Borrowing from this post, I constructed the following example:
\documentclass{article}
\usepackage{stackengine}
\begin{document}
\[
\setstackgap{L}{.7\baselineskip}
\setstackgap{S}{9\baselineskip}
\Vectorstack{H_1 > < H_0}
\]
\[
\setstackgap{L}{.7\baselineskip}
\Vectorstack{\alpha > < H_0}
\]
\[
\setstackgap{L}{.7\baselineskip}
\Vectorstack{\alpha\\ > < H_0}
\]
\end{document}
which produces the output below
My first question is: why doesn't the command \setstackgap{S}{9\baselineskip} result in a huge gap between the items in the first display? As far as I can tell, I'm using setstackgap exactly as in the manual.
My second question is: why is H_1 treated differently from \alpha? I.e., when I simply replace H_ with \alpha to obtain the second display, in the output, there is no space between \alpha and >; to get a space I need in the third display to type \alpha\\. Why this difference?

