Rj	R̅j
Ci	a	b
C̅i	c	d

^*

This is given as (ad − bc)/(ad + bc) (Hall and Oliver, 1997). If the columns are read as the givens, then cell a [when divided by (a + c)] corresponds to p(C_i|R_j). If the rows are read as the givens, then cell a [when divided by (a + b)] corresponds to p(R_j|C_i). R_j must be either R_S or R_L, and the other column then R_L or R_S, respectively. The Z-score associated with the matrix under the null assumption is:

$$z_{\text{ij}}=(x_{ij}-m_{\text{ij}})/\sqrt{m_{\text{ij}}(1-p_{+j})(1-p_{i+})}$$ (1)

where x_ij = observed joint frequency of R and C, m_ij = expected joint frequency of R and C, p_+j = unconditional probability of R, and p_i+ = unconditional probability of C (these probabilities are the row and column marginals). The row C̅_i indicates the absence of behavior C_i in that interval.