DSD with block - Should the block be included during analysis?

[#1]

Hi All,

I've created a DSD DOE - 6 parameters with added blocks with center runs to estimate quadratic effects, in total of 18 runs.

DOE run, data obtained. now come the analysis part. I use this option to analyze the DSD DOE.

The question is: should the Block be included in the X-roles area?

Thanks in advance,

AmirSS

[#2]

Hi @AmirSS ,

Yes.

You should include the block in your analysis.

The reason for including a block in your design is to account for expected differences in the response(s) between your blocks of runs that is not within your control.

You need to account for this uncontrolled variation in your model.

You should find that the Fit Definitive Screening analysis script in your design table will bring up the dialog with all factors and the block included as X's.

After running the Fit Definitive Screening analysis you can click Make Model to bring up the Fit Model dialog with the selected effects. At this point you should add the block as a random effect (see screenshot): Select Block > Attributes red triangle menu > Random Effect. The Method will default to the recommended REML.

This free chapter download from the book Optimal Design: A Case Study Approach talks in more detail about block effects and REML. I highly recommend this book for anyone wanting to learn beyond the basics of DOE.

I hope that helps.

Regards,

Phil

[#3]

Hi @Phil_Kay 

Thanks for the explanation. I find the free chapter is very useful. Nevertheless, a beginner here need further assistance.

I would like to further analyze my DSD. Below are the result generated by JMP after i chose the REML method.

Can you kindly explain how to interpret the parameter estimates, REML variance component estimates and also the fixed effect tests?

Is there something wrong with the DOE that cause the Prob>|t| and Prob>F to be blank?

Thank you in advance.

[#4 · Accepted solution]

@AmirSS, I'm a little late to the discussion, but had some questions/comments and suggestions:

1. DSD are 3-level designs for the most part, so I don't understand what you mean by you added center runs?

2. There is a handy little "?" in the tool bar (just to the right of the arrow).  If you select it and then move it to the place in your output that you want an explanation and click, you will get be forwarded to information about that analysis.

3. Parameter estimates are the beta coefficients in the linear model and the intercept is the Y-intercept.  Variance components are estimates of the variation of each component and fixed effects tests are essentially ANOVA with the model being separated into the individual terms.

4. The reason for no prob. statements is the model is saturated, all degrees of freedom are assigned or there is no estimate of the error term, hence no basis for a statistical test.

I will also add, there are other ways to handle blocks than what is depicted in the chapter previously referenced.  See:

Sanders, D., Leitnaker M., and McLean R. (2002) “Randomized Complete Block Designs in Industrial Studies” Quality Engineering, Vol. 14, Issue 1

[#5]

Sorry @statman , I didn't see this reply before I posted my own reply.

If it is okay, I would like to respond to 2 of your points.

"I don't understand what you mean by you added center runs?"  This is an option is designing DSDs that you can see in the screenshot from @AmirSS at the top of this thread. JMP will add center points to each block that you specify.

"The reason for no prob. statements is the model is saturated" - this is often the explanation for not seeing p-values but I do not think that is what is happening here. The model does not appear to have many effects. I believe that we have a DSD for 6 factors with 4 added runs, which would be 17 runs. Plus there will be more runs for the added center points for the blocks. So I don't think we are in the situation of having as many parameters to estimate as we have runs.

I hope that my responses are helpful.

Regards,

Phil

[#6]

Hi @AmirSS,

First of all, you might like to know that I recorded a short presentation about Model Selection for Designed Experiments with Blocks.

There is not necessarily a problem with your DOE. What you have is a problem with the REML variance components estimation. You have a warning: "Convergence Questionable."

If the estimation method fails to converge then it is not possible to calculate p-values and degrees of freedom.

There are different reasons for why the covergence can fail.

I suggest that you search for "Convergence Questionable" here in the JMP Community. There are lots of threads about this.

You could also attach the data so that we can take a look. You might wish to anonymise it first.

Regards,

Phil