\begin{tabular}{|c|c|c|c|c||c|c|c|c|} \hline
\multicolumn{1}{c}{} & \multicolumn{4}{|c||}{$\beta = 2$} &
\multicolumn{4}{|c|}{$\beta = 8$} \\
\hline
$n$ & $x$ & $y$ & $f$ & $\mu$ & $x$ & $y$ & $f$ & $\mu$ \\ \hline
0 & 10 & 1 & 0 & 3.132 & 10 & 1 & 1.696 & 1.696 \\ \hline
\end{tabular}
Thanks. What I did was look in the pdf user guide docs
using
'multicolumn' as a search word and looked for examples I thought
illustrated what I wanted. Had I known that it was related to hline,
I probably would have found it. I now see upon closer inspection that
there are examples using cline. I just didn't recognize at the time
that some of the examples, in fact, contained the element I was
looking for.
LATEX Tutorials (Indian TEX Users Group)
The Not So Short Introduction to LATEX2m (by Tobias Oetiker)