On the history of MANOVA's null hypothesis...


Can't make spagetti
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).