You will need several data points for different N.
Let's say you get these statistics:
N time(ms)
4 12
8 24
16 48
In this case doubling N doubles the time, so your complexity must be O(N).
But if you get these stats
N time(ms)
4 16
8 64
16 256
In this case doubling n quadruples the runtime, so you complexity must be O(n2).
If time does not change at all, your complexity is O(1)
Similarly, different data points will let you determine the function that satisfies the big(O). The more points you have for different N, the better you can determine that function.