Correct understanding of Manly's $S$ statistic formula I am working on social associations of bats and have a problem with correct understanding of formula from:

Bejder, Lars, D Fletcher, and S BrÄger. 1998. “A Method for Testing
  Association Patterns of Social Animals.” Animal Behaviour 56 (3):
  719–25. doi:10.1006/anbe.1998.0802.

$$S =\sum_{i=1}^3\sum_{j=1}^3(o_{ij} - e_{ij})^2/3^2$$
Is this matrix a correct representation of formula above?
$$
        \begin{matrix}
            & i=1 & i=2 & i=3\\
        j=1 & (o_{11} - e_{11})^2/3^2 & (o_{21} - e_{21})^2/3^2 & (o_{31} - e_{31})^2/3^2 \\
        j=2 & (o_{12} - e_{12})^2/3^2 & (o_{22} - e_{22})^2/3^2 & (o_{32} - e_{32})^2/3^2 \\
        j=3 & (o_{13} - e_{13})^2/3^2 & (o_{23} - e_{23})^2/3^2 & (o_{33} - e_{33})^2/3^2 \\
        \end{matrix}
$$

Hint: Let your matrix be M. Then  
$$\begin{pmatrix} 1&1&1\end{pmatrix} \times M \times \begin{pmatrix} 1\\1\\1\end{pmatrix}=S$$
