Wald Test Statistic

Wald tests are simple statistical tests for determining if an estimated parameter value is significantly different from zero.  The test can take two forms.  The first is where the estimate (minus zero) is divided by its standard error.  The resulting statistic is a z-score that follows a standard normal distribution from which a p-value can be calculated.  The second form is where the difference in the parameter estimate and zero is squared and divided by the variance of the parameter.  This produces a statistic that follows a chi-squared distribution with one degree of freedom.  The two forms of the Wald test statistic are below.

(1)

W=(β^−β0)seˆ(β^)∼N(0,1)

(2)

W2=(β^−β0)2Varˆ(β^)∼χ21

Programs like R, Microsoft Excel, or even online widgets can be used to calculate p-values from a z-score or chi-squared statistic.  Here's how to do it.

R:

P-value=2*(1-pnorm(W))

P-value=1-pchisq(W2,1)

MS Excel:

P-value=2*(1-(NORMDIST(W,0,1,TRUE)))

P-value=CHIDIST(W2,1)