# Understanding the significance of very small p-values [duplicate]

I have calculated p-values of two independent groups (each group contains 17 samples and each sample is 100 points). I used scipy's mann whitney u test. Further, I combined the p-values using Fisher's method as suggested by one of my colleagues. However, the p-values are just too small to make any sense to me. Here is a sample output:

import scipy.stats as stats
p_value_list = [3.3629559156133476e-56, 1.966307600030748e-254, 6.3484089727582271e-103,
3.1221165197874102e-92, 5.8797795864262639e-128, 4.0807369798923832e-130,
1.205918004734663e-187, 8.9953478731039129e-19, 2.1492251770664035e-127,
0.11623743456915718, 6.182421882338173e-13, 3.7920992534448722e-112, 3.5888837913096105e-97,
7.5565994692959197e-134, 0.0026669650138866794, 4.0844220972198632e-16, 4.583685848455044e-95]
results= stats.combine_pvalues(p_value_list)
print (results)


Which gives the following output (p is zero!)

(7172.864625387464, 0.0)


Now, my questions are:

• What is the meaning of small p-values (something like 1.2e-187)?
• How to interpret a p-value that is zero?
• Since I am writing a paper based on this calculation, how can one report this in a peer-reviewed journal?
• With P-values that small you should be able to discern the difference as bloody obvious even without any statistical procedure. Is that a fair description of your results? If not, then you have done something wrong in the calculation. Feb 12, 2017 at 7:20
• Your combined P-value is calculated assuming the 17 P-values are all tests of the same null hypothesis. Is that really the case? You need to give a lot more detail about your data before a clear answer to your questions is possible. Feb 12, 2017 at 7:25
• Feb 12, 2017 at 7:37

1. A P-value of $10^{-187}$ is very strong evidence that the null hypothesis is not true, or that the statistical model used is inappropriate. Very strong indeed.
2. A P-value of zero occurs when the report runs out of decimal places. A P-value of $10^{-187}$ is not really different from a P-value of zero for most purposes.