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Gives probability of a random sample from a distribution with a higher mean to be bigger than a random sample from a distribution with a lower mean.
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It is a simple tool to compare two normal, Poisson or Gamma distributions. Given the means and standard deviations of the distributions it will give a likelihood that a random draw from a population with a higher mean is bigger than a random draw from a population with the smaller mean.

Experimental results often report statistically significant differences that are not very meaningful in every day life, i.e. their actual impact is very small. With big enough sample we can often detect differences, which are very small.

Let's say that some researcher reported that with p-value of 0.001 an African swallow can lift a heavier coconut than a European swallow. This assertion is based on results of an experiment carried on a population of 1,000,000 birds. The researcher also provided information about the experimental results saying that an African swallow on average could carry a coconut weighting 478g (SD=189g), while the European only a coconut weighting 477g (SD=156g). The numbers already look small, but how likely it is that if we took one random African and one random European swallow, the African one could carry a heavier coconut than the European one? (The answer is about 50.11%).

This simple tool calculates an answer to this question and helps in interpreting experimental results.

The output of the script is a result of the test and a graph illustrating the two distributions.


The script has been tested with Python 2.7 (Anaconda Python Distribution - Windows 8.1 64-bit)

Modules required:

  • numpy
  • matplotlib
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