# Split-Plot Power¶

Power for split-plot designs is presented two ways. As a split-plot the extra variation from resetting the hard-to-change factors along with fewer resets (groups) causes the power to detect effects from the hard-to-change factors to plummet.

The signal to noise ratio used to calculate randomized power is computed from the entered standard deviation, the [whole plot] variance ratio and the size of an important effect (Δy).

The entered standard deviation is an estimate of the run to run, subplot, within group variability. The entered standard deviation (s) is squared to compute the run to run variance.

Hard to change factors are only changed from group to group. This causes additional whole plot, group to group variation which is in addition to the run to run variation. This additional variation is estimated by multiplying the run to run variance by the variance ratio.

The two variances are combined and used to compute the signal to noise ratio for estimating the “If Randomized” power.

$$\frac{\Delta y}{\sqrt{s_{entered}^{2}\cdot \left ( 1+variance\, ratio \right )}}$$

## Power¶

Power is meant to be a way to manage expectations for what the analysis will be able to provide. It is calculated by comparing the size of an important effect to an estimate of the standard deviation that will appear on the ANOVA once the analysis is completed. It is the probability that an important effect can be found significant given the expected standard deviation.

Use as many of the following suggestions as possible to get the estimated power to 80%. There is no requirement for 80% power, but we at Stat-Ease, Inc. feel that it makes for a good design.

### Can a higher alpha risk (Type I Error rate) be tolerated?¶

Increase the significance threshold for power under Edit - Preferences, General - Analysis node. Increasing the alpha raises the acceptable risk of detecting false effects. If you are more willing to find false effects, you are more likely to find true effects.

### If more runs are affordable…¶

If a full factorial’s power is less than 60%, the best method is to replicate the whole design using Design Tools, Augment Design, Replicate Design.

For larger full-factorial designs having a power around 65%, but too many runs to replicate in full, use the augmentation tools found under Design Tools, Augment Design, Augment. The factorial optimal is a good choice and will allow adding just a few runs at a time.

If the design is a fractional design, including Min-Run, Irregular, and Optimal, the best way to increase runs is to create a new design. Click yes to Use previous design info, and choose a larger design from the list.

### If no more runs are affordable, look at the design…¶

Will the changes in the factor levels produce a larger change in the response than the stated delta? If so, use the larger estimate of delta to estimate power. Larger effects are easier to detect.

Can the factor settings be run on a wider interval? A bigger change in the factor settings usually translates to a bigger change in the response.

Can you be satisfied finding only larger effects? If so, increase delta.

### If increasing the size of your stated delta is not an option…¶

Use blocks to isolate known, yet uncontrolled sources of variation. For instance, if the experiment will take several days, build a design with one block per day.

### If the noise is coming from your measurement system…¶

Get a better measurement system – this usually means more cost.

Repeat the measurements you are making and record the average as your response.

Note

If the noise is truly coming from the process and none of the above ways to increase power are suitable, do not run this experiment. Most likely no significant effect will arise, and little will be learned about the process.