At what point do significantly different groups start to differ? I have two groups: a control group (N = 91), and a treatment group (N = 54). I did a t-test in SPSS that suggests that there are significant differences between the two groups in terms of the variable of interest (BMI in this case). Is there a way to find out a tipping point? That is, can we find out at what point of BMI, the two groups start to be different? 
 A: The standard $t$-test assumes that the distributions are the same (both normal, and with equal standard deviations), and that they are simply shifted relative to each other.  Put another way, the $t$-test is a simple test of location.  Thus, your distributions are different at every point on the BMI scale.  
If you wanted to predict the probability a person was in one group or the other based on knowledge of their BMI, you should fit a logistic regression model.  Bear in mind that there won't be a point where you go from one group to the other (unless there is complete separation).  Instead, the model will tell you the probability of a person with that BMI being in the target group.  
If you want a quick and easy way to select the most likely group and are willing to stick with the assumptions of normality and equal variance, you can just check which group's mean someone's BMI is closer to.  The groups' probability densities will cross at the point halfway between the two means, and the ratio of the pdfs at a specific BMI can be taken as a measure of how sure you can be.  If you want to assume that the groups are unbalanced in the population, you can weight the ratio of the pdfs.  
A: A simple approach to identifying a "tipping point" would be the following:
1) Create a binary variable for treatment group assignment (For example, if treatment group then tx_group = 1, if control group then tx_group = 0). You probably already have something like this in your dataset.
2) Sum up the number of treatment group subjects (sum of tx_group) and count the number of total subjects with each point of BMI. Then simply divide the number of tx_group/total at each level of BMI to get the percentage of records at a specific point of BMI are in the treatment group. The below table will summarize the necessary fields you will need to create:

As you can see in this mock data, we have 54 subjects in the treatment group and 145 subjects total. Here we can see that the "tipping point" is at BMI = 24 as the percentage of subjects in the treatment group made up > 40% of all subjects at each level of BMI between 18 and 23, but treatment group subjects are almost non-existent at higher BMI's. Obviously, this mock data is a much cleaner break than you will likely observe in your data, but the general idea of a "tipping point" should be capable of viewing if such a break exists between your treatment and control groups.
Please let me know if you need any further assistance in identifying the "tipping point" in your data.
A: I don't think your question really has an answer. A t-test implies your groups are always different. The gist of the test is you are measuring if the difference between the groups is significant. To do that, you have to assume the groups are different. There is no point of BMI where your groups are the same.
Put another way and rephrasing your question, you want to know at what point of BMI your groups have different BMIs. That's just not possible. It doesn't really make sense to ask the question (for instance at a BMI of 23 you can't have anyone who doesn't have a BMI of 23). If what you mean is at what point of BMI are there more people in the control than in the treatment condition, Matt's answer works, but with noisy data there may be many inflection points (i.e. where the % goes below .5 then above .5 then below .5 again). Also, that's kind of an odd thing to do. You are essentially trying to predict condition assignment based on BMI scores. While statistically, you can do that, qualitatively, that violates assumptions of your experiment (e.g. that people were randomly assigned to treatment, which had a causal effect on BMI, rather than vice versa).
Perhaps what you mean is you want to know if people who have certain BMI's respond differently to treatment than people with certain other BMI's. For instance, maybe treatment works for those with high BMI's but not for those with low BMI's. You don't have the necessary information to make this test. In addition to collecting BMI's post-treatment, you would have to collect BMI's pre-treatment. You would then do a linear model predicting post-treatment BMI by treatment interacted with pre-treatment BMI. The resulting model can tell you if the effect of treatment depends on what the person's BMI was prior to treatment.
