How to split a numeric variable into a binary low-high variable I have measured frequency of a certain behavior on 15 individuals. 
I would like to create two groups based on the amount of this behaviour that was observed (i.e., a group exhibiting high levels of the behaviour and a group exhibiting low levels of the behaviour).
I want to see whether this new binary variable predicts a dependent variable that I have measured.
 A: Based on the post and the comments to date:  If you want to create two groups based on a single variable, you are faced with an arbitrary choice.  You can say that below x is "low" and at or above x is "high" but there is not going to be any statistical procedure (certainly not a significance test) that can make that determination for you.  In this situation some people would draw a histogram and look for what seems like a "natural" dividing point, which might simply mean one that would be convincing or defensible to one's particular audience.  Alternatively, one might divide so as to create two equal-sized groups.  There is no right or wrong answer.  But I question the need for dichotomization, for I suspect that whatever methods you plan to apply with two groups could be replaced by other methods at least as informative that preserve the original variable.  For example, rather than dichotomizing and running a T-test using a dependent variable, why not correlate your independent and dependent variables, or create a scatterplot to show their relationship.
A: Assuming you have a single predictor variable that represents frequency of behaviour, I would make the following points
Should you split a numeric variable into high-low groups
I quote the following from one of my blog posts on creating clusters, where I use the term "median split" as a prototypical example of converting a numeric variable into a binary high-low variable.

Many researchers have heard the advice
  to not form median splits (see,
  Howell
  for a discussion), or other kinds of
  binary splits for that matter. The
  same arguments also tend to apply with
  other forms of abrupt grouping into a
  small number of factors. 
Some
  arguments FOR running median splits
  are:  1) it allows you to do an ANOVA
  or t-test and compare group means;  2)
  group differences are easier to
  communicate to a lay audience;  3) it
  reflects the important distinction in
  the underlying continuous variable.
Some arguments AGAINST running median
  splits are: 1) you can always find an
  equivalent analysis that respects the
  continuous nature of the variable
  (e.g., regression); 2) when creating
  median splits, you lose a lot of
  information; 3) the cut-off tends to
  be relatively arbitrary and it varies
  between samples; 4) the resulting
  model based on a median split does not
  reflect the underlying nature of the
  variable; 5) in most cases a binary
  split will have less statistical
  power; 6) if the purpose is to
  communicate to a scientific audience,
  respecting the continuous nature of
  the variable is a necessary
  complexity.
From the above you can see that there
  are generally more reasons in favour
  of maintaining the continuous version
  of the variable. The two occasions
  where splits are tolerable are where
  it makes it easy to communicate
  findings to a lay audience and where
  the underlying effect of interest
  occurs in a stepwise fashion. In the
  case of the latter, the presence of a
  stepwise effect can be tested
  empirically; a quick look at a scatter
  plot should give some sense if there
  is a point where the effect changes
  dramatically. Likewise decisions based
  on test scores are often based on
  pass-fail kinds of categories, and
  there is often a concrete desire to
  draw inferences about these specific
  groups.

Also, check out page 128 of Making Friends with Your Data for further discussion.
In summary, my advice would be to run a correlation or a regression predicting your outcome variable from the continuous version of your predictor. You may or may not want to perform an order preserving transformation of your predictor depending on its distribution.
Creating two groups based on numeric variable
Putting aside the issues raised above, if you decide that you still want to split your predictor variable into high-low groups, the following are some options


*

*Use Statistical properties of your sample

*

*Median split

*Above or below the mean

*Take bottom 25% and top 25% and throw out the middle

*Take bottom third and top third and throw out the middle third


*Use accepted or externally validated cut-offs

*

*e.g., medical diagnoses are often based on certain cut-offs on a continuous scale

*Use your own understanding of the phenomena to define a cut-off


*Examine a histogram or density plot and look for a natural split in the data (as mentioned by @rolando2)

