Theories suggest that filament fragmentation should occur on a characteristic fragmentation length-scale .
This fragmentation length-scale can be related to filament properties , such as the width and the dynamical state of the filament .
Here we present a study of a number of fragmentation analysis techniques applied to filaments , and their sensitivity to characteristic fragmentation length-scales .
We test the sensitivity to both single-tier and two-tier fragmentation , i.e .
when the fragmentation can be characterised with one or two fragmentation length-scales respectively .
The nearest neighbour separation , minimum spanning tree separation and two-point correlation function are all able to robustly detect characteristic fragmentation length-scales .
The Fourier power spectrum and the N ^ { th } nearest neighbour technique are both poor techniques , and require very little scatter in the core spacings for the characteristic length-scale to be successfully determined .
We develop a null hypothesis test to compare the results of the nearest neighbour and minimum spanning tree separation distribution with randomly placed cores .
We show that a larger number of cores is necessary to successfully reject the null hypothesis if the underlying fragmentation is two-tier , N \gtrsim 20 .
Once the null is rejected we show how one may decide if the observed fragmentation is best described by single-tier or two-tier fragmentation , using either Akaike ’ s information criterion or the Bayes factor .
The analysis techniques , null hypothesis tests , and model selection approaches are all included in a new open-source Python/C library called FragMent .