hey everyone! this is kind of a different topic from the "how-to-analyze-my-data" questions, but i think it's kind of relevant.
anyways, so my advisor brought in this question in our previous research meeting. it seems like people phrase MANOVA's null hypothesis in two ways:
1. the vector of means (centroids) are all equal
2. the linear composite of DVs that maximize their difference (in terms of variance) across groups are all equal.
in a kind of follow-up to huberty and morris's (1989) "multivariate analysis versus multiple univariate analyses" on when to use manova VS multiple univariate anovas, my advisor claimed that null#1 is kind of the "multiple anovas" version of it and null#2 the manova version.
i cannot, for the life of me, see those 2 nulls as testing different things (because a MANOVA and multiple univariata anovas are waaaaay different things). i can see how rejecting null#2 has, as a consequence, the rejection of null#1 and the statement of null#1 kind of "hides"or implies the statement of null#2. i just wanted to see if someone out there agrees with me or not.
(ps for those who are interested.- as part of the project i need to find out where in history people started using null#1 or null#2. it seems like null#2 was the first one from hotelling's work on T^2 and fisher's discriminant functions but somewhere in the 60's people started using null #1. i kinda need to now find when the shift started, lol).
anyways, so my advisor brought in this question in our previous research meeting. it seems like people phrase MANOVA's null hypothesis in two ways:
1. the vector of means (centroids) are all equal
2. the linear composite of DVs that maximize their difference (in terms of variance) across groups are all equal.
in a kind of follow-up to huberty and morris's (1989) "multivariate analysis versus multiple univariate analyses" on when to use manova VS multiple univariate anovas, my advisor claimed that null#1 is kind of the "multiple anovas" version of it and null#2 the manova version.
i cannot, for the life of me, see those 2 nulls as testing different things (because a MANOVA and multiple univariata anovas are waaaaay different things). i can see how rejecting null#2 has, as a consequence, the rejection of null#1 and the statement of null#1 kind of "hides"or implies the statement of null#2. i just wanted to see if someone out there agrees with me or not.
(ps for those who are interested.- as part of the project i need to find out where in history people started using null#1 or null#2. it seems like null#2 was the first one from hotelling's work on T^2 and fisher's discriminant functions but somewhere in the 60's people started using null #1. i kinda need to now find when the shift started, lol).