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Level II

## Color Map on Correlations - any advise about correlation value threshold ?

Dear all,

When using color map on correlations, I was wondering if any correlation value threshold was commonly accepted as a limit to not cross to estimate the effect of a single parameter ? 0.3 ? 0.2 ?

Thanks,

Hugo

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Staff

## Re: Color Map on Correlations - any advise about correlation value threshold ?

I assume that you are referring to the plot that is provided in the Design Diagnostic outline part of a design platform, such as Custom Design.

I would say that there is no theoretical or practical threshold. There is no 'rule of thumb' for the correlation of the estimates. Why?

Because the correlation inflates the variance of your estimates. This inflation can be expressed in several ways, such as the Variance Inflation Factor (VIF). That increase will reduce the power of your hypothesis tests for terms or individual parameters. It will increase the length of the confidence intervals for the same estimates. All of these changes are generally in the wrong direction. So we need to examine the correlations as you have done to determine if our design is sufficient. But to evaluate the correlations requires some information about the response variance you are dealing with. If the response variance is small then you can tolerate a larger VIF. If it is otherwise large, then you can tolerate only a smaller VIF. (So the general rule of thumb that "VIF < 10" is also meaningless for the same reason.)

It also depends on the nature of the experiment and luck. For example, if it is a screening experiment and through luck your situation follows the key screening principles, then you will not have to estimate most of the parameters. The original design is now much larger relative to the final terms in the model. The projection of the design into a smaller model will change the correlation for the better. So correlation is not fatal.

Finally, be sure to use a wide range for continuous factors. Why? It will produce a larger effect on the response, which will increase the power and decrease the relative length of the confidence intervals in spite of the correlation.

Learn it once, use it forever!
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Level VI

## Re: Color Map on Correlations - any advise about correlation value threshold ?

Generally speaking, measures of correlation are descriptive, not inferential, statistics. Hence you won't see much if anything in the literature regarding a correlation statistic threshold for parameter estimation. Parameter estimation is at it's core, an inferential statistic, requiring a different statistical methodological approach such as, but not limited to, ordinary least squares regression.

Highlighted
Staff

## Re: Color Map on Correlations - any advise about correlation value threshold ?

I assume that you are referring to the plot that is provided in the Design Diagnostic outline part of a design platform, such as Custom Design.

I would say that there is no theoretical or practical threshold. There is no 'rule of thumb' for the correlation of the estimates. Why?

Because the correlation inflates the variance of your estimates. This inflation can be expressed in several ways, such as the Variance Inflation Factor (VIF). That increase will reduce the power of your hypothesis tests for terms or individual parameters. It will increase the length of the confidence intervals for the same estimates. All of these changes are generally in the wrong direction. So we need to examine the correlations as you have done to determine if our design is sufficient. But to evaluate the correlations requires some information about the response variance you are dealing with. If the response variance is small then you can tolerate a larger VIF. If it is otherwise large, then you can tolerate only a smaller VIF. (So the general rule of thumb that "VIF < 10" is also meaningless for the same reason.)

It also depends on the nature of the experiment and luck. For example, if it is a screening experiment and through luck your situation follows the key screening principles, then you will not have to estimate most of the parameters. The original design is now much larger relative to the final terms in the model. The projection of the design into a smaller model will change the correlation for the better. So correlation is not fatal.

Finally, be sure to use a wide range for continuous factors. Why? It will produce a larger effect on the response, which will increase the power and decrease the relative length of the confidence intervals in spite of the correlation.

Learn it once, use it forever!
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Level II

## Re: Color Map on Correlations - any advise about correlation value threshold ?

Hi Mark and P-Bartell,

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