Default Signal to Noise in Power Calculation in JMP DOE platform

[#1]

For some reason (can't remember why - must be something I picked up a few years ago) I have always assumed in the default Power Calculation in the DOE platform (Power Analysis) with RMSE = 1 and Anticipated Coefficient 1 is calculated for a signal to noise ratio of 2 (ie the signal is defined as twice the size of the Anticipated Coefficient)

Something I have recently seen on a DOE JMP webinar suggests to me that this is wrong and that in fact the Signal = Anticipated coefficient (NOT twice the Anticipated Coefficient) , so the default power is in fact calculated  for a signal to noise ratio of 1  

Can someone put me straight on this

Many thanks

[#2 · Accepted solution]

You are correct. The Anticipated RMSE is 1 by default. The Anticipated Coefficient is also 1 by default. The coded factor levels mean that the total effect is the predicted change in the response when the factor changes from -1 to +1. So the predicted effect is twice the coded estimate of the coefficient. 

[#3]

Mark - thanks for clarification. Good to know that what I've been teaching people for a few years is correct!  I was getting worried

[#4]

Could you please elaborate on the last statement, "So the predicted effect is twice the coded estimate of the coefficient." Could you provide an example case, please? I am also a bit confused with power and how it relates to the signal-to-noise ratio and its impact on effect size calculations. 

[#5]

The coefficient represents the change in Y per unit change in X. The factor range is -1 to +1 on the coded scale, or a range of 2. So the coefficient represents half of the change in Y. Say the coefficient is estimated to be 5. That value represents the change in Y over half the range. The Y would change by 10 over the entire range.

There are five related quantities in hypothesis tests: effect size, random variation, significance, sample size, and power. The signal to noise combines the first two quantities. The larger the ratio, the higher the power for the same significance and sample size. There will be a higher probability of rejecting the null hypothesis when it wrong.

[#6]

In this case, the signal to noise is 1 or 2 when RMSE =1 and coefficient =1? 

[#7]

The signal is 2 * 1 (coefficient is half effect because of coding). The noise is 1 (standard deviation in same units). So signal to noise is 2:1/

[#8]

You can also think of it this way...Since the coefficients are the change in the Y from the intercept for each term in the model, you can't move the entire range because you can only go one direction from the intercept at a time.  You can't have both the negative and positive coefficient at the same time.

[#9]

Hi Mark, for a typical DOE what's the normal signal to noise we need to apply? Should we use setup different signal to noise for all terms or we can also setup individually. any suggestion how to setup these values? Thank you so much.

[#10]

The choice of a meaningful signal-to-noise ratio is subjective and depends on the situation. The benefit of S/N is that it is relative, which might be easier, but still requires thought.

If you are suggesting to try different S/N to see the power, that is not a good way. S/N should be determined from subject matter expert. You can't 'solve for it' or optimize it. It represents the minimum effect that is practically important.