Political Science Rumors Topic: Let's define what the test statistic is
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Political Science Rumors Topic: Let's define what the test statistic isen-USMon, 13 Jul 2020 02:24:18 +0000http://bbpress.org/?v=1.0.2<![CDATA[Search]]>q
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PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807195
Thu, 11 Jun 2020 06:30:19 +0000PoliSci1807195@https://www.poliscirumors.com/<blockquote><p>
The discussion did start in a thread on CG's work, in which her defender made this comment:</p>
<p>Hahahahaha, what's the test statistic? It's a little something called a coefficient. You test it against zero. Which she does in the table.</p>
<p><a href="https://www.poliscirumors.com/topic/some-user-claims-cgharvard-is-a-plagiarist/page/15" rel="nofollow">https://www.poliscirumors.com/topic/some-user-claims-cgharvard-is-a-plagiarist/page/15</a>
</p></blockquote>
<p>Sigh. And that idea appears nowhere in CG's paper and has nothing to do with it. </p>
<p>You can read on that thread where it started -- someone bizarrely stated that there's an error because she reports coefficients and standard errors, so there's no test statistic shown. Seriously. So I said, um, that makes no sense, she's obviously calculating regular old t values from what's shown. Oh, and you're not even technically correct since you could use the coefficient as your test statistic. Then bedlam erupted.</p>
<p>That's it. That's the incredibly lame, dvmb way this all started. And on both counts (the paper and the coefficient) I'm still right.
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807191
Thu, 11 Jun 2020 06:18:31 +0000PoliSci1807191@https://www.poliscirumors.com/<blockquote><p>S/he is trying to distract from the real issue, which is that the CG article that sparked all this discussion has some weird model specifications and doesn't test interaction effects appropriately. But I disagree with the third point. While it is true that some test statistics have more desirable properties than others, any test statistic must meet a minimal set of criteria, which the OLS coefficient doesn't meet.</p>
<p>All of this is false. Issue has literally nothing to do with anything from CG's research. No one has pointed to any "weird model" or other problem, hence your inability to say what it supposedly is.</p>
</blockquote>
<p>The discussion did start in a thread on CG's work, in which her defender made this comment:</p>
<blockquote>
<p>Hahahahaha, what's the test statistic? It's a little something called a coefficient. You test it against zero. Which she does in the table.
</p></blockquote>
<p><a href="https://www.poliscirumors.com/topic/some-user-claims-cgharvard-is-a-plagiarist/page/15" rel="nofollow">https://www.poliscirumors.com/topic/some-user-claims-cgharvard-is-a-plagiarist/page/15</a>
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807188
Thu, 11 Jun 2020 06:15:22 +0000PoliSci1807188@https://www.poliscirumors.com/<blockquote><p>I don't know who CG is, or what the deal about interaction terms is. I saw this thread last night, kept the tab open on my phone, checked the last several pages today. I guess I couldn't look away. Since I sunk some 20 minutes of my life to this thread, I decided to offer some observations.<br />
1) The Marvin/Stacie person is incredibly persistent. The level of commitment to this thread and to continuing the argument with anonymous PSR people is off the charts. Also s/he appears like a borderline deranged person. To be clear, I'm not judging, maybe s/he lets of steam this way, who knows. But that certainly made me want to check out the thread. Not terribly dissimilar to following Trump's tweets.
</p></blockquote>
<p>Marvin Gaye
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807186
Thu, 11 Jun 2020 06:06:08 +0000PoliSci1807186@https://www.poliscirumors.com/<blockquote><p>So if "no criteria is (sic) actually needed", then your sample size can be you test statistic? That's laughable.<br />
Poster above is actually correct on the points you criticize. It's only the last part that they got wrong.
</p></blockquote>
<p>Nope. The sample size is not a statistic, hence it cannot be a test statistic. Big swing and a miss.</p>
<p>Ok, if you think test statistics require some mystery criteria by *definition*, then please cite any source whatsoever for that. It has to say that a test statistic requires some property, not merely that it's useful or common. I've challenged posters here to find such a source and they've failed. I've referenced numerous stats textbooks that support my argument. Good luck.
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807183
Thu, 11 Jun 2020 06:03:12 +0000PoliSci1807183@https://www.poliscirumors.com/<blockquote><p>
The first part up until "Further..." is correct. Your last three sentences are incorrect. You are confusing the ex ante theoretical distribution of the random variable, and the estimates based on the observed sample. Ex ante the beta coefficient doesn't have a known distribution. To see why your reasoning is wrong, note that by your logic you could rearrange terms and derive the exact density of the sample size N. Do you realize how absurd that would be?
