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## Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

I have DOE results that have a Effects Summary section with a p-value of 0.03866 for parameter A.   In the Effect Tests section that same parameter has a p-value of 0.9353.  The Parameter Estimate for that variable is also 0.9353. Why is the Effect Summary different from the Effect Test and the Parameter estimate and what does each test mean?

Thanks

Drink deep, or taste not the Pierian spring
2 ACCEPTED SOLUTIONS

Accepted Solutions
Solution

## Re: Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

If you have modeled more than one response (Y role) at the same time without the option to fit individual models, then the Summary Report displays the the most significant result for each term from one of the models.

In the case of a single response or individual fits, the Summary Report and the Effect Tests are essentially the same. They test the significance of adding a term to a model given the other terms are already entered. The null hypothesis is that the additional term represents a negligible effect.

The Parameter Estimates often appears to be the same as the Effect Tests (redundant information) in some common cases but they are not the same. The parameter estimates table uses a t-test against the null hypothesis that parameter is zero. The effects table uses a F-test against a zero change in the model sum of squares.

The differences between these two reports are more apparent when you have a categorical factor with more than two levels.

There is a hierarchy of sorts of information, top to bottom. The whole model test, the effect tests, and the parameter estimates.

Learn it once, use it forever!
Solution

## Re: Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

If you fit the same model to five responses, you will get five unique sets of parameter estimates, one for each response. So each term has five estimates. The Effect Summary report shows the most significant estimate for each term.

Learn it once, use it forever!
4 REPLIES 4
Highlighted

## Re: Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

Take another look at the Effect Summary, the order of the factors is by importance. The tables of  Effect Tests and Parameter Estimates the factors are listed by user specified order in the model dialog.

If you can, anonymize your data or display a portion of these tables without violating security.

Solution

## Re: Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

If you have modeled more than one response (Y role) at the same time without the option to fit individual models, then the Summary Report displays the the most significant result for each term from one of the models.

In the case of a single response or individual fits, the Summary Report and the Effect Tests are essentially the same. They test the significance of adding a term to a model given the other terms are already entered. The null hypothesis is that the additional term represents a negligible effect.

The Parameter Estimates often appears to be the same as the Effect Tests (redundant information) in some common cases but they are not the same. The parameter estimates table uses a t-test against the null hypothesis that parameter is zero. The effects table uses a F-test against a zero change in the model sum of squares.

The differences between these two reports are more apparent when you have a categorical factor with more than two levels.

There is a hierarchy of sorts of information, top to bottom. The whole model test, the effect tests, and the parameter estimates.

Learn it once, use it forever!

## Re: Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

Thank you for the response it was very helpful.   In fact there is more than one response.  I have one more question regarding your answer.  In the first sentence you state "...then the Summary Report displays the most significant result for each term from one of the models".  By the term one of the models do you mean a model with just one response (Y role?

Thanks

Drink deep, or taste not the Pierian spring
Solution

## Re: Least Squares Fit; Effects Summary vs Effect Tests vs Parameter Estimates

If you fit the same model to five responses, you will get five unique sets of parameter estimates, one for each response. So each term has five estimates. The Effect Summary report shows the most significant estimate for each term.

Learn it once, use it forever!