Increasing the power of the test

There are four factors that can increase the power of a one-sample Z-test or one-sample t-test:

·    a larger effect size (difference) - The greater the difference between m and the reference value, the more likely it is that the sample mean will also be different from the reference value.

·    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.)

·    less variability - When the standard deviation is smaller, smaller differences can be detected.

·    larger sample size - The more observations there are in a sample, the more confident you can be that the sample mean represents m. Thus, the test will be more sensitive to smaller differences.

The most practical way to increase power is often to increase the sample size. However, you can also try to decrease the standard deviation by making improvements in your process or measurement.

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.