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help > RE: ANCOVA with 3 groups
Apr 6, 2015 07:04 PM | Alfonso Nieto-Castanon - Boston University
RE: ANCOVA with 3 groups
Hi Liron,
The two contrasts are exactly equivalent, but the former contrast is just a more parsimonious definition. The reason for this is in the latter contrast the last row is a linear combination of the first two (first row + second row = third row), so the contrast matrix is rank defficient (rank equals 2 despite having 3 rows). Conceptually this simply means that a test for ( A<>B OR B<>C ) is just equivalent to a test for ( A<>B OR B<>C OR A<>C), i.e. the last test in the OR conjunction of the latter contrast does not add any information that was not originally contained in the first two tests. The stats of the two contrasts should be exactly the same (F stats, p-values, and degrees of freedom of the tests), the reason why you are seeing different "beta values / effect sizes" in the table displays is because these are multivariate tests, and to be precise the effect sizes are multivariate (two-dimensional in the former case, and three dimensional in the latter case) but CONN is just summarizing these multivariate effect sizes into a single value for display purposes in those tables (displaying the norm of these vectors). If you look at the actual effect size vectors (e.g. using 'display values' or 'import values') you will see that the latter contrast three-dimensional effect size is just composed of the two values in the former contrast two-dimensional effect size plus one additional value which is always the sum of the first two values.
Hope this helps clarify
Alfonso
Originally posted by Liron Bensky:
The two contrasts are exactly equivalent, but the former contrast is just a more parsimonious definition. The reason for this is in the latter contrast the last row is a linear combination of the first two (first row + second row = third row), so the contrast matrix is rank defficient (rank equals 2 despite having 3 rows). Conceptually this simply means that a test for ( A<>B OR B<>C ) is just equivalent to a test for ( A<>B OR B<>C OR A<>C), i.e. the last test in the OR conjunction of the latter contrast does not add any information that was not originally contained in the first two tests. The stats of the two contrasts should be exactly the same (F stats, p-values, and degrees of freedom of the tests), the reason why you are seeing different "beta values / effect sizes" in the table displays is because these are multivariate tests, and to be precise the effect sizes are multivariate (two-dimensional in the former case, and three dimensional in the latter case) but CONN is just summarizing these multivariate effect sizes into a single value for display purposes in those tables (displaying the norm of these vectors). If you look at the actual effect size vectors (e.g. using 'display values' or 'import values') you will see that the latter contrast three-dimensional effect size is just composed of the two values in the former contrast two-dimensional effect size plus one additional value which is always the sum of the first two values.
Hope this helps clarify
Alfonso
Originally posted by Liron Bensky:
Thank you very much Alfonso, this is very
helpful!! Can I ask a clarification question? What is the
difference between the contrast you specified [1 -1 0 0 0 0 0; 0 1
-1 0 0 0 0], and [1 -1 0 0 0 0 0; 0 1 -1 0 0 0 0; 1 0 -1 0 0 0
0 0]? My guess was that I'll need the later in order to specify any
possible group effects, and I see that these two contrasts give
slightly different beta values. If you could shed some light on
this it would be a great help.
Thank you very much!!
Liron.
Thank you very much!!
Liron.
Threaded View
| Title | Author | Date |
|---|---|---|
| Liron Bensky | Mar 30, 2015 | |
| Alfonso Nieto-Castanon | Apr 6, 2015 | |
| Liron Bensky | Apr 6, 2015 | |
| Alfonso Nieto-Castanon | Apr 6, 2015 | |
| Liron Bensky | Apr 6, 2015 | |
| Fred Uquillas | Apr 7, 2015 | |
| Alfonso Nieto-Castanon | Apr 7, 2015 | |
| Liron Bensky | Apr 13, 2015 | |