When to we accept a hypothesis when using Wald test statistic?

Question

Hello I had to test two hypothesis, one hypothesis gave a wald test statistic with value 0.00015 and the other a value of approximately 40. Is it true when I then say that we accept the hypothesis with the wald test statistic value of 0.0015 but reject the other?

Answer 1

It is true, in the sense that a Wald statistics is expected to be small when the null hypothesis $H_0$ is true and big when is false. Thus, a value of the Wald statistic as small as 0.0015 is likely to lead to a not-rejection for any conventional significance level. Similarly, a value of the Wald statistics as big as 40 is likely lo lead to a rejection. However, to be definite, you should better declare the significance level $\alpha$ of your test. For example, if you are using a normally distributed statistics and $\alpha=0.1$ then the decision rule is:

Reject $H_0$ if |wald statistics|$>z_{\alpha/2}$

Thus, since $z_{\alpha/2}=1.645$, you do not reject $H_0$ at the 0.1 level.

Finally, there is a problem in that it seems you did two tests on the same parameter. This is not correct or, at least, you should adjust the significance level for multiple testing.