DOE: how is Sum of Squares of each effects calculated?

[#1]

Hi,

How is sum of squares (SS) of each effects calculated in DOE parameter estimate table?

any simple 2-3 factors DOE example to share?

Thanks

[#2]

Sure, I'll pile on...The default SS analysis for most, if not all, statistical software programs is Type III.  This is because Type III's are robust to the order which you enter the terms in the model.  When the computer calculates the Type III's, it first accounts for ALL of the other terms in the model and assesses how much does the term in question explain of the remaining variation.  When using Type I, order matters.  The calculations are performed in the order the model is written. Type I would be the appropriate analysis for nested or hierarchical components of variation.

[#3]

The problem is that you set the modeling type of Temperature to Ordinal. I would use Continuous. But Montgomery used Nominal for both Material and Temperature. When I change the modeling type to match, I get the same result:

I just verified that the data in your data table match the data presented in Doug's book.

I added the usual column properties for factors and responses, but it did not change the outcome. I thought that the significance might be affected if the factor levels were not coded first.

JMP makes sure that all the data types, modeling types, and column properties are properly set when you design the experiment with JMP. You have to manually add or adapt all the meta-data when you enter data by hand.

[#4]

If I set the modeling type of Temperature to Continuous then I'm doing linear regression, with slopes and intercepts, and interactions between a linear effect and an attribute effect.  There is then one degree of freedom for Temperature, plus loss of degrees of freedom for interactions between Temperature and Material Type.  That is not what Montgomery did.  Why do the calculations for JMP differ from Montgomery.  Montgomery's demonstration is plain-vanilla ANOVA with two factors each at three (attribute) levels.  

[#5]

Why do the calculations for JMP differ from Montgomery.  Montgomery's demonstration is plain-vanilla ANOVA with two factors each at three (attribute) levels.

If you look at @Mark_Bailey 's latest example, the JMP output is the same.  To have JMP give you plain-vanilla ANOVA based on two categorical factors, set both of the factors to nominal and the default ANOVA table will agree with Montgomery.

[#6]

Doug was illustrating how experimenters and statisticians thought about the analysis 100 years ago when factorial designs were introduced. It is still valid, but it is not the only way to think about it. It is a balanced design and treats all factors as if they were nominal categories. Again, that is still valid but only one way. Why did they do it that way? It was the only way available to them at the time. So that they could perform the analysis by hand. A 'computer' in the 1920s was a job title - no kidding. Modeling the data this way allowed people to compute the simple sums that Doug shows by hand.

Today we use computers and software to perform regression analysis. We can realistically treat Temperature as a continuous effect. We can specify the linear model in very flexible terms and then compute an optimal design for estimating the parameters or the response. The design is fixed in this case but I can propose other modeling types and terms. Here is one possibility:

It might require additional runs to verify one of these models as accurate.

[#7]

JMP uses Type III Sum of Squares by default.

Please see how the factor models determine the results.

[#8]

The book contains JMP output.  Temperature has two degrees of freedom, so it's not being treated as continuous.

[#9]

For sure the setting of Nominal data type caused the difference to Montgomery.  What I'd like to learn is how sums of squares are calculated for nominal factors.

[#10]

on a separate note ... wouldn't it be nice if messages appeared in chronological order; would make it much easier to follow the discussion.

[#11]

Or anyway more compact, like Reddit, to be able to see the indenting without so much which space.  Kudo and Reply button could be on the left and much smaller.