Wald test in logistic regression and its relationship to Z-statistic If I have Z-statistic values in regression analysis, how can I convert them to Wald statistcs?  Can Wald value be negative?
 A: The chi-squared statistic is, in essence, the z-statistic squared* (I'm skipping over the complexities of the degrees of freedom here).  A Wald statistic is any test statistic that can be computed as:
$$
\frac{\hat\theta - \theta_0}{SE(\hat\theta)}
$$
and whose distribution converges to the standard normal as N increases.  Equivalently, it is a test statistic computed as:
$$
\bigg(\frac{\hat\theta - \theta_0}{SE(\hat\theta)}\bigg)^2
$$
whose distribution converges to the chi-squared distribution.  Both are Wald statistics.  In the top form, it can be negative, if your estimated parameter is less than the null value; in the bottom form it will always be positive.  
If your test statistic has more than one degree of freedom, the top form is not used and the bottom form is assumed to be distributed as a chi-squared with that number of degrees of freedom.  Because of this fact, the chi-squared form is somewhat more convenient and is typically used by default.  
*If this makes you wonder why it isn't called z-squared instead, see: Wikipedia.
