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Re: st: 3-way continuous interaction - comparing simple slopes

From   David Hoaglin <>
Subject   Re: st: 3-way continuous interaction - comparing simple slopes
Date   Wed, 22 May 2013 22:48:40 -0400

Dear Roman,

What keeps you from using the result of testing whether the two slopes
are different and taking account of the actual direction of the
difference?  The usual test of the hypothesis of no difference
allocates half of the "Type I error" to each tail.  Thus, if the
difference is significant at a two-sided .05 level and positive AND
you can justify making a one-sided test (i.e., if the true difference
were in the other direction, it would really be of no consequence),
then that positive difference would be significant at a one-sided .025
level.  And if you wanted a one-sided .05 level, you could start with
a two-sided .10 level.

I generally have less interest in testing hypotheses, especially where
the null hypothesis is zero difference, because one knows that the
hypothesis is false without needing to test it.  I would not believe
that the true difference is zero to arbitrarily many decimal places.
The relevant question is whether the size of the difference departs
significantly from zero.  Thus, you should obtain a confidence
interval for the difference.  The CI will reflect the direction of the
difference, and you can judge significance by whether the CI includes

In your data on return on assets, that 3-factor interaction certainly
complicates the interpretation.  Where you are combining r(mean) +
r(sd) or r(mean) - r(sd), you should check that the resulting points
are still in the region of "predictor space" covered by the data.

The data on relative patent performance may require a different sort
of analysis, because of the large frequency of zeros.  If you have the
number of patents and the number of employees (and not just the
ratio), you may be able to use a zero-inflated model (e.g.,
zero-inflated Poisson) or a model that separates zero from nonzero.

I hope this discussion helps.


David Hoaglin

On Wed, May 22, 2013 at 11:28 AM, Roman Wörner <> wrote:
> Dear David,
> what I actually do is to regress two performance measures (return on assets
> and relative patent performance) on two strategies (strategy A and strategy
> B), their interaction and an additional moderator (vertical integration).
> Return on assets is negative for the bigger part of the sample - so, log or
> sqrt won't work. Relative patent performance (#of patents per employee) is
> null for the bigger part of the sample - again, log is not an option.
> I argue, that the relationship of the two strategies changes with the
> vertical integration of the firm. Based on the regression results I plot
> simple slope diagramms (high/low levels of strategy A/B @low levels of
> vertical scope and of high/low levels of strategy A/B @high levels of
> vertical scope). I then want to test if the slopes @high levels of vertical
> scope are significantly lower than the slopes @low levels of vertical scope.
> What the procedure described down below - lincom ($HzHw)-($HzLw) - does is
> to test whether the two slopes are different ("plain different") without
> considering the direction ("is one steeper than the other").
> To get rid of the 3-way interaction I initially considered dichotomizing the
> vertical scope variable into two groups (high/low) and split the sample. But
> I think that would make the situation even worse --> two samples and two
> models would require out of sample tests to compare the slopes...
> Kind regards,
> Roman

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