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

Bert Gunter bgunter.4567 at gmail.com
Tue Mar 6 00:04:28 CET 2018

```But of course the whole point of additivity is to decompose the combined
effect as the sum of individual effects.

"Mislead" is a subjective judgment, so no comment. The explanation I
provided is standard. I used it for decades when I taught in industry.

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 3:00 PM, David Winsemius <dwinsemius at comcast.net>
wrote:

>
> > On Mar 5, 2018, at 2:27 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
> >
> > 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:
>
> >> three groups, no drugA/no drugB, yes drugA/no drugB, yes drugA/yes drug
> B, omitting the fourth group of no drugA/yes drugB.
>
> >
> > 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"))
>
> d2 <- data.frame(trt = c("Baseline","DrugA_only","DrugA_drugB")
> >
> > > 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
>
> I think the labeling above is rather to mislead since what is labeled
> drugB is actually A&B. I think the method I suggest is more likely to be
> interpreted correctly:
>
> > d2 <- data.frame(trt = c("Baseline","DrugA_only","DrugA_drugB"))
> >  y <- c(0,1,3)
> > lm(y ~ trt, data=d2)
>
> Call:
> lm(formula = y ~ trt, data = d2)
>
> Coefficients:
>    (Intercept)  trtDrugA_drugB   trtDrugA_only
>      2.564e-16       3.000e+00       1.000e+00
>
> --
> David.
> >
> > 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
> UNSUBSCRIBE and more, see
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> > > 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
> 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
> >
> >
> >
> >
> >
> >
>
> 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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