PyGellerman: A Python Gellermann series generator

This is a Python implementation of a random genenerator for Gellermann series, pseudorandom binary sequences for human and non-human animal behavioural experiments¹. It includes both a graphical user interface (GUI) as well as a simple Python API.

Gellermann series aim to avoid inflating a partipant's experimental performance by excluding random sequences that would match simple psychological or behavioural patterns. More specifically, a Gellermann series is a random sequence which satisfies five criteria; each series of length $n$:

• must contain an equal number (= $n/2$) of As and Bs;
• must contain at most 3 As or Bs in a row;
• must contain at least 20% (= $n/5$) As and Bs within both the first and last half;
• must contain at most $n/2$ reversals (A-B or B-A transitions);
• must provide a correct response rate close to 50% chance when responses are provided as simple alternation (ABAB...) or double alternation (AABBAA... and ABBAAB...).

A full, open access manuscript introducing PyGellermann and describing its scientific applications and limitations has been published in BMC Research Notes, and is available here. It can be cited as follows:

Jadoul, Y., Duengen, D., & Ravignani, A. (2023). PyGellermann: a Python tool to generate pseudorandom series for human and non-human animal behavioural experiments. BMC Research Notes, 16(1), 135. https://doi.org/10.1186/s13104-023-06396-x

Installation

PyGellermann is available on PyPI and can be installed using pip:

pip install pygellermann

For details on how to use pip, see the Python Packaging User Guide or pip's User Guide.

Alternatively, you can download the GUI as a standalone executable for Linux, macOS, and Windows from the releases page.

Note: On macOS, opening the PyGellermann app bundle might at first be blocked because it is not signed or distributed through the App Store. To override this and open the app, right-click on the app bundle and select Open from the context menu. This will open a dialog asking you to confirm that you want to open the app. After that, you can open the app by double-clicking on it. For more details, see the macOS User Guide.

Usage

Graphical User Interface

After installation, you can run the GUI by typing pygellermann-gui in your terminal or by running the standalone executable (PyGellermann, PyGellermann.app, or PyGellermann.exe). The following window should appear:

Four parameters can be set to customize the generated Gellermann series:

• Sequence length: The length of each generated sequence.
• Number of sequences: The number of sequences to generate.
• Alternation tolerance: How close to 50% chance level a sequence needs to be when compared to single or double alternation.
• Choices: The two possible choices for each stimulus in the sequences.
• Random seed: The seed for the random number generator, allowing to deterministically generate the same sequences.

The Generate button will then generate the requested number of sequences, and display them in the table underneath.

Finally, the generated Gellermann series can be copied to the clipboard (Copy) or saved to a CSV file (Save...).

Python API

The Python API consists of 4 simple functions:

• is_gellermann_series(s, alternation_tolerance=DEFAULT_ALTERNATION_TOLERANCE)

  Check if a binary sequence is a Gellermann series.

  Parameters

  • s : Sequence[Any]

    A binary series (i.e., containing two different elements) of even length.

  • alternation_tolerance : float, optional

    The tolerance around 50% chance level compared to single or double alternation, a value between 0 and 0.5 (default: 0.1).

  Returns

  • bool

    True if the given sequence is a Gellermann series, False otherwise.

  Raises

  • ValueError

    If the sequence length is not even, or if the sequence contains more than two different elements, or if the alternation tolerance is not between 0 and 0.5.

  Examples

  >>> is_gellermann_series(['B', 'B', 'A', 'B', 'A', 'B', 'B', 'A', 'A', 'A'])
  True
  >>> is_gellermann_series('1112212122122211', alternation_tolerance=0.2)
  True
  >>> is_gellermann_series('1112212122122211', alternation_tolerance=0.0)
  False

• generate_gellermann_series(n, m, choices=('A', 'B'), rng=None, **kwargs)

  Generate m random Gellermann series of length n.

  Note that this function returns a generator object. To turn it into a list of series, use list(generate_gellermann_series(...)).

  To generate a single Gellermann series, use next(generate_gellermann_series(n, 1)).

  Parameters

  • n : int

    The length of the series.

  • m : int

    The number of series to generate.

  • choices : Tuple[Any, Any], optional

    The two elements of the series (default: ('A', 'B')).

  • rng : np.random.Generator, optional

    A NumPy random number generator (default: None, which uses the default NumPy random number generator).

  • max_iterations : int, optional

    The maximum number of iterations to try to generate all Gellermann series (default: None, which tries indefinitely).

  • kwargs

    Additional keyword arguments passed to is_gellermann_series.

  Yields

  • Iterator[Sequence[Any]]

    A generator object with m Gellermann series of length n.

• generate_all_gellermann_series(n, choices, **kwargs) Generate all Gellermann series of length n in lexicographic order.

  Parameters

  • n : int

    The length of the series.

  • choices : Tuple[Any, Any], optional

    The two elements of the series (default: ('A', 'B')).

  • kwargs

    Additional keyword arguments passed to is_gellermann_series.

  Yields

  • Iterator[Sequence[Any]]

    A generator object with all Gellermann series of length n.

• generate_gellermann_series_table(n, m, long_format: bool = False, **kwargs)

  Generate a Pandas DataFrame of m random Gellermann series of length n.

  In the wide format, the DataFrame has columns 'series_i', 'element_0', 'element_1', ..., 'element_{n-1}', and each row contains a full series. In the long format, the DataFrame has columns 'series_i', 'element_i', 'element', and each row contains a single element of a series.

  Parameters

  • n : int

    The length of the series.

  • m : int

    The number of series to generate.

  • long_format : bool, optional

    If True, the DataFrame is in long format (default: False).

  • kwargs

    Additional keyword arguments passed to generate_gellermann_series.

  Returns

  • pd.DataFrame

    A Pandas DataFrame of m random Gellermann series of length n.

License

PyGellermann is released under the GNU General Public License v3 or later. See the LICENSE file for details.

PyGellermann was developed at the Comparative Bioacoustics Group of the Max Planck Institute for Psycholinguistics, Nijmegen, the Netherlands.

In scientific publications, PyGellermann can be cited as follows:

Jadoul, Y., Duengen, D., & Ravignani, A. (2023). PyGellermann: a Python tool to generate pseudorandom series for human and non-human animal behavioural experiments. BMC Research Notes, 16(1), 135. https://doi.org/10.1186/s13104-023-06396-x

References

Footnotes

1. Gellermann, L. W. (1933). Chance orders of alternating stimuli in visual discrimination experiments. The Journal of Genetic Psychology, 42, 206-208. ↩