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Link Among Factor Analysis, Parametric Tests and DOE

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  • #54199

    Marc van der Peet
    Guest

    Hi all,

    I’m working on my LSS project at the moment and was wandering my approach is right. After securing my mesasurement system is ok, I come up with several x’s which might influence my Y value. I reduced these x values using FA and am going to test them later using some non-parametric tests. Then afterwards I’m thinking of doing a DOE to test which levels of the response best benefit my Y.

    Good approach?

    Dear Regards,

    Marc

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    #194194

    Robert Butler
    Participant

    I don’t think using factor analysis for variable reduction is the right approach. With factor analysis the idea is that you will take observed variables and model them as linear combinations of factors. You examine the interdependencies between the observed variables in light of these factors as a means of reducing the set of variables in the data set.

    The big issue is the data set you would use to run such an analysis. Unless you have a very unusual situation, the data is going to be happenstance data (production data) which guarantees not only large,meaningless,interdependencies between the variables of interest but also guarantees complete masking of the effects of variables critical to the process.

    A much better approach would be to sit down with the people who run the process and spend a lot of time discussing process variables. Discussions of this type will provide the following:

    1. A list of variables the people in the know either know or suspect might be important.

    2. A list of critical process variables that are closely controlled and whose impact on the process, as seen through the lens of the available data, will not be observed.

    Armed with this list you can then ask that same group for a ranking of the variables on the list. I’d recommend a “secret ballot” approach. What you will quite likely find is very good agreement among the “ballots” and you can use the results of the polling to either run some univariate tests on the identified favorites and/or organize things for a screen design.

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    #194200

    Marc van der Peet
    Guest

    Thanks for the reply Robert. Only one question concerning the last part: “you can use the results of the polling to either run some univariate tests on the identified favorites and/or organize things for a screen design”.

    What do you mean exactly by this? Choose either an ANOVA or MONOVA for example?

    Dear Regards,

    Marc

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    #194202

    Robert Butler
    Participant

    What I meant was plotting and, after plotting, running some simple one X vs. one Y univariate regressions to get an idea of basic significant trending.

    The key point is the plotting – you will want to plot your list of possible X’s against Y (or Y’s as the case may be) and you will want to plot them against one another and look for things like trending, clustering, etc. Looking at the X’s against one another will give you a sense of confounding of the variables of interest.

    Looking at the X’s against the Y’s will give you a sense of correlation between the X and the Y and it will also give you a sense of the control (planned or unplanned) applied to a given X. One of the quickest ways to do this sort of thing is a matrix plot. Most of the better stat packages have this capability. In the event you don’t know what they look like I’m attaching an example to this post.

    Other plots would include histograms of the Y’s and, if the information is available, plots of the Y’s across time for given levels of the various X’s. This is a lot of work but it is what any good statistician does when they are given a data set and it is what any good black belt should do when they are attempting to guide an effort.

    The visual apprehension of the behavior of the data you are going to use as a basis for initial decision making goes beyond you and your immediate team. People are analog, not digital, and a well constructed graph will help you make your points concerning your decisions to anyone who might have an interest in your efforts. (“A picture is worth a thousand words.” isn’t just some cute phrase-it is a summation of the human condition)

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