Rolex

Here is where we differ.....

1) A specific Rolex reference may have had its dial produced by different dial manufacturers. Rolex used multiple suppliers. Similarly, Rolex used numerous suppliers for the hands on their watches. Each of these different suppliers may have varied not only the amount of radioactivity used but also the type of radioactivity used. Hence, it is quite feasible that two watches of exactly the same reference and indeed almost identical serial numbers could have very different radioactive composition on the dial. One could emit nothing and the other could emit high levels of radioactivity. Hence, your suggestion of using non-parametric testing such as Chi-square may be inappropriate for this purpose.

2) Much of the debate has been about whether it is possible for two correct watches to emit very different emission readings. Hence, use of non-parametric tests would not make a neat distinction between two watches. As you point out, virtually everything gives off some radiation even if it is only marginally above background. Hence a does it or does it not emit test would not provide the type of information that could differentiate between watches. 

3) I put my hands up and admit that I have not spent my career as a radioactivity expert. I have, however, spent two degrees and 25yrs professionally using mathematics and in particular statistical testing in order to make a living. Given the very differing options that could confront a 1950s Rolex dial, I think it would be statistical suicide to take a sample of 20 watches and use that as representative of a universe. What if a batch of 20 dominated from just one supplier is tested and shows one set of readings? That may totally distort expectations from other batches that had very different radioactive treatment. Statistical significance is a moving target, for sure. But the confidence in sample size of under 25 is very questionable. I would certainly consider it unscientific. It isn't that it is "wrong". Rather, it is something that wold lead to more Type 2 errors...too much of a chance of that with such a small sample size.

4) Finally, it was suggested that we do not know the nature of the sample distribution. The most recent academic research suggests that a sample size of around 90+ would be needed if one was unsure about the nature of the distribution....I am speaking here specifically about the parametric assumption of normality. 

Happy to debate this further. 

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