Statistical Analysis Methods

Page 1 Footnotes

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The quantitative analysis of confocal microscopy data has several phases from data generation to statistical analysis.   Broadly we regard the following topics:

  • image extraction

  • image analysis and boundary detection

  • extraction of point patterns for foci of interest (nuclear compartments, genomic loci)

  • analysis of colocalization in the point patterns

  • formulation of descriptive or discriminative models for cell speciation

  • formulation of generative mathematical/probabilistic models for system development.

Nucleus Image: PML foci (green) distributed in cell nucleus (red)

with nucleolus (purple)


Here we focus on the analysis of point pattern data, in the absence of information concerning the location of the nuclear boundary, or exclusion regions such as nucleoli.   We refer to the compartments or domains as object types, and the individual foci as objects.


We aim to assess the following two (null) hypotheses:

  1. The observed arrangement of foci corresponding to a single object type is random in the spatial region available (that is, the cell nucleus, possibly with identified exclusion regions).

  2. The observed arrangement of foci corresponding to a multiple object types (say, types considered pairwise, or in triples) does not indicate any spatial association or dependence between the object types.

Rejection of (A) allows us to conclude that there is an underlying organizational scheme active in the compartments of interphase nuclei.  Rejection of (B) allows us to propose that there is a functional association between different object types; functional interaction is necessarily associated with physical proximity between the interacting objects.


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  1. These pages are an attempt to make the statistical analysis of 3D point pattern data accessible to biologists; statistical jargon and mathematical notation is therefore kept to a minimum.
  2. I might fail with 1. ... so if you have any comments or suggestions, please email me
  3. Pages under constant development

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