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help > RE: regression as anova
Jul 24, 2015 07:07 PM | Alfonso Nieto-Castanon - Boston University
RE: regression as anova
Hi Liron,
Well, approximately yes, but not exactly. The three-line contrast will test and OR conjunction of the two-line contrast and the last one-line contrast, so in general terms yes, you would expect to see there any regions that show a significant effect with any of the two original analyses. Now, the result will not be exactly a simple superimposition of those two original results, mainly because the three-line contrast is using an appropriate multivariate test to look at the conjunction of those two hypothesis, while, strictly speaking, simply superimposing the two original analyses masks would increase your false-positives rate beyond the original individual-test thresholds. In other words, when looking at N individual hypotheses, simply superimposing the N individual results can result in a false-positive rate as high as N times your original false-positive threshold (depending on how related those individual hypotheses are). That is why often one uses a conservative Bonferroni correction (dividing your individual hypothesis threhsolds by N) to get still-valid, though somewhat conservative, results. Using a multivariate test (concatenating the individual contrast vectors/matrices) is a typically more sensitive way to look at this sort of OR-conjunction of multiple hypotheses without requiring additional multiple-comparison corrections.
Let me know if that helps clarify
Best
Alfonso
Originally posted by L R:
Well, approximately yes, but not exactly. The three-line contrast will test and OR conjunction of the two-line contrast and the last one-line contrast, so in general terms yes, you would expect to see there any regions that show a significant effect with any of the two original analyses. Now, the result will not be exactly a simple superimposition of those two original results, mainly because the three-line contrast is using an appropriate multivariate test to look at the conjunction of those two hypothesis, while, strictly speaking, simply superimposing the two original analyses masks would increase your false-positives rate beyond the original individual-test thresholds. In other words, when looking at N individual hypotheses, simply superimposing the N individual results can result in a false-positive rate as high as N times your original false-positive threshold (depending on how related those individual hypotheses are). That is why often one uses a conservative Bonferroni correction (dividing your individual hypothesis threhsolds by N) to get still-valid, though somewhat conservative, results. Using a multivariate test (concatenating the individual contrast vectors/matrices) is a typically more sensitive way to look at this sort of OR-conjunction of multiple hypotheses without requiring additional multiple-comparison corrections.
Let me know if that helps clarify
Best
Alfonso
Originally posted by L R:
Thanks so much Alfonso, and I hope the
convention went well!
Your answer helped me clarify the question I had in mind: I do want a single contrast that would identify all of the between-group difference and the association with the emotion covariate, as you suggested. There's one thing that is still not clear to me: the contrast that you suggested [1 -1 0 0 0 0 0 0; 0 1 -1 0 0 0 0 0; 0 0 0 1 0 0 0 0] is supposed to show significant results for all the significant results of [1 -1 0 0 0 0 0 0; 1 -1 0 0 0 0 0] AND all the significant results of [0 0 0 1 0 0 0 0], right? To simplify, if I had 2 significant results for the two-line contrast, and 3 significant results for the one-line contrast, than the three-line contrast should give me all 5 (with the same p-values)? I might be doing something wrong, but this is not the results that I'm getting (despite using an uncorrected p).
Thanks a lot for all of your help!!
L.
Your answer helped me clarify the question I had in mind: I do want a single contrast that would identify all of the between-group difference and the association with the emotion covariate, as you suggested. There's one thing that is still not clear to me: the contrast that you suggested [1 -1 0 0 0 0 0 0; 0 1 -1 0 0 0 0 0; 0 0 0 1 0 0 0 0] is supposed to show significant results for all the significant results of [1 -1 0 0 0 0 0 0; 1 -1 0 0 0 0 0] AND all the significant results of [0 0 0 1 0 0 0 0], right? To simplify, if I had 2 significant results for the two-line contrast, and 3 significant results for the one-line contrast, than the three-line contrast should give me all 5 (with the same p-values)? I might be doing something wrong, but this is not the results that I'm getting (despite using an uncorrected p).
Thanks a lot for all of your help!!
L.
Threaded View
| Title | Author | Date |
|---|---|---|
| L R | Jul 8, 2015 | |
| Alfonso Nieto-Castanon | Jul 9, 2015 | |
| L R | Jul 10, 2015 | |
| Alfonso Nieto-Castanon | Jul 16, 2015 | |
| L R | Sep 30, 2015 | |
| Alfonso Nieto-Castanon | Sep 30, 2015 | |
| Alfonso Nieto-Castanon | Sep 30, 2015 | |
| L R | Jul 21, 2015 | |
| Alfonso Nieto-Castanon | Jul 24, 2015 | |
| L R | Jul 24, 2015 | |