PyGellermann: a Python tool to generate pseudorandom series for human and non-human animal behavioural experiments

Abstract

Objective: Researchers in animal cognition, psychophysics, and experimental psychology need to randomise the presentation order of trials in experimental sessions. In many paradigms, for each trial, one of two responses can be correct, and the trials need to be ordered such that the participant's responses are a fair assessment of their performance. Specifically, in some cases, especially for low numbers of trials, randomised trial orders need to be excluded if they contain simple patterns which a participant could accidentally match and so succeed at the task without learning.

Results: We present and distribute a simple Python software package and tool to produce pseudorandom sequences following the Gellermann series. This series has been proposed to pre-empt simple heuristics and avoid inflated performance rates via false positive responses. Our tool allows users to choose the sequence length and outputs a .csv file with newly and randomly generated sequences. This allows behavioural researchers to produce, in a few seconds, a pseudorandom sequence for their specific experiment. PyGellermann is available at https://github.com/YannickJadoul/PyGellermann .

Keywords: Animal cognition; Experimental psychology; Go/no-go; Psychometrics; Python; Randomization; Simple heuristics; Two-alternative forced-choice.

Fig. 1

A Venn diagram shows how the set of Gellermann series is a strict subset of all possible binary sequences. Some exemplary sequences (in red) violate some of the criteria put forward by [7]. For instance, in red from top to bottom, the set of Gellermann series does not include the sequences (1) ABBAABABAA because it does not contain an equal number of As and Bs, (2) BAAAABBBAB as it contains 4 As in a row, (3) AAABABBBAB because it has only 1 B and in the first half of the sequence and only 1 A in the second, (4) ABABBBAABA because it contains 6 reversals, and (5) ABBBABAAAB as it provides an 80% correct response rate when responses follow a simple alternation pattern (i.e., ABABABABAB). On the contrary, the sequences AABBABAABB, AABABAABBB, AAABBABABB (in green) fulfill all criteria and are included in the nested set of Gellermann series

Fig. 2

Monte Carlo estimates of the proportion of all binary sequences that meet all five of Gellermann’s criteria, in function of the length of the sequence. Since the proportion drops off exponentially and our implementation generates and tests balanced sequences (i.e., those with an equal number of As and Bs) uniformly at random, generating Gellermann series with many more than 100 elements quickly becomes infeasible

Fig. 3

A screenshot of PyGellermann’s GUI shows the various options available to customise the generated series, as well as options to copy the generated series or save them as a table to a CSV file