Using the values of the three power function variables that you entered, Minitab calculates the number of replicates, the effect size, the power of the design, or the number of center points.
If you enter the number of replicates, the power value, and the number of center points, Minitab calculates the effect. The effect is the difference between the means of the response variable at the high and low levels of a factor that you want the design to detect. This difference can be the result of one factor alone (main effect), or of a combination of factors (interaction).
If you enter the number of replicates, the effect size, and the power value, Minitab calculates the number of center points. Center points are experimental runs with all factor levels set halfway between the low and high settings. Center points are mainly used to detect curvature effects, but adding more center points can also increase the power somewhat.
Factors: | 15 | Base Design: | 15, 32 |
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Blocks: | none |
Center Points | Effect | Reps | Total Runs | Target Power | Actual Power |
---|---|---|---|---|---|
0 | 2.0 | 1 | 32 | 0.8 | 0.877445 |
0 | 2.0 | 2 | 64 | 0.9 | 0.995974 |
0 | 0.9 | 4 | 128 | 0.8 | 0.843529 |
0 | 0.9 | 5 | 160 | 0.9 | 0.914018 |
In these results, Minitab calculates the number of replicates to reach the target power. The design that detects an effect of 2 with a power of 0.8 requires 1 replicate. To achieve a power of 0.9, the design requires 2 replicates. The actual power with 2 replicates is greater than 0.99. This actual power is the smallest power value that is greater than or equal to 0.9 and obtainable using an integer number of replicates. To detect the smaller effect of 0.9 with 0.8 power, the design requires 4 replicates. To detect the smaller effect of 0.9 with 0.9 power, the design requires 5 replicates.
Use the power curve to assess the appropriate properties for your design.
The power curve represents the relationship between power and effect size, for every combination of center points and replicates. Each symbol on the power curve represents a calculated value based on the properties that you enter. For example, if you enter a number of replicates, a power value, and a number of center points, then Minitab calculates the corresponding effect size and displays the calculated value on the graph for the combination of replicates and center points. If you solve for replicates or center points, the plot also includes curves for other combinations of replicates and center points that are in the combinations that achieve the target power. The plot does not show curves for cases that do not have enough degrees of freedom to assess statistical significance.
Examine the values on the curve to determine the effect size that the experiment detects at a certain power value, number of corner points, and number of center points. A power value of 0.9 is usually considered adequate. However, some practitioners consider a power value of 0.8 to be adequate. If a design has low power, you might fail to detect an effect that is practically significant. Increasing the number of replicates increases the power of your design. You want enough experimental runs in your design to achieve adequate power. A design has more power to detect a larger effect than a smaller effect.