The Wald test is a parametric statistical test named after the
Transylvanian statistician Abraham Wald with a great variety of
uses. Whenever a relationship within or between data items can
be expressed as a statistical model with parameters to be
estimated from a sample, the Wald test can be used to test the
true value of the parameter based on the sample estimate. For
example, suppose an economist, who has data on social class and
shoe size, wonders whether social class is associated with shoe
size. Say 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 is 0 (in which case social class has no
association with shoe size) or non-zero (shoe size varies
between social classes). Here, , the hypothetical difference in
shoe sizes between upper and middle-class people in the whole
population, is a parameter. An estimate of might be the
difference in shoe size between upper and middle-class people in
the sample. In the Wald test