statistical analysis of events in a given time interval I am attempting to analyze biological data, to see whether the number of events in a given time interval is more/less than expected based on the overall frequency. How would one approach this? 
An example of how I would frame this:
Out of 100 ms, 16/44 events occur in 15 ms, and 28/44 events occur in the remaining 85 ms.
Do more events occur in the 15 ms interval than expected based on the overall frequency? 
And I guess the null hypothesis is that there is a random distribution of the 44 events over the 100 ms. 
 A: 
to see whether the number of events in a given time interval is more/less than expected based on the overall frequency.
An example: Out of 100 ms, 16/44 events occur in 15 ms, and 28/44 events occur in the remaining 85 ms. Do more events occur in the 15 ms interval than expected based on the overall frequency? And I guess the null hypothesis is that there is a random distribution of the 44 events over the 100 ms.

If events are uniformly distributed over the total 100 ms interval, then the expected number of evens in the first 15 ms is the total number of events $\times$ 15/100.
I interpret your question as implying a one tailed alternative, but you should take care about how well justified that is and consider whether the two tailed alternative is what you need.
I will further assume events are independent (this assumption may not be justified, you should consider carefully whether it is reasonable).
Let $X$ be the number of events in the first 15 ms.
Given the assumptions, and conditioning on the total number of events observed, the number of events, $X$ in 15 ms will be binomial with $n=44$ and $p=0.15$.
$H_0: \text{Events occur at the same rate before and after 15ms}$
$H_1: \text{Events occur at a higher rate in the first 15ms}$
Or in symbols:
$H_0: p=0.15$
$H_1: p>0.15$
We observe $x=16$. The probability of observing 16 or more events in the first 15 ms is 0.0004022:

At typical significance levels you'd reject $H_0$ and conclude there was a higher rate of events in the first 15ms.
A: If you know the times of the events to a precision about 100 times that of the average interval or greater, it is possible to use event interval analysis to examine changes in rate. In such an analysis, the intervals between events are used as the primary data, and a uniform distribution of events is the typical null hypothesis. While this has previously been used for event sequences of much lower frequency, the method should be applicable. See Lemon, J. (2014) The analysis of event rates using intervals. The Quantitative Methods for Psychology, 10(1): 68-76.
