Jim Seward <[email protected]> asks:
> With Ken Higbee's help I was able to find -mtest()-. I'm still not sure
> how to use it.
>
> I have a 2 by 2 anova with insignificant main effects but a signifcant
> interaction. I like to explore any differences between cell means. I not
> sure how to specify the matrix for -test[matrix name]-. I suppose it's
> the design matrix but when I use the "simian" approach and try different
> things I get the error message that the matrix is nonconformable.
Moments before I saw Jim's statalist posting I had sent him an
answer to a similar question that I received privately yesterday.
Here is part of what I wrote.
First, if you haven't already, look at the FAQs found at
http://www.stata.com/support/faqs/stat/#anova
In particular,
http://www.stata.com/support/faqs/stat/test1.html
gives some examples of the -test()- option of -test- after -anova-.
Additionally, you might find the following .do files instructive.
just copy them out from below and place them in twobytwo.do and
paint.do respectively. In stata type -do twobytwo- and then read
through the resulting output paying attention to the comments I
placed in the do file. Then you can type -do paint- for a more
involved example. If your emailer wraps lines, you will have to
fix them before running the do files.
Ken Higbee [email protected]
StataCorp 1-800-STATAPC
*================= Begin of twobytwo.do ============================
* some made up data
clear
input a b y
1 1 46
1 1 48
1 1 44
1 2 9
1 2 12
1 2 15
2 1 8
2 1 9
2 1 13
2 2 60
2 2 55
2 2 35
end
* A look at the data
list
tabulate a b , summarize(y) means
* The standard ANOVA
anova y a b a*b
* ========================================================
* Do it as a cell means model
* group goes 1 to 4 for the 4 cells of the overall model
egen group = group(a b)
* this table shows how the a and b relate to group
tabulate a b, summarize(group) means
* this is the cell means model ANOVA
* you might consider this output unimportant ...
anova y group, noconstant
* ... but when you look at the underlying regression ...
anova , regress
* ... you see the means of your 2x2 table
* It is easy to use test after the cell means ANOVA
* to get a test of A1 vs A2, B1 vs B2, and the interaction
mat A = (1,1,-1,-1)
mat B = (1,-1,1,-1)
mat AB = (1,-1,-1,1)
mat C = A \ B \ AB
test , test(C) mtest
* lincom is also sometimes helpful
* What is the estimate of a1 minus a2
lincom (_b[group[1]] + _b[group[2]] - _b[group[3]] - _b[group[4]])/2
* What is the estimate of b1 minus b2
lincom (_b[group[1]] - _b[group[2]] + _b[group[3]] - _b[group[4]])/2
* If you look back at the original table you will see that the -1
* and -3 answers above agree with subtracting the marginal means
* from the table.
* ==========================================================
* Do it using the "overparameterized" model (standard anova)
anova y a b a*b
* The regress option shows the underlying regression. (Notice
* all the dropped rows. This is why the standard ANOVA approach
* is called the "overparameterized" model
anova, regress
* The showorder option of test will show you the order of
* items for creating matrices for the test() option of test.
test, showorder
* Here are the matrices for testing
* The first column is for the constant
* The next two columns are for the 2 levels of a
* The next two columns are for the 2 levels of b
* The last four columns are for the 4 combinations of a and b
mat A = (0, 2,-2, 0,0, 1,1,-1,-1)
mat B = (0, 0,0, 2,-2, 1,-1,1,-1)
mat AB = (0, 0,0, 0,0, 1,-1,-1,1)
mat C = A \ B \ AB
* And here is the test
test , test(C) mtest
* Since this is just a 2x2 example, you will notice if you
* compare this output with what -anova- gave you -- they are
* the same.
*=================== End of twobytwo.do ============================
*================= Begin of paint.do ===============================
* The following data have been created to closely match the
* summary table (Table 8.1) on page 118 of:
* Milliken & Johnson (1984). "Analysis of Messy Data,
* Volume 1: Designed Experiments", Van Nostrand
* Reinhold Company.
clear
input paint paving lifetime
1 1 10.5
1 1 15
1 1 19.5
1 2 22.5
1 2 17
1 2 11.5
1 3 28
1 3 32
1 3 36
2 1 22.5
2 1 27
2 1 31.5
2 2 35
2 2 30
2 2 25
2 3 16
2 3 20
2 3 24
3 1 34
3 1 30
3 1 26
3 2 25
3 2 28
3 2 31
3 3 24
3 3 29
3 3 34
4 1 31
4 1 34
4 1 37
4 2 30
4 2 35
4 2 40
4 3 32
4 3 36
4 3 40
end
compress
label define paint 1 "Yellow I" 2 "Yellow II" 3 "White I" 4 "White II"
label define paving 1 "Asphalt I" 2 "Asphalt II" 3 "Concrete"
label values paint paint
label values paving paving
* This matches Table 8.1
tabulate paint paving, summarize(lifetime) nostandard nofreq
* This matches closely the ANOVA table shown in Table 8.2
* (small differences in Residual and Total Error due to me
* creating the data as best I could from just the means from
* Table 8.1.)
anova lifetime paint paving paint*paving
* The -showorder- option of -test- indicates the number of
* columns and what they represent
test, showorder
* In the book they set out 3 interesting contrasts on paints
* (see Table 8.3)
* c1 is for Yellow I vs. Yellow II
mat c1 = (0, 3,-3,0,0, 0,0,0, 1,1,1,-1,-1,-1,0,0,0,0,0,0)
* c2 is for White I vs. White II
mat c2 = (0, 0,0,3,-3, 0,0,0, 0,0,0,0,0,0,1,1,1,-1,-1,-1)
* c3 is for Yellow vs. White
mat c3 = (0, 3,3,-3,-3, 0,0,0, 1,1,1,1,1,1,-1,-1,-1,-1,-1,-1)
* They indicate 2 interesting contrasts on pavement
* c4 is for Asphalt I vs. Asphalt II
mat c4 = (0, 0,0,0,0, 4,-4,0, 1,-1,0,1,-1,0,1,-1,0,1,-1,0)
* c5 is for Asphalt vs. Concrete
mat c5 = (0, 0,0,0,0, 4,4,-8, 1,1,-2,1,1,-2,1,1,-2,1,1,-2)
* In Table 8.4 they show 6 contrasts for the paint*pavement
* interaction. I could just type them out, but instead I
* use some loops and create them from the c1 - c5 I already
* have
forvalues j=4/5 {
forvalues i=1/3 {
mat c`i'`j' = J(1,20,0)
forvalues k=1/20 {
mat c`i'`j'[1,`k'] = c`i'[1,`k'] * c`j'[1,`k']
}
}
}
* I can combine these row vectors together into a matrix with
* 11 rows and 20 columns
mat C = c1 \ c2 \ c3 \ c4 \ c5 \ c14 \ c24 \ c34 \ c15 \ c25 \ c35
mat list C
* Now I can use that C matrix in the -test()- option of -test-
* The -mtest- option gives me the results for each row
test, test(C) mtest
* I could get Bonferroni adjusted p-values with
test, test(C) mtest(bonferroni)
*=================== End of paint.do ===============================
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
