Pooled standard error and z-score
Grab tested a new driver-incentive banner. The treatment arm converted better — but "better" needs a number attached, because a 0.3-point gap on 800 users and the same gap on 80,000 mean completely different things.
The standard test for a difference in two proportions pools both arms to estimate a shared conversion rate, uses it for the standard error, and divides the observed difference by that error:
p_pool = (x_c + x_t) / (n_c + n_t)
SE = sqrt( p_pool * (1 - p_pool) * (1/n_c + 1/n_t) )
z = (p_t - p_c) / SE
From ab_results, return a single row with z_score, rounded to 4 decimal places.
Schema
| variant | TEXT |
| users | INT |
| conversions | INT |
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