# Convergence of Empirical cumulative distribution functions?

I am exploring the cumulative distribution function of two samples. I am comparing the distribution of observations in which a focal animal was disturbed with the distribution of observations in which a focal animal was not disturbed as a function of distance to the disturbance.

Using program mark I have computed and plotted the ecdf for each population vs distance to disturbance. I have also used the Kolmogorov-Smirnov Test to test if the distributions are different. They are. What I would like to know is if there is a way to determine at what distance from the disturbance these distributions converge and are no longer different.

In playing around with this data I have noted that if I truncate the both samples to only include observations where the disturbance is greater than 0.7 km from the focal animal and rerun the K-S test the D statistic is no longer significant. When plotted the two distributions (using the truncated data) seem to be parallel and similar in shape. I interpret this as an indicator that the divergence in the distributions is occurring in the section of the data when the disturbance is closer than 0.7 km from the focal animal.

I understand that by truncating the observations I am reducing my sample size and effecting the calculation of the p-value. Is this line of thought statistically flawed to the point I am getting spurious results? Any hints on how to explore which section of the data is contributing the the divergent distributions?

Thanks.

• What question are you find out from the data, exactly? – Glen_b Jan 30 '14 at 3:35
• I am trying to understand at which distance the focal animals are more susceptible to flight (disturbance). The species of bird does fly at some rate when not disturbed so I am looking to find out where the distribution of flight observations deviates from the normal. – marcellt Jan 30 '14 at 4:12
• Large differences in probability are much more easy to get when you're near the middle region of probabilities. Consider - as you said - that the normal probability of flight is low. A small increase at a low probability is potentially a much bigger increase in the log-odds of flight than a similar increase in probability when the normal probability is higher (because it's naturally more variable there). For example, if the probability changes from 0.01 to 0.05 that's an increase of 0.04, but it's also showing a five-fold increase in frequency - more impressive than going from 0.51 to 0.55 – Glen_b Jan 30 '14 at 4:18