Home > politics, statistics, taxes > Out of 1,791 IRS lawyers, 38 made big contributions to Democracts and 2 to Republicans—Meaningful?

Out of 1,791 IRS lawyers, 38 made big contributions to Democracts and 2 to Republicans—Meaningful?

What does it tell us if 38 IRS lawyers make big contributions to Democracts and 2 to Republicans, when there are 1,791 IRS lawyers total? The question came up today at Volokh COnspiracy. Isn’t 40 out of 1,791 too small a proportion?

No. Surprisingly, if a sample is chosen randomly, what matters is that the sample be big enough, not how big the population is. Thus, if 40 out of 500 is big enough, so is 40 out of 10,000. That’s why pollsters don’t use samples more than about 1,000— if they’re really random samples, it doesn’t help much go to higher. And that basic point doesn’t depend on whether the population is normally distributed.

That first step tells us that 40 is big enough to get at whether there is a big imbalance of Democrats. What is Fisher’s Exact Test? The first test I’d think of would be some kind of binomial test for the odds of getting 38, 39, or 40 heads when 40 fair coins are tossed (one-sided since we can rule out 38, 39,40 Republics ex ante, tho it won’t make much difference).

Chow Dong’s model over at VC of normally distributed intensity of belief with unknown mean and variance is good. It wouldn’t have to be exactly normal to work well enough. Teh bigger problem is still back at the sampling stage. Not only did all these lawyers show intensity of belief, they all showed willingness to put that intensity on public record.[In fact, I guess someone should ask Prof. Anderson for their names (he responded to an email of mine asking about economists quite quickly)– and see what jobs they hold. And see if the two Republicans have been fired since his publicity about this.] If the IRS, or the Washington Bar, are actually politicized, which is our real question, then regardless of how a lawyer votes personally, he’d want to show his loyalty by making big Democratic contributions, or at least not show his potential neutrality or opposition. It would matter for promotion to management int he IRS and to post-IRS career, which for IRS tax lawyers has huge potential even if they’re honest. Thus, if the null of politicization is correct. we should see more Democratic big-enough-to-be public contributions even if 90% of IRS lawyers actually vote Republican.

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