Easier to use randomisation results

This is an updated version of a previous post.  The key difference is that the significance classification described previously was too confusing, as values could be positive or negative and became more significant as they approached zero.  Instead, Biodiverse now provides relative ranks which can easily be converted to significant/not significant for any alpha cutoff.  This change should not affect many users, as the 0.99_003 release containing it was never announced...

One of the issues users face with the randomisations in Biodiverse is what to do with them once they have been run.

A key point is that the results are stored on the other analysis objects themselves, as extra indices and lists.  The index names themselves are a bit cryptic, but are consistent, and there is a description of what they mean here:  https://purl.org/biodiverse/wiki/AnalysisTypes#where-do-the-randomisation-results-go-and-what-do-they-mean

Even then, it can be difficult working out which of your groups have index scores that are significantly different from the set of randomised results.  This is because the data are plotted as a continuum (which in turn is because it uses the same plotting process as the original index scores).  The first image below is an example of this plotting.

One can easily export the data and work with them in a GIS or stats package, but any tied values need to be factored in for lower tail tests, for example as used in the CANAPE process.

With the next version of Biodiverse this categorisation will become a little easier.  Biodiverse will automatically calculate rank-relative positions that can be easily converted into significance levels.  These are stored in new lists that can be displayed and exported in the same way as any other data.

As an example, imagine you have run a randomisation analysis for a BaseData containing a spatial analysis in which you calculated phylogenetic endemism.  Assume that the randomisation's name is rr (not a good name, but it's convenient to type here), so the spatial analysis will now have three lists you can plot.  The first two are the same as ever:  SPATIAL_RESULTS contains the observed results for each group (cell), and rr>>SPATIAL_RESULTS contains indices to track the randomisations for each index in SPATIAL_RESULTS.  For example, for PE_WE there will be C_PE_WE, Q_PE_WE, T_PE_WE and P_PE_WE collating, respectively, the number of times observed PE_WE was higher than that generated using the randomised data, the number of times observed PE_WE was compared against the scores from the randomised data, the number of times the observed and random scores were tied, and the proportion of iterations that the observed score was higher than the random scores (P_PE_WE = C_WE_PE / Q_PE_WE).

The new list is rr>>p_rank>>SPATIAL_RESULTS.  This contains a set of results using the same names as the original indices in SPATIAL_RESULTS, but converted to their rank relative positions.  Importantly, the lower tail ranks take into account any ties in the comparisons, thus simplifying any code that uses theses results.  Also, any value that would be considered not significant at alpha=0.05 (one tailed, high or low) is converted to undef (null).  This makes any plots of the results clearer within Biodiverse so one can more easily see which groups would pass a one-tailed high or low test.

An example plot is in the second image below.

All the ranks have been combined into the same list to reduce the number of indices and lists generated, and thus use less memory and disk space (an index cannot be simultaneously significantly high and low so there is no overlap).  If you are interested in a one tailed test for high values then ignore the low values, and vice-versa.  The values can be easily separated after exporting the results.

Currently the results are plotted in the same manner as any data, but there are plans to allow users to overlay the randomisation significance results over the top of the observed results, for example by masking our any non-significant scores for a given threshold.

The current system plots all scores, regardless of whether they pass a threshold or not.  This is useful, but is difficult to interpret when looking for significance against the randomisation.

The new randomisation list contains indices for the rank-relative positions of the observed values against the randomly generated values. These can then be used for one and two tailed significance tests.  The plotting could be improved, e.g. in this case it appears there are only two values, but this is simply due to the colour scaling.  However, it works well enough now for exploration - proper maps can also be made using a GIS or stats package.

To try it out you will need the 1.99_004 release (or later).  It can be accessed from https://github.com/shawnlaffan/biodiverse/wiki/Downloads

This is a new implementation, so any feedback about usability would be very useful.  

Shawn Laffan

29-Aug-2016

For more details about Biodiverse, see http://purl.org/biodiverse 

For the full list of changes in the 1.99 series (leading to version 2) see https://purl.org/biodiverse/wiki/ReleaseNotes 

To see what else Biodiverse has been used for, see https://purl.org/biodiverse/wiki/PublicationsList

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