The term difference (or effect) refers to the difference between m and the reference value that you choose for the Z-test. Of course, you never actually know m when you conduct an experiment. Nonetheless, it is important to consider how small a difference you are interested in being able to detect.

If you provide the size of your sample and the power that you would like your test to have, Minitab will calculate the difference that you will be able to detect with the specified power.

Suppose the dietician has 20 bottles of oil, and she wants to know how large a difference the test will be able to detect. She chooses 0.9 as a power level she is comfortable with. For comparison, she also wants to know what kind of effect she could detect with 3 times as many observations.

The results indicate that:

·    with a sample size of 20, the test can detect a difference of 1.88454 with a power of 0.9. This means that the test will have a 90% chance of detecting the difference if it is 1.88454. Since the difference that she is interested in (1.5) is somewhat smaller than this, she may want to find a way to increase the power.

·    with a sample size of 60, the test can detect a difference of 1.08804 with a power of 0.9. This difference is too small to be of interest, so she would not choose to use a sample this large.