contingency_table#

rojak.turbulence.metrics.contingency_table(x_var: DataArray, y_var: DataArray, sum_over: str) → ContingencyTable[source]#

Contingency Table for multidimensional arrays

Computed contingency table as defined as,

\[\begin{split}\begin{array}{c|c|c|c} & Y = 1 & Y = 0 & \text{Total} \\ \hline X = 1 & n_{11} & n_{10} & n_{1\bullet} \\ X = 0 & n_{01} & n_{00} & n_{0\bullet} \\ \hline \text{Total} & n_{\bullet1} & n_{\bullet0} & n \end{array}\end{split}\]

When :math`X` and :math`Y` are response variables, the probability of each case :math`pi_{ij}` is the joint distribution of :math`X` and :math`Y`, where :math`i` and :math`j` denotes the row and column respectively. When :math`Y` is the response variable and :math`X` is the explanation variable, then it conditional distribution of :math`Y` given :math`X`, is defined as,

\[\pi_{j | i} = \pi_{ij} / \pi_{i + } \quad \forall i \text{ and } j\]
Parameters:

  • x_var (DataArray) – First binary variable (:math`x` in contingency table)

  • y_var (DataArray) – Second binary variable (:math`y` in contingency table)

  • sum_over (str) – Dimension to sum over to compute the number of observations

Returns:

Instance of ContingencyTable

Return type:

ContingencyTable