One-Sample Z

Power and Sample Size
Power Analysis - Sample Size

  

Increasing the sample size increases the power of your test. You want enough observations in your sample to achieve adequate power, but not so many that you waste time and money on unnecessary sampling.

If you provide the power that you want the test to have and the difference you want it to be able to detect, Minitab will calculate how large your sample must be. (Since sample sizes are given in integer values, the actual power may be slightly greater than your target value.)

Example Output

1-Sample Z Test

 

Testing mean = null (versus ≠ null)

Calculating power for mean = null + difference

α = 0.05  Assumed standard deviation = 2.6

 

 

            Sample  Target

Difference    Size   Power   Actual Power

       1.5      24    0.80       0.806857

       1.5      27    0.85       0.850323

       1.5      32    0.90       0.903816

       1.5      40    0.95       0.954373

Interpretation

For the cooking oil data, the dietician wants to determine if the true saturated fat content is 1.5% greater than or less than the advertised value of 15%. How many bottles does she need to sample in order to achieve a power of 0.80, 0.85, 0.90, or 0.95 for this test?

The results indicate that:

·    in order to achieve a power of at least 0.80, she needs to sample 24 bottles, which gives her a power of 0.806857.

·    with 27 observations the power is 0.850323.

·    with 32 observations the power is 0.903816.

·    with 40 observations the power is 0.954373.

If the dietician can afford to sample 40 bottles, there is a very good chance (95.4373%) that the test will be able to detect the effect of interest.