Wald test

The Wald test is a statistical test, typically used to test whether an effect exists or not. In other words, it tests whether an independent variable has a statistically significant relationship with a dependent variable. Suppose an economist, who has data on social class and shoe size, wonders whether social class is associated with shoe size. Say θ is the average increase in shoe size for upper class people compared to middle class people: then the Wald test can be used to test whether θ is 0 (in which case social class has no association with shoe size) or non-zero (shoe size varies between social classes). Or, for a medical example, suppose smoking multiplies the risk of lung cancer by some number R: then the Wald test can be used to test whether R = 1 (i.e. there is no effect of smoking) or is greater (or less) than 1 (i.e. smoking alters risk).
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