  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 Nth 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>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.
