Significance Test: This test compares two existing results by calculating a Z-score, which represents the number of standard deviations the two proportions are from one another. This Z-score is then converted into a P-value; if the P-value is below 0.05 (indicating the Z-score is greater than 1.96), the difference is considered statistically significant.

Minimum Sample Size: This formula determines the minimum group size needed to reach statistical significance (P < 0.05). By setting the target Z-score at 1.96 and inputting your expected proportions, the calculation solves for the n required to ensure the "margin of error" does not overlap the difference between the two groups.

Example (pooled, old): 40% vs 46%, both n=700 → x₁=280, x₂=322 → p̂=602/1400=0.43 → SE≈0.02646 → z≈−2.27. At 95%, threshold ±1.96; |−2.27| > 1.96 → significant.