[R-sig-teaching] Unbalanced factorial designs

[Ista Zahn]

On Sat, Feb 28, 2009 at 12:34 AM, G. Jay Kerns <gkerns at ysu.edu> wrote:
> Dear Ista,
>
>> creating those  lovely tables.)  Nice job.
>>
>> Bill
>>
>
> I agree, nice job.  :-)  It is great that you are writing about these
> issues, and even better that you are sharing it.
>
> In my classes, I discuss correlated contrasts using the geometric
> approach which is in many of the classical texts.  I am not sure how
> your audience would respond to this.
>
> I didn't notice any glaring errors in your interpretation, but I
> didn't study it thoroughly, either.  I trust that some of the masters
> on this list will catch mistakes much more efficiently than I do.
>
> A few thoughts that in my view may improve your document:
>
> 1) Page 6, paragraph 2, line 5:  "The problem is that it is pretty
> obvious...".  When I first read this, it was not obvious.  After
> glancing at the table, it was plausible.  But after looking at a
> *graph*, yes, it was obvious.  A visual display here might be a good
> idea.  One option would be a two-way interaction plot.  There is one
> in the HH package, and you can even get one in Rcmdr with
> RcmdrPlugin.HH:
>
> library(HH)
> interaction2wt(salary ~ education + gender, data = D)
>
> (the dataframe D is dumped at the bottom of this email).
>

Thanks, this is an excellent suggestion. You're right that it's much
clearer when you plot the data.

> 2)  I got the same Type III and Type II tables as you did, but the
> Type II table was different...?
>
> library(car)
> options(contrasts=c("contr.Sum", "contr.poly"))
>
> salary.lm <- lm(salary ~ gender + education + gender:education, data = D)
> summary(salary.lm)
>
> Anova(salary.lm)  #  Type II tests
> anova(salary.lm)  #  Type I tests
> Anova(salary.lm, type = "III")  #  Type III tests
>

I'll investigate and try to figure out why we got different results, thanks.
>
> 3)  I typically refrain from using the language that you have used
> concerning "ignoring" and "controlling", etc.   I stick to the
> parametric jargon of column, row, and grand means.  This makes for
> precise statements without any fear of misunderstanding, but again,
> instructors should always keep the background of the audience in mind.
>
I'll probably stick with the current terms, simply because they are
consistent with the textbook we are using.
>
> Regardless of whether you like the ideas or not, the fact that you are
> going to the trouble of preparing a document like this for the class
> is admirable in its own right.  Keep it up.  :-)
>
Thanks for the encouragement!

-Ista


> Cheers,
> Jay
>
> P.S. a once-over with a spell check would be good (it's going to
> students, right?).
>
>
>
> # the data
>
> D <-
> structure(list(ID = 1:22, salary = c(24L, 26L, 25L, 24L, 27L,
> 24L, 27L, 23L, 15L, 17L, 20L, 16L, 25L, 29L, 27L, 19L, 18L, 21L,
> 20L, 21L, 22L, 19L), gender = structure(c(1L, 1L, 1L, 1L, 1L,
> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
> 2L), .Label = c("Female", "Male"), class = "factor"), education =
> structure(c(1L,
> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
> 2L, 2L, 2L, 2L, 2L), .Label = c("Collegeeducation", "Nocollegeeducation"
> ), class = "factor"), congend = structure(c(1L, 1L, 1L, 1L, 1L,
> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
> 2L), .Label = c("1", "-1"), class = "factor"), coneduc = structure(c(1L,
> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
> 2L, 2L, 2L, 2L, 2L), .Label = c("1", "-1"), class = "factor"),
>    congendeduc = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>    2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("1",
>    "-1"), class = "factor")), .Names = c("ID", "salary", "gender",
> "education", "congend", "coneduc", "congendeduc"), class =
> "data.frame", row.names = c(NA, -22L))
>
>
>
>
>
> ***************************************************
> G. Jay Kerns, Ph.D.
> Associate Professor
> Department of Mathematics & Statistics
> Youngstown State University
> Youngstown, OH 44555-0002 USA
> Office: 1035 Cushwa Hall
> Phone: (330) 941-3310 Office (voice mail)
> -3302 Department
> -3170 FAX
> E-mail: gkerns at ysu.edu
> http://www.cc.ysu.edu/~gjkerns/
>