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
The answer to your question can be found in any basic regression textbook. There are some fairly simple calculations that can be performed by hand if you happen to have only a single factor. Otherwise the calculations will involve matrix algebra.
You might want to consider enrolling in the free online statistics course titled "Statistical Thinking for Industrial Problem Solving". Based on the questions you have been asking, you might want to concentrate on the hypothesis testing, regression, and design of experiments portions of that course.
This post is a couple years old, but I too would like to know how the sum of squares is calculated. I refer specifically to the Effect Tests report.
I went to a basic regression textbook to learn. The book is called "Design and Analysis of Experiments" by Douglas C. Montgomery, 6th Edition. In that book there is an example calculation. Example 5-1 is a full factorial experiment with two factors and four replications. I have entered the data into Excel, Minitab and JMP and have compared the results to Montgomery. Minitab and Excel Analysis Toolpak match Montgomery, JMP does not.
The calculations from the text are attached as an image. So are images from Minitab and Excel. Also JMP, with and without the interaction term. The JMP project files is attached, with data table and Fit Least Squares report.
Across all the analyses, the sums of squares match except for JMP's Sum of Squares for Material Type in Effects Test. Therefore, its p-value is also different, making it appear as if the factor is insignificant. How is this particular SS calculated?
In the JMP output, Sum of Squares for Model in the Analysis of Variance matches the sum of SS from the model terms in Montgomery, Minitab, and Excel. It is not equal to the sum of SS for the model terms in JMP's Effect Test report. Why is this?
When the interaction is removed from the model, then the Sum of Squares for Material Type is the same as in Montgomery. Why is that? Why does the inclusion of the interaction term affect the sum of squares for that particular main effect? The sum of Sum of Squares in the Effect Test is equal to the Sum of Squares for the Model term in the ANOVA table. Why does it work if the interaction is not in the model?
According to Montgomery's analysis, all three terms are significant (two main effects and interactions). According to JMP, one main effect and the interaction are significant. I really need to understand why JMP gets a different result for the significance of Material Type.
I didn't see anything in the JMP project. Would you mind attaching the data table so we can take a closer look.
Here is the data table.
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.
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.
The book contains JMP output. Temperature has two degrees of freedom, so it's not being treated as continuous.
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.
