Notation of probability matrix corresponding to a contingency table Contingency tables are typically formatted as tables similar to matrices in mathematics, see this example.
Is the equation below an accepted notation of expressing the probabilities of the outcomes as a matrix? If not, what would be the accepted way? Are there any published materials using the same notation?
$$
\widehat{Pr_\text{outcome}} = 
\begin{matrix}
 &
\begin{matrix}
\text{RH} & \text{LH}
\end{matrix}
\\
\begin{matrix}
\text{male} \\ \text{female}
\end{matrix}
&
\begin{bmatrix}
43 & 9 \\
44 & 4
\end{bmatrix}
\end{matrix}
\cdot \frac{1}{100}
=
\begin{matrix}
 &
\begin{matrix}
\text{RH} & \text{LH}
\end{matrix}
\\
\begin{matrix}
\text{male} \\ \text{female}
\end{matrix}
&
\begin{bmatrix}
0.43 & 0.09 \\
0.44 & 0.04
\end{bmatrix}
\end{matrix}
$$
 A: I'm not sure I can justify what I'm about to say, but I would be uneasy about expressing probabilities in a form like this. The structure is too reminiscent of other things that don't properly apply and suggests you should be able to do stuff like matrix multiplication that wouldn't mean anything here.
If the goal is to express a set of 4 mutually-exclusive outcomes, then your probabilities should be a single vector with 4 entries adding to 1.
OTOH, if it is to express a structure within that -- the difference in the handedness distribution by sex -- then it would make more sense if each of the rows added to 1.
And if what you actually want is a contingency table, use a contingency table. Dividing through by the total count doesn't really gain you anything.
Using a convention whereby all entries in a matrix add to 1 seems to me, well, unconventional. But I admit this objection is a bit subjective and hand-wavy.
A: It looks reasonable to me. Though realize that with an N larger than say 1,000, your table of probabilities won't represent exact counts because you'll end up truncating to three or so decimal places.
