$X\rightarrow \neg C$) expresses a negative dependency. We note that $X\rightarrow C$, $C\rightarrow X$, $\neg X \rightarrow \neg C$, and $\neg C \rightarrow \neg X$ express the same dependency.

When two dependency rules are compared, it is often useful to study the conditional dependence of one rule (e.g., $Q\rightarrow C$) on another with the same consequent attribute (e.g., $X\rightarrow C$). This is equivalent to studying conditional dependencies between $Q$ and $C$ given $X$ or $\neg X$. Now $Q$ and $C$ are conditionally independent given $ X{=}x$, $x\in \{0,1\}$, if $$P( X{=}x,Q,C)=\frac{P( X{=}x,Q)P( X{=}x,C)}{P( X{=}x)}.$$

Otherwise they are considered conditionally dependent. To measure the strength of the conditional dependence, we extend the leverage measure. *Conditional leverage* of $Q\rightarrow C$ given value $X$ is $$\delta_c(Q,C|X)=P(X,Q,C)-P(X,Q)P(C|X)$$ and given value $\neg X$ it is $$\delta_c(Q,C|\neg X)=P(\neg X,Q,C)-P(\neg X,Q)P(C|\neg X).$$ The sign of the conditional leverage determines whether the given conditional dependency is positive or negative.

Specious dependency rules
-------------------------

In this paper, we are interested in detecting and pruning out specious dependency rules. These are rules that occur only as side-products of other dependencies. Ultimately, specious dependency rules are a phenomenon of the unknown population from which the sample data is drawn. Therefore, we 