Comparison of two Proportions

Question 1

How do we perform a hypothesis test in the comparison of two independent proportions?

Answer 1

1. Calculate the difference in proportions
2. Calculate the SE
3. Calculate confidence intervals
4. Establish the null hypothesis (that there is no difference between two groups and they both have a common proportion - pi)
5. Use the common proportion p from the two samples and calculate the pooled standard error.
6. Calculate the test statistic (z)

Question 2

How do we tackle small samples when hypothesis testing two independent proportions?

Answer 2

1. Use the continuity correction (a modified formula for the z-test).
2. Use an exact test in very small samples