One Proportion

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 comparison proportion, 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

Test for One Proportion

 

Testing p = 0.65 (versus ≠ 0.65)

α = 0.05

 

 

              Sample  Target

Comparison p    Size   Power  Actual Power

         0.6     726     0.8      0.800040

         0.6     977     0.9      0.900064

         0.7     698     0.8      0.800283

         0.7     927     0.9      0.900080

Interpretation

Suppose the firm wants to determine if the proportion of responses is greater than or less than the national average of 0.65 by at least 0.05. How many households do they need to sample to achieve a power of 0.80 or 0.90 for this test?

The results indicate that:

·    with 726 observations the power for detecting a comparison proportion of 0.6 is 0.800040. (This means that if the true population proportion is 0.60, then there is a 80% chance that the test will detect this difference.)

·    with 977 observations the power for detecting a comparison proportion of 0.6 is 0.900064.

·    with 698 observations the power for detecting a comparison proportion of 0.7 is 0.800283.

·    with 927 observations the power for detecting a comparison proportion of 0.7 is 0.900080.