[R] data analysis for partial two-by-two factorial design

[Bert Gunter]

David:

I believe your response on SO is incorrect. This is a standard OFAT (one
factor at a time) design, so that assuming additivity (no interactions),
the effects of drugA and drugB can be determined via the model you rejected:

For example, if baseline control (no drugs) has a response of 0, drugA has
an effect of 1, drugB has an effect of 2, and the effects are additive,
with no noise we would have:

> d <- data.frame(drugA = c("n","y","y"),drugB = c("n","n","y"))
> y <- c(0,1,3)

And a straighforward inear model recovers the effects:

> lm(y ~ drugA + drugB, data=d)

Call:
lm(formula = y ~ drugA + drugB, data = d)

Coefficients:
(Intercept)       drugAy       drugBy
  1.282e-16    1.000e+00    2.000e+00

As usual, OFAT designs are blind to interactions, so that if they really
exist, the interpretation as additive effects is incorrect.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Mon, Mar 5, 2018 at 2:03 PM, David Winsemius <dwinsemius at comcast.net>
wrote:

>
> > On Mar 5, 2018, at 8:52 AM, Ding, Yuan Chun <ycding at coh.org> wrote:
> >
> > Hi Bert,
> >
> > I am very sorry to bother you again.
> >
> > For the following question, as you suggested, I posted it in both
> Biostars website and stackexchange website, so far no reply.
> >
> > I really hope that you can do me a great favor to share your points
> about how to explain the coefficients for drug A and drug B if run anova
> model (response variable = drug A + drug B). is it different from running
> three separate T tests?
> >
> > Thank you so much!!
> >
> > Ding
> >
> > I need to analyze data generated from a partial two-by-two factorial
> design: two levels for drug A (yes, no), two levels for drug B (yes, no);
> however, data points are available only for three groups, no drugA/no
> drugB, yes drugA/no drugB, yes drugA/yes drug B, omitting the fourth group
> of no drugA/yes drugB.  I think we can not investigate interaction between
> drug A and drug B, can I still run  model using R as usual:  response
> variable = drug A + drug B?  any suggestion is appreciated.
>
> Replied on CrossValidated where this would be on-topic.
>
> --
> David,
>
> >
> >
> > From: Bert Gunter [mailto:bgunter.4567 at gmail.com]
> > Sent: Friday, March 02, 2018 12:32 PM
> > To: Ding, Yuan Chun
> > Cc: r-help at r-project.org
> > Subject: Re: [R] data analysis for partial two-by-two factorial design
> >
> > ________________________________
> > [Attention: This email came from an external source. Do not open
> attachments or click on links from unknown senders or unexpected emails.]
> > ________________________________
> >
> > This list provides help on R programming (see the posting guide linked
> below for details on what is/is not considered on topic), and generally
> avoids discussion of purely statistical issues, which is what your query
> appears to be. The simple answer is yes, you can fit the model as
> described,  but you clearly need the off topic discussion as to what it
> does or does not mean. For that, you might try the stats.stackexchange.com
> <http://stats.stackexchange.com> statistical site.
> >
> > Cheers,
> > Bert
> >
> >
> > Bert Gunter
> >
> > "The trouble with having an open mind is that people keep coming along
> and sticking things into it."
> > -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> >
> > On Fri, Mar 2, 2018 at 10:34 AM, Ding, Yuan Chun <ycding at coh.org<mailto:
> ycding at coh.org>> wrote:
> > Dear R users,
> >
> > I need to analyze data generated from a partial two-by-two factorial
> design: two levels for drug A (yes, no), two levels for drug B (yes, no);
> however, data points are available only for three groups, no drugA/no
> drugB, yes drugA/no drugB, yes drugA/yes drug B, omitting the fourth group
> of no drugA/yes drugB.  I think we can not investigate interaction between
> drug A and drug B, can I still run  model using R as usual:  response
> variable = drug A + drug B?  any suggestion is appreciated.
> >
> > Thank you very much!
> >
> > Yuan Chun Ding
> >
> >
> > ---------------------------------------------------------------------
> > -SECURITY/CONFIDENTIALITY WARNING-
> > This message (and any attachments) are intended solely f...{{dropped:28}}
> >
> > ______________________________________________
> > R-help at r-project.org<mailto:R-help at r-project.org> mailing list -- To
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> posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius
> Alameda, CA, USA
>
> 'Any technology distinguishable from magic is insufficiently advanced.'
>  -Gehm's Corollary to Clarke's Third Law
>
>
>
>
>
>

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