A Statistical Analysis of Coughing Patterns on ‘Who Wants to Be a Millionaire?’

A quick Google result shows that 592 total episodes have been filmed of the show. Under the null hypothesis that there was no cheating in any of the shows, you would still expect more likely than the chance that some show has a strong p-value of 0.3% for cheating to be 1-.997^592 = 83%.

As a jury, I don't think I would convict with just a p-value of 0.3% alone. You'd want something like a DNA test with a p-value expressed in 10^-6 or something to reduce the problem of multiple hypothesis testing / setup assumptions. Or you'd want to rely on other evidence like a confession or wiretap.

The second argument goes through each of the questions, but doesn't really show any evidence for cheating. Question 8 has no suspicious coughs (coughs close to the correct answer), and Ingram knows the answer quickly. Question 9 contains one suspicious cough, but only after the second mention of the correct answer. Again Ingram is quite sure about this answer and does not consider any other answer.

Question 10 is the first question (of that day) Ingram struggles with. There are 7 coughs recorded, 5 cough "clusters" (coughs very close to each other), 2 cough cluster could be suspicious. The first potentially suspicious cough cluster is pretty far away from the answers , while the second one is close to the correct answer. The next notes that these coughs didn't come from the phantom cougher, but from his wife. On the other hand there are lots of better place to insert a cough to cheat. This is one of the few questions where he changes his mind.

Question 11 has five coughs in total and three suspicious coughs, but cough 2-5 are very close together (and very late). Ingram is focused on the correct answer from the beginning, and does not really consider any other answer.

Question 12 has one cough after an incorrect answer at the very beginning. There is one cough cluster later on after the correct answer, but the correct answer is said 5 times, whereas the only one other answer is mentioned once, and only considered for a few seconds. The other coughes are relatively far away from any answer.

Question 13 has a cough after the correct answer in the very beginning, but it is not called as a significant cough in the linked youtube video from WWTBAM. Only the correct answer is considered.

In Question 14 Ingram struggles similar to question 10. there are 12 coughs. 6 coughs are heard shortly after a wrong answer (coughs 1, 2, 3, 4, 5 and 9), and 4 coughs are heard shortly after the right answer (coughs 6, 10, 11, 12). The next mentions a muttered "no", but any muttering loud enough to inform the contestant surely must be heard by the host and the crew. If they cheated using coughs, why muttering very obviously?

Question 15 has 23 coughs, 7 are close to wrong answers and 10 are close to the right answer. Ingram speaks the correct answer 11 times, and lists the incorrect answers 4 times. Most of the suspicious coughing happens in the very end, when he basically made his decision. Most of the coughing close to the incorrect answers happens early. If coughing was used, why did he not lock into one of the incorrect answers? The text mentions Ingram muttering "I think I know..." and calls that suspicious, but that phrase seems a very natural choice here.

The questions, coughing and answering doesn't follow a pattern: Sometimes there is a cough very early after the correct answer and Ingram picks that option, sometimes there is a cough very early after the incorrect answer put Ingram doesn't pick that option. Sometimes for unclear questions there are multiple coughs after the correct option, and Ingram picks that option; sometimes for unlcear options there are multiple coughs after the incorrect option and Ingram does not pick that option. On some unclear questions there is no coughing at all, but Ingram still guesses correctly. On some clear questions there is coughing, although Ingram did not even consider any wrong answer.

Next the blog post compares distributions of elapsed time since last answer for correct and incorrect answers. It does not use a statistical test (e.g. Kolmogorow-Smirnow-Test), but just counts coughs to some threshold. Resolution is very rough, the subsampling for that plot only done once. While simulations show that there are more coughs after an correct answer then expected, there are also more coughs after an incorrect answer then expected. The simulations disregard that for most incorrect answers there is not a lot of time until the next answer is spoken. Indeed often the incorrect answers are simply listed and immediately disregarded.

While the presented data might call for some scrutiny, it is far away from justifying the damning tone.

And what's the big deal? Is it actually a crime to win a game show? I'm confused.

The analysis seems to focus on the wrong things. A proof of cheating should focus more on identifying specific and reliable patterns in the coughs. I don't think generic statistical analysis of this kind makes a strong case at all.