ztest_proportion_two_samples

create function 
ztest_proportion_two_samples
(total_a float, conv_a float,  total_b float, conv_b float, one_sided boolean)

--INPUTS:
-- total_a = total number that saw A
-- conv_a = converters for version A
-- total_b = total number that saw B
-- conv_b = converters for version B
-- one_sided = one or two sided test

RETURNS float
--OUTPUT: 
--Returns p value
STABLE 
AS $$
    import numpy as np
    from scipy.stats import norm
    
    p1 = conv_a/total_a
    p2 = conv_b/total_b    

    p = (conv_a+conv_b)/(total_a+total_b)
    se = p*(1-p)*(1/total_a+1/total_b)
    se = np.sqrt(se)
    
    z = (p1-p2)/se
    p = 1-norm.cdf(abs(z))
    p *= 2-one_sided # if not one_sided: p *= 2
    return p

$$LANGUAGE plpythonu;