Increasing the power of the test

There are three basic factors that can increase the power of a test of two proportions:

·    a larger effect size - The greater the real difference between proportion 1 and proportion 2, the more likely it is that the sample proportions will also be different.

·    a higher a-level (the level of significance) - If you choose a higher value for a, you increase the probability of rejecting the null hypothesis, and thus the power of the test. (However, you also increase your chance of type I error.)

·    larger sample sizes - The more observations there are in your samples, the more confident you can be that the sample proportions represent the population proportions. Thus, the test can be more sensitive to smaller differences.

The most practical way to increase power is often to increase the sample size.

If appropriate, you may also consider using a directional hypothesis. A directional hypothesis has more power to detect a difference in the specified direction, but has no power at all to detect a difference in the opposite direction.