Defining a hypothesis encompassing multiple variables

Hi all!

I have a question regarding a topic I am currently exploring. I have a dataset with multiple governance-related shareholder proposals and an evaluation whether each proposal is on a material topic . I also have 14 different firm variables, like total assets, Research & development expenses, etc. One of the analyses I want to do is test whether there are differences in firm characteristics between firms who receive a material proposal and firms who receive an immaterial proposal. In addition I would like to test whether different shareholders (like hedge funds, labor unions, etc.) are more likely to propose material proposals.

Is it academically allowed to set a hypothesis incorporating multiple variables? For example, is it correct to state a hypothesis like:
H1: Firms that receive a material governance proposal have different firm characteristics than firms that receive an immaterial proposal
H2: Certain sponsor types file more material governance proposals than others

Usually, I see hypotheses stated in a way where 1 variable has an effect on another, but in this case that would mean stating 14 different hypotheses, one for each variable. Same goes for the sponsor types. How would one structure a hypothesis for such a test?

Thanks in advance & have a great day!



No cake for spunky
There are tests that see if multiple variables are jointly significantly which is another way of saying if at least one is.
For example a F test that var1=0,var2=0,var3=0 etc. If any are the f test will show it.
Hi @noetsi ! Thank you for your fast reply. In some preliminary testing I ran a logistic regression with the dummy variable materiality as the dependent variable, and firm characteristics (all 14) as independent. I can see that 3 differ significantly. I saw this strategy employed in earlier research as well. In any case, my question is more on whether there are certain 'rules' in how I should define my hypothesis, as I usually see them written down as "X has an effect on Y", but in this case there are multiple variables I take into consideration for this.


No cake for spunky
I do the same thing :p Be careful to distinguish actual rules like say the gauss markov assumptions from rules of thumb. And realize that academics strongly disagree with each other on some rules. I run into this all the time - it drives me crazy since I am not a statistician and don't know who is right. One person says you can do this, another says you absolutely can not. I have considered abandoning statistics from time to time since I am never sure who is can mean my analysis is wrong if I do one and the other is right.

This is particularly an issue with time series I think. Which is one of the more complex approaches. Silly economists....

Here is an example from time series of what I meant.

The F-test [for the bound test] is simply a test of the hypothesis of no cointegration among the variables against the existence of cointegration among the variables, denoted as:
@noetsi Thanks for your reply! I guess I was simply misinterpreting the goal of a hypothesis (being a beginner in statistics). The way I now understand it is that a hypothesis is basically 'my expectation' and can therefore define it the way I did it in my first post :).


No cake for spunky
a hypothesis is what you be believe reality to be put in a form you can test statistically. Usually the null hypothesis is what you do not believe is true and the alternate hypothesis is what you do believe is true or are interesting in testing to see if it is true.

Formally you can never prove the null hypothesis with a statistical test although some times writers will forget this and say the null was accepted or shown to be true.