One Variance

Power and Sample Size
Power Analysis - Ratio

  

Ratio refers to the ratio between the comparison variability and the hypothesized value. A ratio close to 1 suggests equality between the comparison and null variability values. Of course, you never actually know these values when you conduct an experiment. Nonetheless, it is important to consider the ratio between variability values that you are interested in being able to detect.

Example Output

 

Test for One Standard Deviation

 

Testing StDev = null (versus ≠ null)

Calculating power for (StDev / null) = ratio

α = 0.05

 

 

Sample

  Size  Power    Ratio

    50    0.8  1.31620

    50    0.8  0.74353

    50    0.9  1.38104

    50    0.9  0.71319

Interpretation

For the lumber data, the manager wants to know what ratio between variability values he can detect with a sample size of 50 and power of 0.8 or 0.9. The results indicate that:

·    With a sample size of 50, the lumber company can detect a less than ratio of 0.74353 and a greater than ratio of 1.31620 with a power of 0.80. This means that the test will have 80% chance of detecting a ratio of 0.74353 or 1.31620.

·    With a sample size of 50, the lumber company can detect a less than ratio of 0.71319 and a greater than ratio of 1.38104 with a power of 0.90.