Statistical interpretation of a split-plot DOE design

Question

Hi,

I am not used to statistical interpretation of split-plot DoE and I don't know what is the impact if I have a "wald p value" < 5%.

I know that if it is higher than 5%, whole plot and subplot have no impact on the plan so if its value is < 5% it meas that whole plot and sub plot have an impact on the plan, but how can I analyze that?

Thank you for your help.

statman · Answer

It is much easier to provide interpretation advice if you share your data table (you can anonymize it). Think of it this way...It's like you've run two experiments.  Ann experiment including the whole plot effects whose statistical significance is compared to the whole plot error (which is estimated by the replication).  And the split-plot factors whose statistical significance is estimated by the MSE.

First step in analysis is practical significance.  Did the response variable change enough for the study to provide insight?  Graph the results and evaluate from a scientific or engineering perspective.  Then you can do the stats. I'm personally not a big fan of p-values as the ultimate test for significance unless you really understand what makes up the error term (e.g., factors and interactions of factors that are not specifically manipulated in your experiment but do vary aka. noise) and have some knowledge as to how representative the error terms are to the true random errors.  I prefer Daniel plots (Normal and half normal plots) for the whole plot and subplot separately (as each has its own associated estimate of random errors).  Less chance of biasing the errors and give a good relative comparison of effects.

Victor_G · Answer

Hi @Zhou69,

Welcome in the Community !
Have you already checked the JMP help section related to split plot design and an example of an analysis ? : https://www.jmp.com/support/help/en/17.2/index.shtml#page/jmp/splitplot-experiment.shtml#ww557792

The analysis done under "REML Variance Component Estimates" display several interesting informations related to your question :
First, you can evaluate how much variance can be attributed to the random whole plot effect, compared to the total variation. This way you can compare if the error term associated with the whole plot replication is smaller or bigger than the residual error term. In other words, how much variability is captured through the random whole plot effect, and how big is this variability compared to total experimental variability (aka the "practical" impact of the random whole plot effect on the experimental variability). This can help you evaluate and compare the practical impact of the whole plot variability on the experimental results total variability.
Second, you can effectively use the Wald p-value displayed, to assess if the random whole plot effect is statistically significant, meaning the response variance depends on the random effect. This can help you evaluate the statistical significance of the random whole plot effect.

You can combine these two informations to assess how much variability is captured through the whole plot effect, and assess if this variance component is statistically significant.

I hope this answer will help you,