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Yes … if p = 0.05 means that 5% of the time you will get those results, then it ought to be a uniform distribution: 10% of the time you will get p = 0.1, etc.

Point is not so much that the distribution is expected, more that I hadn’t thought much about what distribution to expect until now. And that distribution is very non-gaussian.

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May 25, 2016 at 4:46 pm

Tom, the sort of simulations that you ran are great for exploring the nature of P-values and for tuning your intuition. You might be interested in the relationship between P-values and likelihood functions that can be exposed by them .

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Reply to this comment
May 25, 2016 at 2:09 pm

I think my comment earlier disappears, so here goes attempt no. 2:

With the caveat that I’ve only glanced at the paper, I don’t see how your criticism is valid. It’s clear from the abstract and tables that it is *not* the case that the authors only find an effect if they divide their subjects into particular groups. Rather, there’s notably worse performance by the laptops-in-class group; again, this is the claim that’s made in the abstract. *In addition,* one can look at sub-groups and poke around — this seems to be a minor point of the paper.

Furthermore, even if one argues that they shouldn’t be looking at sub-groups, your criticism that the authors make the mistake that “The difference between “significant” and ‘not significant’ is not itself statistically significant” seems wrong. It’s not that they are comparing the different GRE/ACT-scoring groups with each other, but rather comparing e.g. high-level students in laptop-classes with high-level students in no-laptop classes. Your simple adding-the-variance calculation isn’t actually adding the relevant variances. (It’s possible my quick reading is incorrect; feel free to correct me.)

Overall, your characterization of this seems rather irresponsible.

Reply to this comment
May 25, 2016 at 5:09 pm

The paper does report on differences between the ‘smart’ and ‘poor’ student subgroups, and it offers a few lines of speculation for what might be driving those differences (other than noise). That said, they also acknowledge that, “the point estimates […] are statistically indistinguishable, so these could be chance findings.” In essence they’re saying, “this could be noise, but if it’s not, here’s what we think might be going on.” I see no problem with that.

I know that the scientists were really worried that one or both of the bombs would be a dud. They worried a lot about having one land unexploded and recovered by the Japanese. Didn’t they have some kind of failsafe built in to destroy an unexploded bomb? What if they called for the Japanese to watch a demonstration and nothing happened?

I agree with you that a demonstration was not really on the table and it is not really clear that the two bombs really influenced the final surrender, even if it was mentioned by the Emperor in his famous speech. I find it very interesting that all of our military leaders did not think dropping the bombs were necessary. Nimitz, Halsey, MacArthur, Eisenhower, Marshall, Leahy, King, not one said it was necessary. I know that Nimitz and Halsey both advocated for a blockade and continuation of “conventional” bombing, if you want to consider firebombing conventional. That might be an interesting counter factual to explore.

Great Post!

March 6, 2015 at 3:41 pm

The question for me is at what point does that function of war, the politics by other means, become too blatant to coexist with narratives of bringing peace, liberation, good postwar intentions, etc. For a country like the USA, which generally dislikes having to justify its actions with might-makes-right, it presents a troublesome public relations issue.

As for the failsafes: they did not think Little Boy design would be a dud (even if it failed to detonate exactly correctly it would still probably detonate anyway, because of its simplicity of assembly method), and the Fat Man bomb had scuttling charges in the nose (the four plungers you see in the photographs) that would guarantee at least a “dirty bomb” scattering of plutonium should the firing mechanism fail to trigger. They had high but not unlimited confidence in the bombs going off.

As an aside, I like to point out that firebombing did have a much lower mortality rate per square mile than the atomic bombs did, even at Tokyo. And Tokyo is the exceptional death count for the firebombing, by a long shot — it accounts for something like 90% of the firebombing deaths during the Japanese campaign, as I understand it.

March 7, 2015 at 6:23 pm

In a book Compton wrote several years later, he said Oppenheimer under-estimated the number of atomic bomb deaths by a factor of four, because he neglected to account for the fact (obvious, ex post) that Japanese civilians would have no warning and would have no time to run for shelter. As a technical point, I do not know by how much atomic bomb deaths could be reduced, if there were (say) a ten-minute air raid warning and shelter to run to.

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I would recommend on this subject Richard B. Frank’s Downfall: the End of the Imperial Japanese Empire that contains a detailed description of the debates within the highest levels of the Japanese Army, the Imperial government, and the Emperor’s inner circle in August 1945. Frank judges that the Soviet invasion was not decisive because the leadership of the Army and the Emperor did not initially realize the extent of the collapse of Japanese defenses in Manchuria. Frank notes that when the Emperor intervened decisively in the early hours of 10 August he explained his decision to his leadership citing Japan’s internal situation (collapsing morale from the blockade and bombing) and two military considerations: inadequate preparation to resist invasion and the vast destructiveness of the two atomic bomb attacks along with the toll from conventional bombing. He made no reference to the Soviet intervention.

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