# DOE Vs Regression Analysis

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• #37587

Nikunj
Participant

Hi,
What is diference between a regression analysis and DOE?
I mean to say when to use DOE and when Regression?
What is the advantage of DOE over regression and vice versa
Regards
Nikunj

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#110916

Robert Butler
Participant

They are two aspects of the same problem.  The object of a regression is to identify correlations between predictor (X’s) and response (Y’s) the object being to use the resultant equation as a means of identifying how changes in the X’s will impact the Y’s.
The object of an experimental design is to run the minimum number of experiments needed to allow the investigation of possible correlations between the X’s and the Y’s. Thus, the data from a design is the foundation which allows the construction of a correlation (regression) equation.
Design data, as opposed to happenstance data, also guards against the many pitfalls to which regression is prone.  Regression models are based on least squares which is a geometric fit to data and not a fit based on first principles.  Issues such as confounding, range of data, etc. play a crucial role in the adequacy of a regression model and, if they are not taken into account, they can completely undermine your efforts.

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#110917

Nanni
Participant

Simple:

Regression Analysis:
Y – Metric
X – Metric

DOE (ANOVA)
Y –  Metric
X – NO Metric

Logistic Regression Analysis:
Y – Ordinal or Nominal
X – Metric

Regards,
Nanni

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#110922

Robert Butler
Participant

One of the necessary limitations of six sigma training with respect to statistics is the need to establish a set of conservative rules for its use. If this isn’t done, the complexity of statistics is such that a beginner will almost certainly make serious mistakes when attempting to use statistics for the first time.
It is important to remember that these rules are conservative and deliberately ignore many accepted statistical practices precisely because to do otherwise would cause real problems for the beginner.  Consequently, it is your responsibility to recognize the need to constantly check those first usage rules against the reality of the statistics discipline as you continue to work as a six sigma professional.
The idea that DOE is ANOVA and that DOE applies only to Y as a metric and X as No metric is one of these beginner rules. A quick check of almost any good book on DOE will show that X and Y are more often than not metric and that the main reason for building a DOE is to be able to quantify, through a regression equation, the actual impact a unit change in an X will have on a response Y.
In a similar vein, the X’s and Y’s in a regression can be both metric and non-metric.  In the case of non-metric Y’s there are a number of regression methods such as logistic, log-linear, or negative binomial which are the regression methods of choice.  For each of these, the X’s can be both metric and non-metric as well.  In the case of the non-metric X’s the usual procedure is to employ dummy variables when running the regression analysis.

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#110925

Anonymous
Guest

Absolutely …
I once heard someone describe Six Sigma as a statistical method without any assumptions!
Of course, this is not quite true since most practitioners do realize that normality and homoscedasticity are important conditions.
Best regards,
Andy

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#110954

Nanni
Participant

Robert, I agree with you, but I want to add another thing.
When Y is non metric and X is non metric, sometimes you cann´t use the regression analysis, even with dummy variables. Then, Which analysis to use? Chi-square test is an option,  this is not a rule it depends which is your study objective.
But  you have to have in mind that not always  regression analysis is the solution.
Regards!

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#110956

Orlando
Participant

Hi Nikunj
I read somewhere awhile back and I come to agree that Regression does everything a DOE do plus more.  The writer went on to explain that the reason DOE is taught was because it was much easier to understand than Regression.  I’ll find that book if it’s still in my garage.

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#110965

Fer
Participant

Robert,
could you please suggest any book of statistics for Six Sigma practitioners?
Do you think that some of the most famous Six Sigma handbooks (Breyfogle, Pyzdek, etc) are enough detailed from this point of view?
Thanks

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#110989

Nikunj
Participant

Hi Orlando,
Could you name the author and title of the book
regards
Nikunj

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#110999

Robert Butler
Participant

Fer,
Back in February I made some recommendations concerning various statistics books I thought would be of value.  The link is below:
https://www.isixsigma.com/forum/showmessage.asp?messageID=39941
A few additional comments. The book by Hicks is old and as one other poster to that thread observed it can get tedious.  I value the book because of its examples.  It has numerous worked examples complete with the data. All of them are short enough so you can run the analysis with whatever statistics package you happen to have and compare your output to the book – a very inexpensive way to do hands on learning.
I don’t think there is any one book that would give you enough detail for the various facets of analysis.  I think the books I listed in the post above are the bare minimum.
Nanni,
To the best of my knowledge you can run regression with anything. In the case of categorical Y’s and X’s the question that should be asked is  – why would you want to analyze this kind of data with regression methods?  As you noted – categorical analysis would probably be the tool of choice.
The point of my comments concerning regression was not to propose the method as some kind of cureall.  I responded as I did because, if one was not aware of the caveats surrounding basic six sigma training, your post, which is identical to the “crib” sheet I was given in my six sigma course,  strongly implies that DOE and regression are not connected.This is simply not true.
If one fails to understand that a DOE is the best base one can have for constructing a meaningful regression equation then the value of efforts with respect to both (design and regression) are much diminished.
While I don’t know the specifics of Orlando’s statement “Regression does everything a DOE do plus more.”  I would suggest the only way an author could make such a claim would be if that individual failed to understand the relationship between DOE and regression.

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#111055

Orlando
Participant

Hi Nikunj
I looked all over my garage and I can’t find the book but I’ll know I’ll find it later when I won’t be looking for it.  Let me try and remember why the author made that statement.
I believe the author was refering to analysis of covariance where the features of analysis of variance and regression are combined.  It can be used for observational studies or design experiments.  Qualitative factors as well as quantitative factors can be used together.  If only quantiative factors are used, then we have regression.  If only qualitative factors are used, then we have regression with Indicator (dummy) factors.  His statement that the reason analysis of variance was even taught was because it was much easier to understand.  Oh well.
I’ll try to organize my statistical books in the near future and find that damn thing.

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