Thursday, October 30, 2014

Testing......1, 2, 3, ......

I often think that most courses in econometric theory are somewhat unbalanced. Much more attention is given to estimation principles and estimator properties than is given to the principles of hypothesis testing, the properties of tests.

This always strikes me as somewhat ironic. In econometrics we're at least as interested in testing some interesting economic hypotheses as we are in estimating some particular parameters.

For that reason, even my introductory undergraduate "economic statistics" course always includes some basic material on the properties of tests. By this I mean properties such Uniformly Most Powerful; Locally Most Powerful; Consistent; and Unbiased. (With respect to the last two properties I do  mean test properties, not estimator properties.)

After all, when you're first learning about hypothesis testing, it's important to know that there are sound justifications for using the particular tests that are being taught. We don't use the "t-test" simply because it was first proposed by a brewer! Or, for that matter, because tables of critical values are in an appendix of our text book. We use it because, under certain circumstances, it is Uniformly Most Powerful (against one-sided alternative hypotheses).

If tests aren't motivated and justified in this sort of way, we're just dishing out recipes to our students. And I've never liked the cookbook approach to the teaching of statistics or econometrics.

There's a lot to blog about when it comes to hypothesis testing. In some upcoming posts I'll try and cover some testing topics which, in my view, are given too little attention in traditional econometrics courses.

To whet your appetite - the first two will be about the distributions of some standard test statistics when the null hypothesis is false; and how this information can be used to compute some power curves.



© 2014, David E. Giles

4 comments:

  1. you have posted a great idea here, i strongly agree with you, and waiting for your furthers post contain information about "testing of hypothesis" someties i also feel helpless to justify my test when i do make analysis about testing of hypothesis,

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  2. I am looking forward to your posts on hypothesis testing. Hopefully, I'll be able to understand the concepts with my rudimentary grasp of econometrics!

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  3. While I agree that it is useful to introduce students to the properties of various test procedures, motivating standard tests based on "optimality" properties quickly becomes a dead end, and we have to fall back on claiming the test procedure seems "reasonable".

    We have good answers for how to construct a test in the case of a simple null vs. a simple alternative, and to justify t-tests (UMP for one-sided alternative, and slightly less satisfying UMPU for two-sided alternatives). But once we get to multivariate hypotheses, the justification for using the F-test statistic in the classical linear normal model becomes pretty weak (it has highest power in the class of all tests that have uniform power against all alternatives lying on a family of ellipsoids...). And if we have a mixed equality and inequality null on a vector of parameters, well...(And that's even before we start discussing the robustness of our test procedures.)

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    1. I guess I'm not as pessimistic as you are regarding this. How often do students encounter a mixed equality/inequality null? And robustness issues apply to estimators just as much as they do to tests.

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