pMoSS: p**-value **Model using the Sample Size

minimal Python version License

pMoSS (p**-value **Model using the Sample Size) is a Python code to model the p-value as an n-dependent function using Monte Carlo cross-validation.

This statistical method uses the relationship between the p-value and the sample size to characterize the data of an experiment and decide, robustly, when the null hypothesis can be rejected.

The method is presented at E. Gómez-de-Mariscal, V. Guerrero, A. Sneider, H. Jayatilaka, J. M. Phillip, D. Wirtz and A. Muñoz-Barrutia, "Use of the p-values as a size-dependent function to address practical differences when analyzing large datasets." Scientific Reports, 2021.

How to cite

  title={Use of the p-values as a size-dependent function to address practical differences when analyzing large datasets},
  author={G{\'o}mez-de-Mariscal, Estibaliz and Guerrero, Vanesa and Sneider, Alexandra and Jayatilaka, Hasini and Phillip, Jude M. and Wirtz, Denis and Mu{\~{n}}oz-Barrutia, Arrate},
  journal={Scientific Reports},
  URL = {},
  doi = {10.1038/s41598-021-00199-5}

Conditions of use

pMoSS is an open-source software (OSS) under the BSD 2-Clause License. All the resources provided here are freely available for non-commercial and research purposes. Their use for any other purpose is generally possible, but solely with the explicit permission of the authors. You are expected to include adequate references whenever you present or publish results that are based on the resources provided.

Whatch these short tutorials to become an expert user of pMoSS

Get pMoSS ready in Google Colab Analysis of new data using Google Colab

Brief description

The method uses Monte Carlo cross-validation to estimate the distribution of the p-value using samples of different sizes, and fits an exponential curve. When the p-value of a certain statistical hypothesis test is treated as a function of n, it is possible to get quantitative indicators of the data, such as the decay of the function or the minimum data size needed to get statistically significant differences (nα).

The following figure illustrates a common output of the method. Here the cell body roundness is tested when cancer cells are treated with Taxol.


(Leftmost) The cell roundness distribution of control cells and cells treated at 1 nM Taxol have lower values than that of cells treated at 50 nM. (Right) The three groups were compared, the p-values were estimated and p(n) was fitted for each pair of compared groups. When Taxol at 50 nM is evaluated (blue and yellow dashed curves), nα is lower and the decay of p(n) is higher (a and c parameters of the exponential function ), i.e. it decreases much faster than the one corresponding comparison of control and Taxol at 1 nM (orange curve).


This package is tested on Python 3.6 and 3.7. The code can be used either in a local machine or in Google Colab.

Local Machine

You need to have Python installed previously. For non-expert users, it is highly recommended to download the Anaconda distribution of Python to obtain the dependencies easily.

Create a new virtual environment with Python 3 and avoid any version compatibility issues. There are three different ways to do it:

  • Create a virtual environment with Python (advanced users).
  • Open Anaconda Prompt and create a virtual environment called your_virtualenv using conda create:
    conda create -n your_virtualenv python=3.6
  • Open Anaconda Navigator and create a virtual environment using the GUI.

Download or clone this repository in your local machine.

Open Anaconda Prompt and activate your virtual environment using conda activate:

conda activate your_virtualenv

Once your_virtualnv is activated, place the working path in the directory where you downloaded/cloned this repository:

cd to/the/directory/where/code/and/requirements.txt/are/located/

Install all the packages specified in the requirements file with pip:

pip install -r requirements.txt

To run the notebook of the examples, you can install Jupyter Notebook either using Anaconda Navigator or Anaconda Prompt. Do not forget to do it in your virtual environment. So if necessary, activate your_virtualenvusing conda activate (as it was done in previous lines) and install Jupyter with the following command:

pip3 install --upgrade pip
pip3 install jupyter
jupyter notebook

In Jupyter, you have access to the directories in your local machine. Open the notebook in the examples and run the code written on it.

Google Colab

Open the notebook of the examples in Google Colab (File -> Open notebook... -> GitHub -> URL to the notebook). Note that you need to save a copy of this notebook in your drive to keep any change (File -> Save a copy in Drive)

Add the following code lines at the beginning of the notebook:

  • If the code and data are located in your drive, then you need to mount it so Google Colab can access to your private files. Otherwise, you can skip this step.
from google.colab import drive
  • Clone this github repository:

    !git clone
  • Install the requirements:

    !pip install -r /content/pMoSS/requirements.txt
  • Modify the first line of the notebook indicating the correct path:

    • If you cloned the repository:
      # Load the path containing all the functions to use pMoSS
      from sys import path
    • If you have the entire code in your drive:
      # Load the path containing all the functions to use pMoSS
      from sys import path
      path.append('/content/drive/My Drive/the_path_in_your_drive/pMoSS/pMoSS/')
  • Update the path to the data indicating the correct path:

    path = r'/content/pMoSS/data/morphology/'


    path = r'/content/drive/My Drive/path_to_the_data_in_your_drive/'
  • If necessary, update the name of the data:

    file_name = r'new_data.xlsx'

    You are ready to run the code in the notebook!

System requirements

Operating systems.

  • Windows
  • Mac OSX
  • Linux

Python version and packages:

  • Python 3.6 (or newer)
  • numpy
  • scipy>=1.1.0
  • pandas
  • matplotlib
  • xlrd>=1.0.0
  • seaborn
  • statsmodels>=0.9.0
  • glob2
  • pytest-shutil


You can find examples of data analysis in the example folder. A Google Colab notebook is provided for a quick test.

Please, note that the software is not implemented for GPU so Monte Carlo cross-validation takes quite a long time. The user can target the process by observing for a certain n-value, when a entire cross-validation has finished.

Get the latest version of the code in the Releases. There you will find a file which contains the estimated p-values of the examples:

  • p-values for the morphology changes with the increase of cellular age.
  • p-values for the morphology changes in cancer cells and their protrusions after being treated with Taxol.

To avoid heavy computations and make a quick test of the code, download the data. Then, place it into the folder of the cloned repository, so the links in the notebooks work properly. Otherwise, change the links in the notebooks.

Feedback and contributions

  • All kind of feedback is welcome. Specially if it supports the use of the code and a better understanding on how to work with it.
  • Controbutions are also welcome. Please, create a new pull request on a new development branch to add new features, correct bugs or make changes in the code.
  • Please, if possible, use GitHub Issues to report any bug or ask questions.


pMoSS (p-value Model using the Sample Size) is a Python code to model the p-value as an n-dependent function using Monte Carlo cross-validation. Exploits the dependence on the sample size to characterize the differences among groups of large datasets

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