One Proportion

Power and Sample Size
Power Analysis - Comparison Proportion

  

The comparison proportion is the value you want to compare with the hypothesized proportion. When you provide values for the sample size and power of the test, Minitab will calculate the comparison proportion the test can detect.

Example Output

Test for One Proportion

 

Testing p = 0.65 (versus ≠ 0.65)

α = 0.05

 

 

Sample

  Size  Power  Comparison p

   500    0.8      0.708905

   500    0.8      0.589679

  1000    0.8      0.691851

  1000    0.8      0.607441

Interpretation

Suppose the firm wants to know how large a difference between the population proportion and the national average of 0.65 (the hypothesized proportion) must be for them to be able to detect it with a power of 0.8. For comparison, they also want to know what comparison proportions they can detect with half the sample size.

The results indicate that:

·    with 500 observations, the test has an 80% (power of 0.8) chance of detecting a comparison proportion of 0.708905 or 0.589679.

·    with a sample size of 1000, the test has an 80% chance  of detecting a comparison p of 0.691851 or 0.607441.