Supplemental Material for Counterbalancing for Serial Order Carryover Effects in Experimental Condition Orders
Psychological Methods · 2012
PROGRAMS FOR GENERATING SEQUENCESBelow is a Matlab/Octave program that can be used to create a serial-order counterbalanced sequence of conditions, i.e. ensuring that every condition is preceded equally often by every other condition (for first-order counterbalancing) or every nTuple of conditions of length n (for nth-order counterbalancing).The program uses the Kandel et al. 1996 method for finding an Euler path through the graph.This algorithm selects uniformly from all available sequences. Matlab/Octave Function -carryoverCounterbalance.mThis function has been written to function equivalently in Matlab and Octave.Matlab (http://www.matlab.com)Mathworks, Natick, MA, USA) is a commercially-available technical computing environment.Some universities/departments have a site license for Matlab.Check with your IT administrator.Octave (http://www.gnu.org/software/octave/) is a freely-available numerical computing environment similar to Matlab.This function works by entering the name of the .mfile at the command line in Matlab or Octave (see detailed instructions in the Matlab/Octave Function Code & Usage section below).It was written in Matlab version 7.10.0.499 (R2010A) but should be compatible with most versions.No toolboxes are required.Make sure that the .mfile is in the Matlab path before trying to run it.A counterbalanced condition sequence is output as an array of numbers.For access to the code open the .mfile in Matlab or Octave editor.The subfunction eulerPathKandelMethod_carryoverCounterbalance (included in the same .mfile) computes the Euler circuitthrough a directed graph given the adjacency matrix for that graph.This subfunction can be extracted and saved as a separate m-file if one wants to generate more complicated designs than those available with the carryoverCounterbalance function, for instance, if one wants to create sequences in which some conditions occur more often than others. Further information on the INPUT parameters:-numConds: number of unique conditions.Must be a positive integer.-cbOrder: depth/order of counterbalancing.Must be a positive integer.First-order counterbalancing ensures that every condition is preceded by every other condition equally often.nth-order counterbalancing ensures that every condition is preceded equally often by every n-length sequence (nTuple) of conditions.e.g.2nd-order counterbalancing would ensure that condition 1 is preceded equally often by each set of 2 conditions, 1 1, 1 2, 2 1, 2 2.-reps: The number of times each condition is preceded by every other condition (first-order) or every nTuple (nth-order).Must be a positive integer.This can be used to increase the total number of trials while maintaining counterbalancing.-omitSelfAdjacencies: Determines whether the same condition can occur directly adjacent to another instance of that same condition.0 = include condition self-adjacencies (e.g. 2 2 1 2 1 2); 1 = exclude condition selfadjacencies (e.g. 1 2 1 2 1 2) Executable Program -carryoverCounterbalanceGUI Download from: http://www.icn.ucl.ac.uk/counterbalance/This is an executable version of the carryoverCounterbalance.m Matlab/Octave program that can be used without a Matlab license.It also includes a graphical user interface (GUI) that allows easy entry of the parameters.In order to run this executable file you will also need to install the Matlab Compiler Runtime (MCR) that is distributed for free along with this program (http://www.mathworks.co.uk/products/compiler/).One version is provided for Microsoft Windows-based machines (created on Windows XP SP3).Another version is provided for Apple Mac-based computers.