Manova, Hotelling's T^2, t-test or Anova?


For my final thesis, a few questions arose during the pre-registration process and I would be very happy to receive answers.
I will conduct an experiment with three groups (1, 2, 3) and 3 dependent variables (a, b, c) to find answers to the following 2 hypotheses:

H1: M(2) > M(1) - global and for a each dependent variable:
  • a): Ma(2) > Ma(1)
  • b): Mb(2) > Mb(1)
  • c): Mc(2) > Mc(1)
H2: M(3 > M(2) - global and for a each dependent variable:
  • a): Ma(3) > Ma(2)
  • b): Mb(3) > Mb(2)
  • c): Mc(3) > Mc(2)

I'm not sure which statistical tests are best for testing the two (or actually 8: H1 + H1a + H1b + H1c + H2 + H2a + H2b+ H2c) hypotheses.

Does it make sense for each of the hypotheses to plan a one-way Manvoa with two-groups - or a Hotelling's T^2 test - and three dependent variables first and then three t-tests or Anovas? In the case of two groups, as far as I know, a t-test for 2 independent samples is comparable to a one-way anova with 2 group. Do I understand correctly that t-tests are the method of choice for one-tailed hypotheses?

As you can see, I do not really unterstand the difference between Manova and Hotelling's T^2 in the case of 2 groups.
In addition, I have not found an answer to whether I can carry out a Manova with 2 groups in order to answer a one-tailed hypothesis in the form of M(1) > M(2) in the case of H1 respectively M(3) > M(2) in the case of H2.

I hope I made myself understandable in describing my problem. In any case, I would be very happy to receive your support.
Many greetings


TS Contributor
You can do 1 MANOVA and in addition three ANOVAS,
each with a planned linear contrast "group 3 > 2 > 1".

I am not sure, though, why you do MANOVA if you are interested
in each dependent variable separately.

With kind regards