Compare two independent proportions

Under H0: p1=p2, pool phat=(x1+x2)/(n1+n2). The test SE is √[phat(1-phat)(1/n1+1/n2)] and z=(phat1-phat2)/SE. Check independence within and between samples and adequate expected counts. A confidence interval for the difference uses an unpooled SE instead; do not reuse the null pooling mechanically.