e.g. $0^\circ$ and $360^\circ$ are identical, which must be respected in analysis. 
How to deal with circular data in R (or any other specific software) is off-topic here but there are certainly dedicated packages, and indeed a dedicated book by Arthur Pewsey and friends
Testing for a difference in wind directions between March and April in wind directions strikes me, scientifically, as an artificial problem, because  the conventional divisions of the calendar have no intrinsic meteorological or climatological significance. That's not to say that wind direction might not vary systematically with time of year. 
If you have daily data, then it's best to work with those. It seems that for some reason you have data only for two months; even then, plotting and more generally analysing in terms of time of year (e.g. days since 1 January) is a much better way to think about seasonal variations. 
If your data arise aggregated by month, and that's not reversible, I will still stress that there is only indirect meaning to the question. 
If you wish to persevere with a two-sample test, then various tests associated with the names of Watson, Kuiper and Wheeler-Watson-Mardia (or the same names in different order) are among those available. Strictly, daily measurements of direction are unlikely to be independent, which is not addressed by those tests. 
A: I think that the solution would consist of two steps (unless you need something more complex):


*

*convert these categorical variables into numeric ones (using cut(),
for example);

*perform a Student's t-test for both samples.

