significance.sql

create or replace function
 public.significance(control_size integer,
              control_conversion integer,
              experiment_size integer,
              experiment_conversion integer)
 returns float
 stable as $$
   from scipy.stats import norm

   def standard_error(sample_size, successes):
     p = float(successes) / sample_size
     return ((p * (1 - p)) / sample_size) ** 0.5

   def zscore(size_a, successes_a, size_b, successes_b):
     p_a = float(successes_a) / size_a
     p_b = float(successes_b) / size_b
     se_a = standard_error(size_a, successes_a)
     se_b = standard_error(size_b, successes_b)

     numerator = (p_b - p_a)
     denominator = (se_a ** 2 + se_b ** 2) ** 0.5
     return numerator / denominator

   def percentage_from_zscore(zscore):
     return norm.sf(zscore)

   exp_zscore = zscore(control_size, control_conversion,
                       experiment_size, experiment_conversion)
   return percentage_from_zscore(exp_zscore)
 $$ language plpythonu;