</p></blockquote>
<p>Leann's post isn't 100% accurate, but no part of this is right. There's no confusion with any "ex ante distribution." Nor does the argument imply you could calculate a "density" for N, which makes no sense. Only way I can think you got there is by thinking "t (n-2)" means t times (n-2)? </p>
<p>As I've pointed out, Leann's conclusion on the implied uncertainty of beta is literally just the familiar formula for beta's confidence interval: beta +- t_alpha*se. So if you conclude that's wrong, you've made a mistake somewhere.
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807181
Thu, 11 Jun 2020 06:00:04 +0000PoliSci1807181@https://www.poliscirumors.com/<p>So if "no criteria is (sic) actually needed", then your sample size can be you test statistic? That's laughable.</p>
<p>Poster above is actually correct on the points you criticize. It's only the last part that they got wrong. </p>
<blockquote><p>And if you disagree with that, please point out the mistake in the logic; I genuinely believe the claims in that post and would be grateful to know where they are wrong.</p>
<p>Your general logic is correct. However, two problems. First, that is not part of the *definition* of a test statistic. No criteria is actually needed at all. Second, that's not what people mean by a known distribution because it depends on the estimated standard error (which is not part of H0). However, it is correct that this will give you the correct p-values (and is trivially identical to the usual t test).
</p></blockquote>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807179
Thu, 11 Jun 2020 05:53:16 +0000PoliSci1807179@https://www.poliscirumors.com/<blockquote><p>And if you disagree with that, please point out the mistake in the logic; I genuinely believe the claims in that post and would be grateful to know where they are wrong.
</p></blockquote>
<p>Your general logic is correct. However, two problems. First, that is not part of the *definition* of a test statistic. No criteria is actually needed at all. Second, that's not what people mean by a known distribution because it depends on the estimated standard error (which is not part of H0). However, it is correct that this will give you the correct p-values (and is trivially identical to the usual t test).
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807176
Thu, 11 Jun 2020 05:49:39 +0000PoliSci1807176@https://www.poliscirumors.com/<blockquote><p>S/he is trying to distract from the real issue, which is that the CG article that sparked all this discussion has some weird model specifications and doesn't test interaction effects appropriately. But I disagree with the third point. While it is true that some test statistics have more desirable properties than others, any test statistic must meet a minimal set of criteria, which the OLS coefficient doesn't meet.
</p></blockquote>
<p>All of this is false. Issue has literally nothing to do with anything from CG's research. No one has pointed to any "weird model" or other problem, hence your inability to say what it supposedly is.</p>
<p>No, test statistics do not need any minimal set of criteria as a *definition*, as has been proven by quoting from Casella & Berger. You might say that to be useful, they need some minimal criteria, such as providing correct p-values in some test. It's been shown (and is frankly trivial) that the coefficient can do that.
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807175
Thu, 11 Jun 2020 05:43:05 +0000PoliSci1807175@https://www.poliscirumors.com/<blockquote><p>Hold up.<br />
A test statistic is a quantity computable from sample data that has a known probability distribution under the null hypothesis H0.<br />
For regression coefficients b where H0 specifies b = b0, a central limit theorem holds that the standardized coefficient (b - b0)/SEb converges to a standard normal distribution as n -> infinity, if the standard error SEb is known. If b0 = 0, this simply says that b/SEb converges to standard normal.<br />
If SEb is not known but estimated from data as SEhat, then (b - b0)/SEhat converges to Student's t with n-2 degrees of freedom. If b0 = 0, this simply says that b/SEhat converges to students t (n-2).<br />
Further, this implies that b converges to a *scaled* t (n-2), where the scale term is SEhat.<br />
Therefore, a regression coefficient is computable from sample data, and has a known (limit) distribution under H0. That makes it a test statistic.
</p></blockquote>
<p>The first part up until "Further..." is correct. Your last three sentences are incorrect. You are confusing the ex ante theoretical distribution of the random variable, and the estimates based on the observed sample. Ex ante the beta coefficient doesn't have a known distribution. To see why your reasoning is wrong, note that by your logic you could rearrange terms and derive the exact density of the sample size N. Do you realize how absurd that would be?
</p>PoliSci on "Let's define what the test statistic is"
https://www.poliscirumors.com/topic/lets-define-what-the-test-statistic-is/page/15#post-1807174
Thu, 11 Jun 2020 05:37:17 +0000PoliSci1807174@https://www.poliscirumors.com/<p>And if you disagree with that, please point out the mistake in the logic; I genuinely believe the claims in that post and would be grateful to know where they are wrong.
</p>